Designing a Toasting Oven in Order to Produce Corn Flakes

Prof. Dr. Suat Ungan Fd. E. 425 Food Engineering Design Coordinator Middle East Technical University Food Engineering Department Ankara 06531 November 25, 2011 Dear Mr. Ungan, Please acknowledge the going with Work Term Report, pointed structuring a toasting broiler so as to deliver corn chips. In the structured framework 10 tons corn chips for each day is created. After certain procedures, corn chips enters the broiling stove at 20% mugginess and ways out at 4%humidity. The simmering broiler can work at (Â ±10 ? C) 225 0C. Toasting broiler is planned by thinking about its length, territory and working temperature.Optimizations are finished by these variables on the expense of the all out structure. In the plan framework, turning drum drier is utilized. 350 days of the year plant works and creation happens 16 hours in a day. Corn chips enter the stove at 225 0C . Measure of air is determined as 0,648 kg dry air/s . Length of the drier is determined as 2. 27 m. in the aftereffect of enhancements done by appropriate drying time and dryer breadth. Warmth vitality expected to raise the delta temperature of air to 225 0C, is found as 157kw and warmth misfortune is found as 23. 6kw.Through these information, complete venture which contains dryer cost and power cost is found as 92794. 98TL. Truly, bunch 3 individuals TABLE OF CONTENT SUMMARY In this plan a rotating dryer is intended for drying of corn drops which have the dampness content 20%. Corn drops are dried with air 9 % dampness content. The creation is accomplished for 16 hours in a day and 10 tons corn chips are delivered every day. Underway procedure, corn chips are cooked under tension. In the wake of cooking step, enormous masses are broken to pieces and sent to driers so as to get the dampness level at 20%. After this procedure, roduct is chipped between huge steel chambers and cooled with interior water stream. Delicate drops are sent to rotational dryers so as to drying out to 4% last dampness substanc e and toasting. In the toasting broiler, drops are presented to 225 0C air for 2-3 min. The drier length is determined as 2. 27 m with the distance across of 0. 082m with the presumption of 4%moisture substance channel air and 9%content outlet air. Stream pace of feed is determined as 0. 206kg/s. Mass stream pace of the delta air is determined as 0,648 kg dry air/s. Vitality required for carry the temperature of air to 225 0C is determined as 157kw and warmth misfortune in the framework is 23. kw. By making enhancements complete capital venture is determined as92794. 98TL which incorporates 84881TL power cost and 7913TL dryer cost. At last by making enhancements, so as to have least length and reasonable vitality for the drier, 215 0C is picked the best temperature for the bay air. I. Presentation Rotary dryers conceivably speak to the most seasoned persistent and without a doubt the most well-known high volume dryer utilized in industry, and it has developed a larger number of adju stments of the innovation than some other dryer characterization. [1] Drying the materials is a significant utilization process.It is additionally one of the significant parts in concrete creation procedure, and influences the quality and utilization of the granulating machine. Drum dryer is the fundamental hardware of drying materials, it has straightforward structure, dependable activity, and advantageous to oversee. Anyway there are a few issues which are immense warmth misfortune, low warm effectiveness, high warmth utilization, more residue, and hard to control the dampness out of the machine. It assumes a critical job in improving drying innovation level and warm productivity in drying process, lessen the warm and creation lost. 2] In this structure we are approached to plan a revolving drier which works 16 hours in a day and produces 10 tones corn chips for every day. Additionally it is referenced that, corn chips enters to drier at 20 %humidity and ways out 3-5%humidity. Thi s report is tied in with structuring a rotational dryer with its measurements for considering to get the base all out expense. Improvements are finished by gulf temperature of the air to the drier. In the structure framework heat required for warming the bay temperatures and length of the rotational dryer as material expense is suspected, and advancement is finished by thinking about least all out expense for the system.II. Past WORK Drying is maybe the most established, most normal activity of compound building unit tasks. More than 400 kinds of dryers have been accounted for in the writing while more than one hundred unmistakable sorts are normally available[3] Drying happens by affecting vaporization of the fluid by giving warmth to the wet feedstock. Warmth might be provided by convection (direct dryers), by conduction (contact or backhanded dryers), radiation or by microwave. More than 85 percent of modern dryers are of the convective sort with hot air or direct burning gases a s the drying medium.Over 99 percent of the applications include evacuation of water. [3] * Rotary Dryer; All revolving dryers have the feed materials going through a pivoting chamber named a drum. It is a round and hollow shell normally developed from steel plates, somewhat slanted, regularly 0. 3-5 m in distance across, 5-90 m long and turning at 1-5 rpm. It is worked now and again with a negative inside weight (vacuum) to forestall dust escape. Contingent upon the course of action for the contact between the drying gas and the solids, a dryer might be named immediate or backhanded, con-current or counter-current.Noted for their adaptability and overwhelming development, rotating dryers are less delicate to wide vacillations in throughput and item size. [4] * Pneumatic/Flash Dryer;The pneumatic or ‘flash’ dryer is utilized with items that dry quickly attributable to the simple evacuation of free dampness or where any required dispersion to the surface happens promptly. Drying happens surprisingly fast. Wet material is blended in with a surge of warmed air (or different gas), which passes on it through a drying conduit where high warmth and mass exchange rates quickly dry the product.Applications incorporate the drying of channel cakes, gems, granules, glues, slop and slurries; in truth practically any material where a powdered item is required. * Spray Dryers; Spray drying has been one of the most vitality expending drying forms, yet it stays one that is basic to the creation of dairy and food item powders. Fundamentally, shower drying is cultivated by atomizing feed fluid into a drying chamber, where the little beads are exposed to a surge of hot air and changed over to powder particles.As the powder is released from the drying chamber, it is gone through a powder/air separator and gathered for bundling. Most splash dryers are prepared for essential powder assortment at productivity of around 99. 5%, and most can be provided with auxiliary assor tment gear if important * Fluidised Bed Dryer; Fluid bed dryers are found all through all businesses, from substantial mining through food, fine synthetic compounds and pharmaceuticals. They give a compelling strategy for drying moderately free streaming particles with a sensibly tight molecule size distribution.In general, liquid bed dryers work on a through-the-bed stream design with the gas going through the item opposite to the heading of movement. The dry item is released from a similar segment. * Hot Air Dryer-Stenter; Fabric drying is normally done on either drying chambers (middle of the road drying) or on stenters (last drying). Drying chambers are fundamentally a progression of steam-warmed drums over which the texture passes. It has the downside of pulling the texture and successfully decreasing its width.For this explanation it will in general be utilized for middle of the road drying * Contact Drying-Steam Cylinders/Can; This is the least complex and least expensive met hod of drying woven textures. It is chiefly utilized for middle drying instead of last drying (since there is no methods for controlling texture width) and for pre drying preceding stentering. * Infra red drying; Infrared vitality can be created by electric or gas infrared warmers or producers. Every vitality source has points of interest and disadvantages.Typically, gas infrared frameworks are increasingly costly to purchase since they require security controls and gas-taking care of hardware, however they regularly are more affordable to run since gas for the most part is less expensive than power. Gas infrared is regularly a decent decision for applications that require a great deal of vitality. Items, for example, nonwoven and material networks are models where gas regularly is a decent decision. [5] * III. Conversation For the structured framework a turning drum dryer is picked. Revolving drum dryerâ is utilized for drying material with mugginess or granularity in the enterpri ses of mineral dressing, building material, metallurgy and chemical.It has bit of leeway of sensible structure, high productivity, low vitality consumption[6] Â advantages of drum dryer: | Suitable for dealing with fluid or pale feeds. Item is fine, flaky structure Uniform drying because of uniform utilization of film. Medium range limits. High warm productivity Continuous activity Compact establishment Closed development is possibleâ [7] By hot air stream, heat for Toasting of the chips in the drier, or in the stove, is given rather utilizing level preparing surfaces. Contingent upon the creation type and stream rate, drum dryer fulfills turning at a consistent speed, the incline and the length.The drum is likewise punctured so that permits the wind current inside. The puncturing ought not an excessive amount of huge but rather additionally forestall the departure of drops. Additionally, during the warm treatment cooking, extension degree, surface, flavor, stockpiling steadiness is resolved. So as to acquire the right qualities, the drying temperature and time ought to be balanced appropriately. For the improvement of the framework, length of the drier, breadth esteem, working temperature are influence fixed cost, variable expense and the warmth misfortune from the framework is considered.First by any means, changing by temperature how influence vital length is determined T air in| Z| 210| 2,308504| 215| 2,296091| 220| 2,284367| 225| 2,273274| 230| 2,262764| 235| 2,252792| It is see

Ancient Women Powerfull or Powerless Essay

In old world, men’s and women’s life were profoundly isolated. Man worked in broad daylight places while ladies were limited to their homes, where they dealt with the family unit and brought up kids with the assistance of slave. This doesn't imply that ladies didn't have a social, open and financial life. David Cohen says that Athenian ladies partook in numerous exercises, for example, working in fields, going about as medical attendant and numerous different exercises. Ladies were viewed as week before men, role’s of men were given more significance than jobs of ladies. The job of ladies may contrast contingent on the class of the ladies or the district of Greece she have a place. It is accepted that Spartan ladies delighted in more opportunity than Athenian ladies. Ladies additionally partook in strict celebrations and in a penance as said by Cohen. The relationship of ladies with man is made obvious through the family, government and in wars. Ladies additionally had some political capacity which has been made apparent through the play Lysistrata by Aristophanes where Lysistrata depicts the political capacity by bringing the staggering Peloponnesian was to an end. The jobs played by people in antiquated Greek society are made apparent through the play Lysistrata by Aristophanes. In the play a sign is given of women’s job in the family units and their relationship with man. As this play was composed by a male dramatist it additionally gives a male perspective towards ladies. Ladies job were restricted to the house where they produce authentic kids and guaranteeing that that family exercises were executed. Sarah Pomeroy state, â€Å"The essential obligation of resident ladies towards the polis[city] was the creation of real beneficiaries to the oikoi, or families, whose total involved the populace. † The ladies place was seen being inside the home as Lysistrata gives proof of this when, Cleonice, states, â€Å"†¦but it’s difficult, you know, for ladies to go out. One is caught up with pottering about her significant other; another is getting the worker up; a third is putting her kid sleeping or washing the rascal or taking care of it. Family units were the main spot wherein ladies have power, as they were in order. The job of ladies to deliver real youngsters was seen as a most significant obligation of ladies. Ladies likewise took an interest in customs and ceremonies. The internment rituals were no doubt the mid ceremonial ladies were engaged with. The jobs of ladies in ceremonies are worried about how Athenian ladies took an interest in strict celebrations as expressed in Lysistrata. This shows Greek ladies took an interest in ceremonies and customs. The elationship among people in antiquated Greek society outlines the job of ladies was according to family unit obligations and regular undertakings. A Women’s activities were required to be conscious towards men and were reliant upon their spouses. The women’s were not additionally ready to have a start correspondence with one, as it is shown in Lysistrata when Lysistrata addresses the officer who at that point answers back, â€Å"You nauseating creature,† as he is dismayed with her protester way. Men didn't accept that women’s were equipped for running the state as their political jobs were seen with hatred; in spite of the way that they run the family units in a proficient way. Governmental issues was not the matter of ladies their business was restricted to their family unit exercises. This is shown in Lysistrata when she gets some information about the undertakings of the state and the reaction she gets is, â€Å"Shut up and stay out of other people's affairs! † The association of ladies in war is found similarly as their inclusion in governmental issues. Proceed to take care of your work; let war be the consideration of the men people. † This is from Lysistrata demonstrates the answer to women’s contribution on the war exertion. In any case, Lysistrata says that ladies contributed enormously to the war, â€Å"We’ve given you children, and afterward needed to send them off to battle. † Women had power inside the family units yet the y didn't have any control over men, this is the motivation behind why ladies didn't groups numerous jobs in the legislative issues. The male perspective on ladies depicted all through the play is debasing of ladies. Prominent sentiment through the play is that ladies are boozers and sex-crazed. In Lysistrata it states, â€Å"If it had been a Bacchus festivity they’d been approached to go to †or something to pay tribute to Pan or Aphrodite †especially Aphrodite! You wouldn’t have had the option to move. † This concentrate shows the supposition as Bacchus was the lord of wine and Aphrodite the goddess of affection, subsequently inferring that these are the celebrations the ladies enjoyed. The men likewise saw ladies as being sub-human as said in Lysistrata, â€Å"There is no brute as bold as a ladies. The women’s were likewise accepted to be touchy and passionate. The general male view about ladies were viewed as unimportant and an irritation. Every one of these jobs played by ladies were marginally shifted between the various societies. Athenian ladies were not quite the same as Spartan ladies as their lives were a lot more liberated, as is insinuated in Lys istrata when the Spartan, Lampito, remarks on her day by day exercises, â€Å"If we were in preparing. † There is likewise notice of the Metic ladies in Lysistrata who had the option to complete business jobs. In any case, regardless of these distinctions, the ladies of resident families, whether they were of working class or eminence, despite everything did similar jobs and still had next to no opportunity and rights. It is made clearly obvious all the jobs which ladies played in old Greek society and their relationship with men through these jobs. Ladies in antiquated Greece were offered practically zero opportunity and rights, and their solitary genuine spot of intensity was in the family.

Online School vs. Public School Essay

Sloan Consortium expressed that, â€Å"More than one million understudies went to classes through the Internet in 2008. Of those million, around 200,000 were joined up with full-time virtual schools, which means they go to the entirety of their classes online.† I have been doing Online Schooling for a long time however before that I went to government funded school. Internet tutoring is a superior decision than open tutoring on the grounds that you have more control, there is no dramatization, and you have all the more available time. I favor web based self-teaching since I can control my pace. I get the opportunity to choose when I need to work and I don’t need to concentrate throughout the day, regular like I ordinarily would. The course plan is likewise up to me; courses should be possible each in turn or in gatherings. During my first year at an online school I completed five courses one after another. It’s now my subsequent year and I am doing each course in turn, which I certainly like. At Public schools, course plans are picked for me and I would have no control. You likewise can’t control what is happening in your school condition. Probably the best thing about online school is that there will never be any dramatization. I truly despise tattling, which is a major issue at state funded schools. Since I just associate with different children from my school by method of the web there is no negligibility between us. Children my age battle about companions and sweethearts or lady friends. There’s nothing to quarrel over when you live as distant from one another as we do. At ordinary schools however, you see everybody regular. When your continually with a similar gathering of individuals, someone’s sentiments are continually getting injured and there is consistent contentions. A considerable lot of circumstances include your â€Å"friends†. In the event that your companions with somebody you can’t be companions with anybody they don’t like, which can get convoluted. 3 When doing school on the web, you have significantly more spare time. In the event that I remain made up for lost time, I’m ready to get things done after school and on the ends of the week. At the point when I was in government funded school, I had a great deal an excess of schoolwork to do anything. Presently I’m ready to take a couple of vacation days for excursion or in light of the fact that I’m debilitated and not need to stress over falling a long ways behind. While at government funded school the entirety of my time was filled by schoolwork, yet now I’m ready to go through hours after school with my pony or simply unwinding. A portion of my family has communicated worry about me notâ interacting with kids my age since I don’t go to government funded school. On account of web based tutoring, I’m ready to spend time with my companions at our animal dwellingplace. Before I exchanged I never observed any of my companions outside of school since I never had the opportunity. Web based tutoring is a greatly improved decision than open tutoring. The advantages of online school far exceed those of open tutoring. With Online tutoring you have such a significant number of more options, everything is up to you! There are a wide range of tutoring decisions however internet tutoring has made my life simpler and tranquil. I unquestionably propose that you investigate web based tutoring as an option in contrast to government funded school. It may not be directly for everybody, except it may be directly for you.

Supply and Demand Essay Example for Free

Flexibly and Demand Essay Part 3â€Supply and Demand Question 1. Draw an interest bend with a harmony cost and amount, show what occurs on your graph when every one of the accompanying occasions happens. Clarify whether every one of the accompanying occasions speaks to an (I) move of the interest bend or (ii) a development along the interest bend. (an) A storekeeper finds that clients are happy to pay more for umbrellas on blustery days (b) When XYZ Telecom, a significant distance telephone utility supplier, offered scaled down costs for its administrations on ends of the week, the volume of end of the week calling expanded strongly. Question 2. The accompanying table speaks to the interest and gracefully for orchids (a sort of bloom). Plot the bends on the chart beneath a) Graph both the gracefully (S0) and the interest (D0) bends. What is the present harmony cost and amount? b) Something has happen to the gracefully of orchids and the new flexibly bend is given previously. Diagram the new flexibly bend. Is there an impermanent deficiency or surplus before the market alters? What is the new balance cost and amount? c) Name all the variables that could move the gracefully bend like it has? Question 3. In the accompanying circumstance, draw the market for wheat After every occasion portrayed underneath, what will befall the balance cost and amount subsequently? Draw a graph and make certain to mark everything. (I) Due to great climate, 1997 was a generally excellent year for Prairie wheat cultivators, who delivered a guard yield of wheat. Simultaneously, there is a declaration by the Canadian Health Organization saying that corn is awful for your heart.

Alexander Popes An Essay On Man -- Alexander Pope An Essay On Man

Alexander Pope's An Essay On Man Alexander Pope's An Essay On Man is commonly acknowledged as a magnificently agreeable mass of couplets that accumulate an assortment of philosophical tenets in a diverse and (in light of its logical nature) antithetic obfuscate. No pundit denies that Pope's Essay On Man is among the most flawlessly composed and best of his works, however few likewise deny that Pope's Essay On Man is a unintelligible combination of mixed up scraps (A Letter... 88) of philosophical maxims. In framing An Essay On Man into maybe the best philosophical sonnet at any point composed, Pope magnificently joins inferences and similitudes in which to tighten a universe of importance into the minimal work that refrain must be, in contrast with exposition. Maybe, at that point, Pope's most noteworthy blemish is that, in light of the fact that a work of theory must be sound and complete so as to be fruitful much of the time, An Essay On Man is too hard to even think about deciphering in light of the fact that the structure and grouping of the work, just as implications and representations, while adding to the nature of refrain, decrease the nature of the philosophical work. Pope's just error recorded as a hard copy An Essay On Man is his endeavor to fit an excessive amount of data into such a packed work. Notwithstanding, saw as isolated musings, most of entries in the Essay appear to remain constant - not a focal and cognizant truth, yet a precise and fragmented truth (De Quincey 224). As a philosophical contention spoke to in section, the rearrangements of such a significant number of shifting speculations can't be kept away from. While the Essay needs focal doctrinal intelligence, it despite everything prevails as a sonnet, even to the detriment of its way of thinking (Edwards 37). One should likewise perceive the enormity of the work itself, in spite of its absence of centra... ...ondsworth: Penguin Books, 1971. 224. Edwards, Thomas. The Mighty Maze: An Essay on Man. Modern Critical Views: Alexander Pope. Ed. Harold Bloom. New York: Chelsea House, 1986. 37-50. Hazlitt, William. From On Dryden and Pope. Penguin Critical Anthologies: Alexander Pope. Eds. F.W. Bateson and N.A. Joukovsky. Harmondsworth: Penguin Books, 1971. 197. Quicker, Frederick. Presentation. An Essay on Pope. New York: Columbia University Press, 1974. 8. Magill, Frank, ed. Basic Survey of Poetry: Revised Edition. Vol. 6. Pasadena: Salem Press, 1992. 2632-2635. Pope, Alexander. An Essay On Man. Ed. Maynard Mack. Twickenham Edition. London: Methuen, 1950. Warton, Joseph. From An Essay on the Genius and Writings of Pope. Penguin Critical Anthologies: Alexander Pope. Eds. F.W. Bateson and N.A. Joukovsky. Harmondsworth: Penguin Books, 1971. 111-115.

Mid-January Updates

Mid-January Updates Hello! Heres the latest: We have begun reading regular action applications. It looks like application numbers will be up once again this year. Lots of reading to be done! If you are a regular action applicant, please check your application tracking on MyMIT today. If you are missing an application component, such as a transcript or teacher evaluation, now is a good time to follow up on that and make sure we have it as soon as possible. If you are in the regular action pool (regular action applicant or early action deferred), and you are in an American school, please try to get us your Mid-Year Grade Report as soon as possible after the grades are available (if youre on a trimester system, we probably already have all the grades we need). If you are an early action deferred student, and you are looking to send us an update, I would recommend doing so in the next couple weeks, before we go into selection committee. The financial aid deadline is quickly approaching. Be sure to have all of your documents to the financial aid office by February 15. I havent forgotten about the Mini-contest. Ill post some great entries tomorrow! Finally, I hope you can start to relax. Im still getting some really stressed out comments and emails, but this interim period between submitting your application and receiving your decision is a good time to focus on family, friends, and school. You can worry again about college once you have to start making your decision ;)

A Study Of The Indian Stock Market - Free Essay Example

1.0 Introduction Seasonal variations in production and sales are a well known fact in business. Seasonality refers to regular and repetitive fluctuation in a time series which occurs periodically over a span of less than a year. The main cause of seasonal variations in time series data is the change in climate. For example, sales of woolen clothes generally increase in winter season. Besides this, customs and tradition also affect economic variables for instance sales of gold increase during marriage seasons. Similarly, stock returns exhibits systematic patterns at certain times of the day, week or month. The most common of these are monthly patterns; certain months provide better returns as compared to others i.e. the month of the year effect. Similarly, some days of the week provides lower returns as compared to other trading days i.e. days of the week effect. The existence of seasonality in stock returns however violates an important hypothesis in finance that is efficient market hypothesis. The efficient market hypothesis is a central paradigm in finance. The EMH relates to how quickly and accurately the market reacts to new information. New data are constantly entering the market place via economic reports, company announcements, political statements, or public surveys. If the market is informationally efficient then security prices adjust rapidly and accurately to new information. According to this hypothesis, security prices reflect fully all the information that is available in the market. Since all the information is already incorporated in prices, a trader is not able to make any excess returns. Thus, EMH proposes that it is not possible to outperform the market through market timing or stock selection. However, in the context of financial markets and particularly in the case of equity market seasonal component have been recorded. They are called calendar anomalies (effects) in literature. The presence of seasonality in stock returns violates the weak form of market efficiency because equity prices are no longer random and can be predicted based on past pattern. This facilitates market participants to devise trading strategy which could fetch abnormal profits on the basis of past pattern. For instance, if there are evidences of à ¢Ã¢â€š ¬Ã‹Å"day of the week effectà ¢Ã¢â€š ¬Ã¢â€ž ¢, investors may devise a trading strategy of selling securities on Fridays and buying on Mondays in order to make excess profits. Aggarwal and Tandon (1994) and Mills and Coutts (1995) pointed out that mean stock returns were unusually high on Fridays and low on Mondays. One of the explanation put forward for the existence of seasonality in stock returns is the à ¢Ã¢â€š ¬Ã‹Å"tax-loss-selling hypothesis. In the USA, December is the tax month. Thus, the financial houses sell shares whose values have fallen to book losses to reduce their taxes. As of result of this selling, stock prices declin e. However, as soon as the December ends, people start acquiring shares and as a result stock prices bounce back. This lead to higher returns in the beginning of the year, that is, January month. This is called à ¢Ã¢â€š ¬Ã‹Å"January effectà ¢Ã¢â€š ¬Ã¢â€ž ¢. In India, March is the tax month, it would be interesting to find à ¢Ã¢â€š ¬Ã‹Å"April Effectà ¢Ã¢â€š ¬Ã¢â€ž ¢. 2.0 Theoretical Background The term à ¢Ã¢â€š ¬Ã‹Å"efficient marketà ¢Ã¢â€š ¬Ã¢â€ž ¢ refers to a market that adjusts rapidly to new information. Fama (1970) stated , à ¢Ã¢â€š ¬Ã‹Å" A market in which prices always fully reflect available information is called efficient.à ¢Ã¢â€š ¬Ã¢â€ž ¢ If capital markets are efficient, investors cannot expect to achieve superior profits by adopting a certain trading strategy. This is popularly called as the efficient market hypothesis. The origins of the EMH can be traced back to Bachelierà ¢Ã¢â€š ¬Ã¢â€ž ¢s doctoral thesis à ¢Ã¢â€š ¬Ã‹Å"Theory of Speculationà ¢Ã¢â€š ¬Ã¢â€ž ¢ in 1900 and seminal paper titled à ¢Ã¢â€š ¬Ã‹Å"Proof That Properly Anticipated Prices Fluctuate Randomlyà ¢Ã¢â€š ¬Ã¢â€ž ¢ by Nobel Laureate Paul Samuelson in 1965. But it was Eugane Famaà ¢Ã¢â€š ¬Ã¢â€ž ¢s work (1970) à ¢Ã¢â€š ¬Ã‹Å"Efficient Capital Marketsà ¢Ã¢â€š ¬Ã¢â€ž ¢ who coined the term EMH and advocated that in efficient market securities prices fully reflect all the information. It is important to note that efficiency here does not refer to the organisational or operational efficiency but informational efficiency of the market. Informational efficiency of the market takes three forms depending upon the information reflected by securities prices. First, EMH in its weak form states that all information impounded in the past price of a stock is fully reflected in current price of the stock. Therefore, information about recent or past trend in stock prices is of no use in forecasting future price. Clearly, it rules out the use of technical analysis in predicting future prices of securities. The semi-strong form takes the information set one step further and includes all publically available information. There is plethora of information of potential interest to investors. Besides past stock prices, such things as economic reports, brokerage firm recommendations, and investment advisory letters. However, the semi-strong form of the EMH states that current market p rices reflect all publically available information. So, analysing annual reports or other published data with a view to make profit in excess is not possible because market prices had already adjusted to any good or bad news contained in such reports as soon as they were revealed. The EMH in its strong form states that current market price reflect all à ¢Ã¢â€š ¬Ã¢â‚¬Å"both public and private information and even insiders would find it impossible to earn abnormal returns in the stock market. However, there is the notion that some stocks are priced more efficiently than others which is enshrined in the concept of semi-efficient market hypothesis. Thus, practitioners support the thesis that the market has several tiers or that a pecking order exist. The first tier contains well-known stocks such as Reliance Industries and Sail which are priced more efficiently than other lesser-known stocks such as UCO Bank. However, instead of considering stocks, we analyzed this phenomenon using Nif ty Junior index which is an index of next most liquid stocks after SP Nifty. 3.0 Review of Literature Seasonality or calendar anomalies such as month of the year and day of the week effects has remained a topic of interest for research since long time in developed as well as developing countries. Watchel (1942) reported seasonality in stock returns for the first time. Rozeff and Kinney (1976) documented the January effect in New York Exchange stocks for the period 1904 to 1974. They found that average return for the month of January was higher than other months implying pattern in stock returns. Keim (1983) along with seasonality also studied size effects in stock returns. He found that returns of small firms were significantly higher than large firms in January month and attributed this finding to tax-loss-selling and information hypothesis. A similar conclusion was found by Reinganum (1983), however, he was of the view that the entire seasonality in stock returns cannot be explained by tax-loss-selling hypothesis. Gultekin and Gultekin (1983) examined the presence of stock market seasonality in sixteen industrial countries. Their evidence shows strong seasonalities in the stock market due to January returns, which is exceptionally large in fifteen of sixteen countries. Brown et al. (1985) studied the Australian stock market seasonality and found the evidence of December-January and July-August seasonal effects, with the latter due to a June-July tax year. However, Raj and Thurston (1994) found that the January and April effects are not statistically significant in the NZ stock market. Mill and Coutts (1995) studied calendar effect in FTSE 100, Mid 250 and 350 indices for the period 1986 and 1992. They found calendar effect in FTSE 100. Ramcharan (1997), however, didnà ¢Ã¢â€š ¬Ã¢â€ž ¢t find seasonal effect in stock retruns of Jamaica. Choudhary (2001) reported January effect on the UK and US returns but not in German returns. Fountas and Segredakis (2002) studied 18 markets and reported seasonal patterns in returns. The reasons for the January effect in stock returns in most of the developed countries such as US, and UK attributed to the tax loss selling hypothesis, settlement procedures, insider trading information. Another effect is window dressing which is related to institutional trading. To avoid reporting to many losers in their portfolios at the end of year, institutional investors tend to sell losers in Decembers. They buy these stocks after the reporting date in January to hold their desired portfolio structure again. Researchers have also reported half- month effect in literature. Various studies have reported that daily stock returns in first half of month are relatively higher than last half of the month. Ariel (1987) conducted a study using US market indices from 1963 to 1981 to show this effect. Aggarwal and Tandon (1994) found in their study such effect in other international markets. Ziemba (1991) found that returns were consistently higher on first and last four days of the month. The holiday effect refers to higher returns around holidays, mainly in the pre-holiday period as compared to returns of the normal trading days. Lakonishok and Smidt (1988) studied Dow Jones Industrial Average and reported that half of the positive returns occur during the 10 pre-holiday trading days in each year. Ariel (1990) showed using US stock market that more than one-third positive returns each year registered in the 8 trading days prior to a market-closed holiday. Similar conclusion were brought by Cadsby and Ratner (1992) which documented significant pre-holiday effects for a number of stock markets. However, he didnà ¢Ã¢â€š ¬Ã¢â€ž ¢t find such effect in the European stock markets. Husain (1998) studied Ramadhan effect in Pakistan stock market. He found significant decline in stock returns volatility in this month although the mean return indicates no significant change. There are also evidences of day of the week effect in stock market returns. The Monday effect was identified as early as the 1920s. Kelly (1930) based on three years data of the US market found Monday to be the worse day to buy stocks. Hirsch (1968) reported negative returns in his study. Cross (1973) found the mean returns of the SP 500 for the period 1953 and 1970 on Friday was higher than mean return on Monday. Gibbons and Hess (1981) also studied the day of the week effect in US stock returns of SP 500 and CRSP indices using a sample from 1962 to 1978. Gibbons and Hess reported negative returns on Monday and higher returns on Friday. Smirlock and Starks (1986) reported similar results. Jaffe and Westerfield (1989) studied day of the week effect on four international stock markets viz. U.K., Japan, Canada and Australia. They found that lowest returns occurred on Monday in the UK and Canada. However, in Japanese and Australian market, they found lowest return occurred on Tuesday. B rooks and Persand (2001) studied the five southeast Asian stock markets namely Taiwan, South Korea, The Philippines, Malaysia and Thailand. The sample period was from 1989 to 1996. They found that neither South Korea nor the Philippines has significant calendar effects. However, Malaysia and Thailand showed significant positive return on Monday and significant negative return on Tuesday. Ajayi al. (2004) examined eleven major stock market indices on Eastern Europe using data from 1990 to 2002. They found negative return on Monday in six stock markets and positive return on Monday in rest of them. Pandey (2002) reported the existence of seasonal effect in monthly stock returns of BSE Sensex in India and confirmed the January effect. Bodla and Jindal (2006) studied Indian and US market and found evidence of seasonality. Kumari and Mahendra (2006) studied the day of the week effect using data from 1979 to 1998 on BSE and NSE. They reported negative returns on Tuesday in the Indian stoc k market. Moreover, they found returns on Monday were higher compared to the returns of other days in BSE and NSE. Choudhary and Choudhary (2008) studied 20 stock markets of the world using parametric as well as non-parametric tests. He reported that out of twenty, eighteen markets showed significant positive return on various day other than Monday. The scope of the study is restricted to days-of-the week effect, weekend effect and monthly effect in stock returns of SP CNX Nifty and select firms. The half month effect and holiday effect are not studied here. 4.0 Objective The objective of the study are as follows: To examine days of the week effect in the returns of SP CNX Nifty To examine weekend effect in SP CNX Nifty returns. To examine the seasonality in monthly returns of the BSE Sensex. 5.0 Hypotheses a) Our first hypothesis is that returns on all the days of weeks are equal. Symbolically, H 0 : ÃŽÂ ²1 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²2 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²3 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²4 H1 : at least one ÃŽÂ ²i is different b) Our second hypothesis is as follows: H 0 : ÃŽÂ ²1 à ¯Ã¢â€š ¬Ã‚ ½ 0 H1 : ÃŽÂ ²1 à ¢Ã¢â‚¬ °Ã‚  0 c) Our third hypothesis is: H 0 : ÃŽÂ ²1 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²2 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²3 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²4 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²5 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²6 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²7 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²8 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²9 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²10 à ¯Ã¢â€š ¬Ã‚ ½ ÃŽÂ ²11 H1 : at least one ÃŽÂ ² is different 6.0 Data and its Sources The monthly data on SP Nifty for the period April 1997 to March 2009 obtained from the Handbook of Statistics on Indian Economy published by the Reserve Bank of India. We also collected daily data on SP Nifty from 1st January 2005 to 31st December 2008 from www. nseindia.com for studying the above objectives. 7.0 Research Methodology To examine the stock market seasonality in India, first we measure stock return of Nifty as given below: Rt à ¯Ã¢â€š ¬Ã‚ ½ (ln Pt à ¢Ã‹â€ ln Pt à ¢Ã‹â€ 1 ) *100 (1) where Rt is the return in period t, Pt and Pt-1 are the monthly (daily) closing prices of the Nifty at time t and t-1 respectively. It is also important to test stationarity of a series lest OLS regression results will be spurious. Therefore, we will first test whether Nifty return is stationary by AR(1) model. We also use DF and ADF tests which are considered more formal tests of stationarity. For testing stationarity, let us consider an AR(1) model yt à ¯Ã¢â€š ¬Ã‚ ½ à ?1 yt à ¢Ã‹â€ 1 à ¯Ã¢â€š ¬Ã‚ « et (2) The simple AR(1) model represented in equation (2) is called a random walk model. In this AR(1) model if | à ?1 |à ¯Ã¢â€š ¬Ã‚ ¼1, then the series is I(0) i.e. stationary in level, but if à ?1 à ¯Ã¢â€š ¬Ã‚ ½1 then there exist what is called unit root problem. In other words, series is non-stationary. Most economists think that differencing is warranted if estimated à ? à ¯Ã¢â€š ¬Ã‚ ¾ 0.9 ; some would difference when estimated à ? à ¯Ã¢â€š ¬Ã‚ ¾ 0.8 . Besides this, there are some formal ways of testing for stationarity of a series. . Dickey-Fuller test involve estimating regression equation and carrying out the hypothesis test The simplest approach to testing for a unit root is with an AR(1) model:. Let us consider an AR(1) process: yt à ¯Ã¢â€š ¬Ã‚ ½ c à ¯Ã¢â€š ¬Ã‚ « à ? yt à ¢Ã‹â€ 1 à ¯Ã¢â€š ¬Ã‚ «ÃƒÅ½Ã‚ µt (3) where c and à ? are parameters and is assumed to be white noise. If à ¢Ã‹â€ 1 p à ? p1, then y is a stationary series while if à ? à ¯Ã¢â€š ¬Ã‚ ½1 , y is a non-stationary series. If the absolute value of à ? is greater than one, the series is explosive. Therefore, the hypothesis of a stationary series is involves whether the absolute value of à ? is strictly less than one. The test is carried out by estimating an equation with yt à ¢Ã‹â€ 1 subtracted from both sides of the equation: à ¢Ã‹â€ Ã¢â‚¬  yt à ¯Ã¢â€š ¬Ã‚ ½ c à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ³ yt à ¢Ã‹â€ 1 à ¯Ã¢â€š ¬Ã‚ «ÃƒÅ½Ã‚ µt (4) where ÃŽÂ ³ à ¯Ã¢â€š ¬Ã‚ ½ à ? à ¢Ã‹â€ 1 , and the null and alternative hypotheses are H0 : ÃŽÂ ³ à ¯Ã¢â€š ¬Ã‚ ½ 0 H1 : ÃŽÂ ³ p0 The DF test is valid only if the series is an AR(1) process. If the series is correlated at higher order lags, the assumption of white noise disturbances is violated. The ADF controls for higher-order correlation by adding lagged difference terms of the dependent variable to the right-hand side of the regression: à ¢Ã‹â€ Ã¢â‚¬   yt à ¯Ã¢â€š ¬Ã‚ ½ c à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ³ yt à ¢Ã‹â€ 1 à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ´ 1 à ¢Ã‹â€ Ã¢â‚¬   yt à ¢Ã‹â€ 1 à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ´ 2 à ¢Ã‹â€ Ã¢â‚¬   yt à ¢Ã‹â€  2 à ¯Ã¢â€š ¬Ã‚ « . à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ´ p à ¢Ã‹â€ Ã¢â‚¬   yt à ¢Ã‹â€  p à ¯Ã¢â€š ¬Ã‚ «ÃƒÅ½Ã‚ µt (5) This augmented specification is then tested for H0 : ÃŽÂ ³ à ¯Ã¢â€š ¬Ã‚ ½ 0 H1 : ÃŽÂ ³ p0 in this regression. Next, to test the presence of seasonality in stock returns of Nifty, we have used one technique called dummy variable regression model. This technique is used to quantity qualitative aspects such as race, gender, religion and after that one can include as an another explanatory variable in the regression model. The variable which takes only two values is called dummy variable. They are also called categorical, indicator or binary variables in literature. While 1 indicates the presence of an attribute and 0 indicates absence of an attribute. There are mainly two types of model namely ANOVA and ANCOVA. This study uses ANOVA model. Analysis of variance (ANOVA) model is that model where the dependent variable is quantitative in nature and all the independent variables are categorical in nature. To examine the weekend effect and days of the week effect, the following dummy variable regression model is specified as follows: Nifty returns à ¯Ã¢â€š ¬Ã‚ ½ÃƒÅ½Ã‚ ± à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²1Monday à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²2Tuesday à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²3 wednesday à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²4thrusday à ¯Ã¢â€š ¬Ã‚ « à ¯Ã¢â‚¬Å¡Ã‚ µ (6) The variables Monday, Tuesday, Wednesday and Thursday are defined as: Monday = 1 if trading day is Monday; 0 otherwise Tuesday = 1 if trading day is Tuesday; 0 otherwise, Wednesday = 1 if the trading day is Wednesday; 0 otherwise Thursday = 1 if the trading day is Thursday; 0 otherwise ÃŽÂ ± represents the return of the benchmark category which is Friday in our study. Similarly, to find whether there are monthly effects in Nifty returns, we used ANOVA model specified below as: Nifty returns à ¯Ã¢â€š ¬Ã‚ ½ÃƒÅ½Ã‚ ± à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²1 DJune à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²2 DJuly à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²3 DAug à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²4 Dsep à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²5 DOct à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²6 DNov à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²7 DDec à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²8 DJan à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²9 DFeb à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²10 DMar à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²11 DApril à ¯Ã¢â€š ¬Ã‚ « à ¯Ã¢â‚¬Å¡Ã‚ µ (7) where Y = Monthly returns of Nifty D1= 1 if the month is June; 0 otherwise D2 = 1 if the month is July; 0 otherwise D3 = 1 if the month is August; 0 otherwise D4 = 1 if the month is September; 0 otherwise D5 = 1 if the month is October; 0 otherwise D6 = 1 if the month is November; 0 otherwise D7 = 1 if the month is December; 0 otherwise D8 = 1if the month is January; 0 otherwise D9 = 1 if the month is February; 0 otherwise D10 = 1 if the month is March; 0 otherwise D11 = 1 if the month is April; 0 otherwise ÃŽÂ ± represents the mean return on the May month where as ÃŽÂ ²1 to ÃŽÂ ²11 indicate the shift in mean returns across months. Statistically significant values of ÃŽÂ ²Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢s imply significant shifts in mean monthly returns, thus confirming the existence of the month of the year effect. The problem with this approach is that disturbance error term may have autocorrelation. Besides this, residual may contain ARCH effect. Therefore, we will test autocorrelation and ARCH effect in residual and improve our (6) and (7) model accordingly. 8.0 Results At the outset, we plotted the trend of SP CNX Nifty in Fig.1 which shows the movement of index over the sample period. For a long time hovering between 1000 and 2000, Nifty crossed the 2000 mark November 2005. Since then the one can see rising trend in Nifty till September 2008. After September 2008, we witnessed a stock market crash in the backdrop of mortgage crisis in the US followed by economic slowdown round the world which is quite visible in the movement of Nifty also. Fig. 1 Next, we computed descriptive statistics of returns of Nifty and Junior Nifty. The results are reported in Table 1 which show the mean returns of Nifty and Junior Nifty for the period April 1997 and March 2009 are 0.93 and 1.38 percent respectively. Junior Nifty provided higher mean return than the Nifty over the sample period. As the Nifty and Junior Nifty returns are not normally distributed evident from coefficient of skewness and kurtosis, one can use median return instead of mean to represent returns of Nifty and Junior Nifty which are 1.58 and 2.38 percent respectively. Thus, it is clear that Junior Nifty yielded better returns over the sample period. Table 1: Descriptive Statistics (%) Summary Statistics Nifty Junior Nifty Mean 0.93 1.38 Median 1.58 2.38 Standard Deviation 6.71 9.75 Minimum -23.71 -27.66 Maximum 17.01 32.09 Skewness -0.6029 -0.44 Kurtosis 0.5049 0.97 The variability in returns as measured by standard deviation which is the square root of variance The standard deviation is a conventional measure of volatility. Volatility as measured by standard deviations of returns of the sample period for Nifty and Junior Nifty are 6.71 and 9.75 percent respectively. Thus, it is evident that Junior Nifty is more volatile than the Nifty implying investment in Junior Nifty is more riskier. Table 2: AR(1) Model Monthly Series Level Series Return Series Niftyt = 35.0224 + 0.989 Niftyt à ¢Ã‹â€ 1 Niftyt = 0.58 + 0.2686 Niftyt à ¢Ã‹â€ 1 (1.21) (83.725) (0.9) (3.29) NJuniort = 35.0224 + 0.989 NJuniort à ¢Ã‹â€ 1 NJuniort = 35.0224 + 0.989 NJuniort à ¢Ã‹â€ 1 (1.21) (83.725) (0.74) (4.11) Daily Series Level Series Return Series Niftyt = 11.87 + 0.9969 Niftyt à ¢Ã‹â€ 1 Niftyt = 0.79 + 0.07 Niftyt à ¢Ã‹â€ 1 (1.46) (466.11) (0.33) (2.25) NJuniort = 20.01 + 0.997 NJuniort à ¢Ã‹â€ 1 NJuniort = 0.0154 + 0.1624 NJuniort à ¢Ã‹â€ 1 (1.17) (409.28) (0.00) (5.18) In time series econometrics, it is now customary to check stationarity of a series before using it in regression analysis in order to avoid spurious regression. We tested the stationarity of Nifty, Junior Nifty by AR(1) model and augmented Dickey-Fuller Test; while the former is an informal test, the later is a formal test of stationarity. The results of AR(1) model and ADF are reported in Table 2 and Table 3. The results of AR(1) model show that monthly and daily Nifty and Nifty Junior series are not stationary in their level form. However, AR(1) model fitted to Nifty and Nifty Junior return series are stationary. Table 3: Results of ADF Test Series Original Series Return Series Monthly Nifty -1.1851 -4.59* Monthly Junior Nifty -1.564 -4.2 Daily Nifty -1.48 -15.15 Daily Junior Nifty -1.32 -15.46 * MacKinnon critical values for rejection of hypothesis of a unit root at 1%, 5% and 10% are -3.4786, 2.8824 and -2.5778 respectively. The results of augmented Dickey-Fuller test is very much in consistent with AR(1) model. Table 3 shows that both monthly and daily Nifty and Nifty Junior are non-stationary in their level form. However, return series of Nifty and Nifty Junior are stationary as the null of unit root can be rejected at conventional level of 1%, 5% and 10%. Thus, analysis of stock market seasonality is based on return series of Nifty and Nifty Junior as they are stationary. Next, we estimated model (6) to study days of the week effects in daily Nifty and Nifty Junior returns. The results for Nifty are reported in Table 4. The benchmark day in the model is Friday represented by the intercept which provided a return of 0.08 percent on an average of the sample period. Table 4. Results of Equation (6) for Nifty Variables Coefficients t-statistic P-Value Intercept 0.0836 0.624 0.53 Monday -0.0875 -0.46 0.64 Tuesday -0.0405 -0.21 0.83 Wednesday -0.0432 -0.22 0.82 Thursday -0.0784 -0.41 0.68 R2 =0.0002 F Statistic = 0.06( 0.99) Ljung-Box Q(2) = 0.7045 (0.40) D-W Statistic = 1.86 ARCH LM Test(1): F- stat = 54.31 (0.00) Note: Figures in () are p-values Returns of Monday, Tuesday, Wednesday and Thursday can be found out by deducting the coefficients of these days from the benchmark day, that is, Friday which were 0.1711, 0.1241, 0.1268 and 0.162 respectively. The coefficient of Monday is not significant at 5 percent level which indicates that there is no weekend effect in Nifty returns. Further, none of the coefficients are significant at conventional levels of significance indicating that there is no days of the week effects in the Nifty returns. R2 is 0.0002 which is very low, and F-statistic indicates that the overall fit of the model is poor. Further, Durban-Watson statistic of 1.86 indicates autocorrelation in the residuals. The Ljung-Box Q statistic for the hypothesis that there is no serial correlation upto order of 2 is 0.7045 with an insignificant p-value of 0.40 which indicates that we have autocorrelation problem of order one. However, return series exhibits autoregressive conditional heteroskedasticity (ARCH) effects. We corrected the results for autocorrelation of order one by including an AR(1) term on the right hand side of the dummy regression model and ARCH effect is taken care of by fitting a benchmark GARCH (1,1) model. Table 5: Results of Equation (6) for Nifty corrected for autocorrelation and ARCH Effect Mean Equation Variables Coefficients t-statistic P-Value Intercept 0.2368 2.53 0.01 Monday -0.0838 -0.72 0.46 Tuesday -0.1362 -1.018 0.30 Wednesday -0.0912 -0.70 0.47 Thursday -0.0164 -0.13 0.89 AR(1) 0.0767 2.03 0.04 Variance Equation C 0.09 4.94 0.00 ARCH(1) 0.1674 8.45 0.00 GARCH(1) 0.8086 40.53 0.00 Ljung à ¢Ã¢â€š ¬Ã¢â‚¬Å"Box Q (5) = 5.33 (0.25) ARCH LM Test(1): F- stat = 0.1645(0.68) Table 5 shows that after correcting for serial autocorrelation and ARCH effect, we found Friday effect in Nifty returns. However, our analysis do not find weekend effect. The Ljung-Box Q statistic shows that there is no pattern in residual. ARCH LM test also indicate that there is no ARCH effect in residual now. We also examined the presence of seasonality in Nifty Junior. The results are given in Table 6 which shows that there is neither weekend effect or days of the week effects in Nifty Junior. Table 6. Results of Equation (6) for Nifty Junior Variables Coefficients t-statistic P-Value Intercept 0.1824 1.20 0.22 Monday -0.2988 -1.40 0.16 Tuesday -0.0766 -0.35 0.72 Wednesday -0.2191 -1.024 0.30 Thursday -0.3149 -1.46 0.14 R2 =0.003 F Statistic = 0.84 (0.49) Ljung-Box Q(5) = 26.55 (0.00) D-W Statistic = 1.70 ARCH LM Test(1): F- stat = 145.54 (0.00) Note: Figures in () are p-values. The coefficient of Monday is not significant at 5 percent level which indicates that there is no weekend effect in Nifty Junior returns. None of the coefficients are significant at conventional levels of significance implying that there are no days of the week effects in the Nifty Junior returns. R2 is 0.003 which is very low, and F-statistic indicates that the overall fit of the model is poor. Further, Durban-Watson statistic of 1.7 indicates autocorrelation in the residuals. The Ljung-Box Q statistic for the hypothesis that there is no serial correlation upto order of 5 is 26.55 with a significant p-value of 0.00 which indicates that we have autocorrelation problem of higher order. Nifty Junior series also exhibits autoregressive conditional heteroskedasticity (ARCH) effects. We corrected the results for autocorrelation of order one by including an AR(1) term on the right hand side of the dummy regression model and ARCH effect is taken care of by fitting a benchmark GARCH (1,1) mod el. Autoregressive conditional heteroskedasticity (ARCH) model was first introduced by Engle (1982), which does not assume variance of error to be constant. In ARCHGARCH models, the conditional mean equation is specified, in the baseline scenario, by an AR(p) process i.e. is regressed on its own past values. Let the conditional mean under the ARCH model may be represented as: y à ¯Ã¢â€š ¬Ã‚ ½ÃƒÅ½Ã‚ ± à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ² x à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ² x à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ² x à ¯Ã¢â€š ¬Ã‚ « à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ² x à ¯Ã¢â€š ¬Ã‚ «Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â‚¬Å¡Ã‚ µ and à ¯Ã¢â‚¬Å¡Ã‚ µ ~ (N ,0, à Ã†â€™ 2 ) (8) t 1 1 2 2 3 3 n n t t t In equation (8), the dependent variable yt varies over time. Similarly, conditional variance of à ¯Ã¢â‚¬Å¡Ã‚ µt may be denoted as à Ã†â€™t2 , which can be represented as: à Ã†â€™t2 à ¯Ã¢â€š ¬Ã‚ ½ var(ut | ut à ¢Ã‹â€ 1 ,ut à ¢Ã‹â€ 2 ..) à ¯Ã¢â€š ¬Ã‚ ½ E[(ut à ¢Ã‹â€  E(ut )2 | ut à ¢Ã‹â€ 1 ,ut à ¢Ã‹â€ 2 .)] It is usually assumed that E(à ¯Ã¢â‚¬Å¡Ã‚ µt ) à ¯Ã¢â€š ¬Ã‚ ½ 0 , so: à Ã†â€™t2 à ¯Ã¢â€š ¬Ã‚ ½ var(ut | ut à ¢Ã‹â€ 1 ,ut à ¢Ã‹â€ 2 .) à ¯Ã¢â€š ¬Ã‚ ½ E(ut2 | ut à ¢Ã‹â€ 1 ,ut à ¢Ã‹â€ 2 ,.) (9) Equation (9) states that the conditional variance of a zero mean is normally distributed random variable ut is equal to the conditional expected value of the square of ut . In ARCH model, à ¢Ã¢â€š ¬Ã‹Å"autocorrelation in volatilityà ¢Ã¢â€š ¬Ã¢â€ž ¢ is modeled by allowing the conditional variance of the error term, à Ã†â€™t2 , to depend immediately previous value of the squared error. This may be represented as: à Ã†â€™t2 à ¯Ã¢â€š ¬Ã‚ ½ÃƒÅ½Ã‚ ±0 à ¯Ã¢â€š ¬Ã‚ «ÃƒÅ½Ã‚ ±1ut2à ¢Ã‹â€ 1 (10) The above model is ARCH (1) where, the conditional variance is regressed on constant and lagged values of the squared error term obtained from the mean equation. In equation (5.12), conditional variance must be strictly positive. To ensure that these always result in positive conditional variance, all coefficients in the conditional variance are usually required to be non- negative. In other words, this model make sense if ÃŽÂ ±0 à ¯Ã¢â€š ¬Ã‚ ¾ 0 and ÃŽÂ ±1 à ¢Ã¢â‚¬ °Ã‚ ¥ 0 . However, if ÃŽÂ ±1 à ¯Ã¢â€š ¬Ã‚ ½ 0 , there are no dynamics in the variance equation. An ARCH (p) can be specified as: ht à ¯Ã¢â€š ¬Ã‚ ½ à Ã¢â‚¬ ° à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ± 1ÃŽÂ µ t2à ¢Ã‹â€ 1 à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ± 2 ÃŽÂ µ t2à ¢Ã‹â€  2 à ¯Ã¢â€š ¬Ã‚ « .. à ¯Ã¢â€š ¬Ã‚ «ÃƒÅ½Ã‚ ± p ÃŽÂ µt2à ¢Ã‹â€ p (11) This ARCH model might call for a long-lag structure to model the underlying volatility. A more parsimonious model was developed by Bollerslev (1986) leading to generalized ARCH class of models called GARCH in which, the conditional variance depends not only on the squared residuals of the mean equation but also on its own past values. The simplest GARCH (1, 1) is: à Ã†â€™ 2 à ¯Ã¢â€š ¬Ã‚ ½ à Ã¢â‚¬ ° à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ± ÃŽÂ µ 2 à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²Ãƒ Ã†â€™ 2 (12) t 1 t à ¢Ã‹â€ 1 1 t à ¢Ã‹â€ 1 The conditional volatility as defined in the above equation is determined by three effects namely, the intercept term given by w , the ARCH term expressed by ÃŽÂ ± ÃŽÂ µ2 and the forecasted 1 t à ¢Ã‹â€ 1 volatility from the previous period called GARCH component expressed by ÃŽÂ ²Ãƒ Ã†â€™1 t2à ¢Ã‹â€ 1 . Parameters w and ÃŽÂ ± should be higher than 0 and ÃŽÂ ² should be positive in order to ensure conditional variance à Ã†â€™2 to be nonnegative. Besides this, it is necessary thatÃŽÂ ±1 à ¯Ã¢â€š ¬Ã‚ « ÃŽÂ ²1 p1 . This condition secures covariance stationarity of the conditional variance. A straightforward interpretation of the estimated coefficients in (12) is that the constant term à Ã¢â‚¬ ° is the long-term average volatility, i.e. conditional variance, whereas ÃŽÂ ± and ÃŽÂ ² represent how volatility is affected by current and past information, respectively. Table 7: Results of Equation (6) for Nifty Junior corrected for autocorrelation and ARCH Effect Mean Equation Variables Coefficients t-statistic P-Value Intercept 0.3572 3.74 0.001 Monday -0.2962 -2.47 0.01 Tuesday -0.2183 -1.53 0.12 Wednesday -0.2849 -2.1 0.03 Thursday -0.1672 -1.27 0.2 AR(1) 0.1667 4.74 0.00 Variance Equation C 0.1387 4.78 0.00 ARCH(1) 0.1833 9.41 0.00 GARCH(1) 0.789 41.99 0.00 F-stat = 2.28 (0.02) Ljung à ¢Ã¢â€š ¬Ã¢â‚¬Å"Box Q (5) =7.12(0.12) ARCH LM Test(1): F- stat = 1.37 (0.24) Table 7 shows that after correcting for serial autocorrelation and ARCH effect, we found weekend effect in Nifty Junior returns. Our study also found significant seasonality in Nifty Junior returns across the days. Returns of Monday, Wednesday and Friday are significantly different from each other. The F-statistic shows that at least one beta coefficient is different from zero. The Ljung-Box Q statistic shows that there is no pattern in residual. ARCH LM test also indicate that there is no ARCH effect in residual now. We also examined seasonality of Nifty and Nifty Junior return using monthly data. We estimated equation (7). The results for Nifty are reported in Table 8. The benchmark month in the model is May represented by the intercept which provided negative return of -0.7132 percent on an average over the sample period. None of the coefficients are significant except December month which indicate the presence of December effect in Nifty monthly returns. Table 8: Results of Equation (7) for Nifty Variables Coefficients t-statistic P-Value Intercept -0.7132 -0.35 0.71 June -0.8535 -0.30 0.76 July 3.1781 1.13 0.25 August 1.5309 0.54 0.58 September 2.1704 0.77 0.44 October -0.2136 -0.07 0.93 November 1.8055 0.64 0.52 December 5.047 1.79 0.07 January 3.4969 1.24 0.21 February 1.1607 0.41 0.67 March -0.2425 -0.08 0.93 April -0.2809 -0.09 0.92 R2 =0.06 F Statistic = 0.84( 0.59) Ljung-Box Q(5) = 11.85(0.03) D-W Statistic = 1.46 ARCH LM Test(1): F- stat = 0.8851 (0.34) Note: Figures in () are p-values R2 is 0.06 which is very low, and F-statistic indicates that the overall fit of the model is poor. Further, Durban-Watson statistic of 1.46 indicates autocorrelation in the residuals. The Ljung-Box Q statistic for the hypothesis that there is no serial correlation up to order of 5 is 11.85 with a significant p-value of 0.03 which indicates that we have autocorrelation problem of higher order. However, monthly Nifty returns do not exhibits autoregressive conditional heteroskedasticity (ARCH) effects. Therefore, we augmented the model specified in equation (7) with autoregressive order of 5 and moving average order of 1 and 5 on a trial and error basis. The results are reported in Table 9 which shows the presence of seasonality in monthly returns of Nifty. The coefficients of July, September and January are statistically significant at 5 percent level. The coefficient of December month is statistically highly significant at 1 percent level of significance. The augmented model has R-squ are of 0.22 which shows that 22 percent of the variations are explained by these months. F-statistic is 2.62 with significant p-value of 0.002 implying that the null of all slope coefficients is rejected at 1 percent level of significance. Table 9: Results of Equation (7) for Nifty Variables Coefficients t-statistic P-Value Intercept -1.6045 -1.03 0.30 June -0.13 -0.06 0.94 July 4.3899 1.97 0.05 August 2.2566 0.91 0.36 September 3.9858 1.86 0.06 October -0.0504 -0.02 0.98 November 3.1714 1.54 0.12 December 5.8317 2.52 0.01 January 4.8644 2.08 0.03 February 2.5038 1.07 0.28 March 0.1636 0.07 0.94 April 0.7953 0.39 0.69 AR(5) 0.6094 6.77 0.00 MA(1) 0.3559 453.72 0.00 MA(5) 0.689 -9.89 0.00 R2 =0.22 F Statistic = 2.62( 0.002) Ljung-Box Q(5) = 1.73 (0.42) D-W Statistic = 1.96 Note: Figures in () are p-values Ljung à ¢Ã¢â€š ¬Ã¢â‚¬Å"Box Q statistic of augmented model of order up to 5 is 1.73 with insignificant p value of 0.42 which implies that there is no pattern left in residual. This is also evident from D-W statistics of 1.96 which is very close to 2. Table 10: Results of Equation (7) for Nifty Junior Variables Coefficients t-statistic P-Value Intercept -0.0106 -0.0037 0.99 June -3.1408 -0.79 0.42 July 2.5269 0.63 0.52 August 2.78 0.70 0.48 September 1.6919 0.42 0.67 October -2.1813 -0.55 0.58 November 1.6522 0.41 0.67 December 7.2491 1.82 0.06 January 4.0079 1.01 0.31 February 0.131 0.03 0.97 March -3.3807 -0.85 0.39 April -0.3954 -0.09 0.92 R2 =0.09 F Statistic = 1.20( 0.28) Ljung-Box Q(5) = 19.31(0.00) D-W Statistic = 1.33 ARCH LM Test(1): F- stat = 12.36 (0.00) Note: Figures in () are p-values Finally, we examined the seasonality of monthly Nifty Junior returns. We estimated the model specified in equation (7) for Nifty Junior. The results are reported in Table 10 which shows that December effect is present in Nifty Junior returns. Besides this, the coefficient of June month is found to be statistically significant at 5 percent level indicating the presence of seasonality in the returns of Nifty Junior. In this regression model, R2 is 0.09 which is very low, and F-statistic indicates that the overall fit of the model is poor. Further, Durban-Watson statistic of 1.33 indicates autocorrelation in the residuals. The Ljung-Box Q statistic for the hypothesis that there is no serial correlation up to order of 5 is 19.31 with a significant p-value of 0.00 which indicates that we have autocorrelation problem of higher order. However, unlike Nifty monthly Nifty Junior returns exhibits autoregressive conditional heteroskedasticity (ARCH) effects. Table 11: Results of Equation (7) for Nifty Junior corrected for autocorrelation and ARCH Effect Mean Equation Variables Coefficients t-statistic P-Value Intercept 1.9045 0.85 0.39 June -4.67 -1.93 0.05 July 2.3638 0.48 0.62 August 0.6749 0.17 0.86 September 0.253 0.06 0.94 October -2.9230 -0.80 0.42 November 0.038 0.01 0.99 December 5.86 1.69 0.08 January 2.7228 0.70 0.47 February -1.2328 -0.33 0.74 March -2.7668 -1.01 0.31 April -0.7839 -0.29 0.76 AR(1) 0.364 4.08 0.00 Variance Equation C 8.13 0.11 ARCH(1) 0.1648 0.10 GARCH(1) 0.00 0.7393 F-stat = 1.73(0.04) Ljung à ¢Ã¢â€š ¬Ã¢â‚¬Å"Box Q (5) = 2.07 (0.72) ARCH LM Test(1): F- stat = 0.0142 (0.9051) Note: Figures in () are p-values Table 11 shows that after correcting for serial autocorrelation and ARCH effect, we found June and December effect in monthly Nifty Junior returns because the coefficient of these dummy variables are found statistically significant at 5 and 10 percent respectively. The F-statistic shows that at least one beta coefficient is different from zero. The Ljung-Box Q statistic shows that there is no pattern in residual. ARCH LM test also indicate that there is no ARCH effect in residual now. 9.0 Conclusion In this study, we tried to examine the seasonality of stock market in India. We considered the SP CNX Nifty as the representative of stock market in India and tested whether seasonality are present in Nifty and Nifty Junior returns using daily and monthly data sets. The study found that daily and monthly seasonality are present in Nifty and Nifty Junior returns. The analysis of stock market seasonality using daily data, we found Friday Effect in Nifty returns while Nifty Junior returns were statistically significant on Friday, Monday and Wednesday. In case of monthly analysis of returns, the study found that Nifty returns were statistically significant in July, September, December and January. In case of Nifty Junior, June and December months were statistically significant. The results established that the Indian stock market is not efficient and investors can improve their returns by timing their investment.