Time series analysis

To prepare for the future, it is very important to look at the past to see what has occurred so that one knows what to expect in the future. Hence, time series analysis is of importance to any person who is interested in buying shares, starting a business or any other form of investment of their money. Hence, the study of cycles in important.

This paper investigates the existence of the day of the week effect on the JSE TOP 40 index.

Zafar, Chughtai and Amjad (2012) define calendar anomalies as any market irregularity or consistent pattern that cannot be defined by any accepted theory of finance. Other publications may define that differently.

The Efficient Market Hypothesis states that markets are informationally efficient and therefore excess returns cannot be achieved consistently. A calendar effect is any market anomaly or economic effect which appears to be related to the calendar. Such effects include the apparently different behaviour of the stock market on various days of the week, different times of the month and different times of the year.

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Mbulula & Chipet's (2012) studied nine sector indices and found out that there is only one sector that showed significant evidence of the day of the week effect. So this research will use the most recent data to test for the existence of calendar anomalies. The focus will be on the day of the week effect of the JSE TOP 40 index.

The JSE's Top40 is chosen because of their capitalisation on the JSE and hence greater weightings in the market.

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These Top40 are often regarded as the blue chip firms. By definition, a blue chip firm has a sound and consistent business practices and has a very strong balance sheet (Plimsoll, Saban, Spheris,and Rajaratnam ;2013:320). According to the work of Brockman & Chung (2003), regarding returns, the blue chip firms have minimum volatility relative to stock markets.


The study of various cycles has caught the interest of many thinkers in many different human civilisation over a period of time. The study of cycles can be dated back from the Chinese history whereby two astronomers Hi and Ho lost their heads because they failed to forecast a solar eclipse. In the 18th century the philosopher Griambattista Vico developed a cyclical theory of history in which human civilisations passed through determinate stages of growth and decay. Also cycles can be found in natural sciences, where the idea of cycles has been central to the development of both classical and quantum physics (Bernet, 2016).

Among the social sciences it is within economics that the study of cycles has currently reached its most advanced level. The idea of fluctuations in various aspects of economic activity has existed for many centuries. William Stanly Javons, one of the leaders in marginal revolution in economics in the 1870's, noted that cycles in agriculture had been identified as early as 1662 by Sir William Petty. In 1837 Lord Overstone distinguished ten stages in the state of trade, including quiescence, improvement, prosperity, convulsion, stagnation and distress. The study of economic cycles proper can be dated from the work of Javons and Juglar of 1862, although specific aspects of cyclical movement had been identified well before this date. While Overstone listed a number of possible causes of cycles from the character of the human mind to legislative enactments, a more systematic investigation would not occur until 1862 and the work of pioneers, Javons and Juglar. (Bernet, 2016)


There are many economic cycles that have been studied in the past but the well-known cycle are Kitchin, Juglar Kuznets and Kontratiev wave ( de Groot and Franses, 2012).

1. Kitchin cycle

The kitchin stock cycle was discovered in 1923. Kitchin found a pattern of fluctuation that lasted for about 3 to 4 years. He explained these fluctuations by stating that after a recession firms had too little stock of raw materials, parts, half fabricates and final products. While aiming to get their stock at an acceptable level, firms create demand that influences the entire economy. Demand increases until the firms find out that their expansion has become too large. I order to diminish the excess stock, firms cut back on their stock orders and will lower their output. This in turn can drag the economy back into recession ( de Groot and Franses, 2012).

2. Juglar cycle

The Juglar cycle is a fixed investment cycle of about 7 to 15 years identified by Clement Juglar. Within the Juglar cycle on can observe oscillation of investments into fixed capital and not just changes in the level of employment of the fixed capital, as is observed with respect to the Kitchin cycle.

Legrand and Hagemann (2007) stated that Juglar was ranked by Joseph Schumpeter in his "History of Economic Analysis" as one of the best command of scientific method, amongst the greatest economists of his time. Clement Juglar is well known mainly because of the Juglar cycle named after him. Legrand and Hagemann (2007) points out that Juggler's work deserves more attention. They emphasize this by mentioning Juglar's theory on business cycle as highly original and often complete than often supposed. In the theory of the business cycle, according to Juglar the cycle is caused by an overheated boom is a speculation fuelled by easy credit.

3. Kuznets swing/cycle

The Kuznets cycle is widely accepted by economists as well as it is corroborated by plenty data material. The cycle is related to investments in construction and lasts for about somewhere in between 15 to 25 years (de Groot and Franses, 2012). This cycle is named after Simon Kuznets who discovered this cycle, hence it is named after him. Korotayer and Tsirel (2010) stated that Kuznets first connected the cycles with demographic processes, in particular with foreign inflows/outflows and the changes in construction intensity that they caused, that is the reason why these cycles are denoted as demographic or building cycles/swings.

4. Kontratiev wave

The Kontratiev cycle was found by many authors from different theoretical backgrounds very interesting and hence it was studied extensively (de Groot and Franses, 2012). The Kontratieve wave is a long economic cycle that is associated with technological innovations and lasts for about 45 to 60 years in duration. The Kontratiev wave is also known as K-wave, surge or long wave. The Kontratiev wave is named after Nikoli Kontratiev.


There are other indices that rank the top companies in the stock exchange in other countries besides South Africa's Johannesburg Stock Exchange (JSE). For instance in the United States of America (USA) they have S&P 500 stock market index which measures the stock performance of the 500 large companies listed on the stock exchange in the United States. Similarly, other countries have:

  • Japan has Nikkei 225 index with 225 large companies,
  • China has Shangai Stock Exchange Composite index.,
  • Germany has (Deutscher Aktein index) DAX 30,
  • France has CAC 40,
  • Spain has IBEX 35,

Just to name a few. Some of these countries mentioned above are economically better than South Africa. Hence, most of the companies operating in the first world countries like the US and Japan have a very strong balance sheet. That is why they have indices with 225 and 500 top companies listed on them,


South Africa is a country which its economy is very dependent on foreign investments. This means that the currency of South Africa is very volatile to any unrest that happens in the country. When the unrests happen investors tend to want to pull out their investments and this in turn causes the currency to depreciate.

Zafar, Chughtai and Amjad (2012) define calendar anomalies as any market irregularity or consistent pattern that cannot be defined by any accepted theory of finance. Other publications may define that differently, for instance the other definition of calendar anomalies is that calendar effect is any market anomaly or economic effect which appears to be related to the calendar. Such effects include the apparently different behaviour of the stock market on various days of the week, different times of the month and different times of the year.

There are many empirical tests that were made in the past years to illustrate the information efficiency of the markets (Barone, 1990:6). In contrast, there were some writers who wrote papers do demonstrate their inefficiency by identifying systematic differences in stock prices related to the calendar of the civil year.

The Day of The week effect

The weekend effect (also known as the Monday effect, the day-of-the-week effect or the Monday seasonal) refers to the tendency of stocks to exhibit relatively large returns on Fridays compared to those on Mondays. The tendency of the stock market to act this way will be discussed more on the results section and also investigate why the stock market acts this way. Benson and Ryston (1989; 75) explained the day of the week effect by referring to a typical week of people. They explain this by stating that Mondays are not the same as the other days of the week. For most people it the beginning of five long days preceding two days of leisure. Some people start their week with some reluctance. Monday have a reputation of being a bad day. Other days of the week do not share the reputation. Fridays, most people are usually looking forward to the weekend with positive attitude (Benson & Ryston 1989; 75). Barone and Ryston (1989) implied that there is now an abundant evidence that the financial markets also reflect these weekend attitudes.

In South Africa the stock market opens on Monday and closes on Friday. There is no trading of stock during the weekends. However, this is not true for every country. This may be because of differences in cultural or religious beliefs in other countries. But this will not be discussed in depth in this paper. It was to highlight that some countries have different times of trading.

The use of daily data makes it possible to inspect the relationship between the changes that occur in stock prices from one trading day to the next (Barone, 1990:60).

Other market anomalies defined

The January effect

The January effect is a seasonal increase in stock prices during the month of January. Analysts generally attribute this rally to an increase in buying, which follows the drop in price that typically happens in December when investors, engaging in tax-loss harvesting to offset realized capital gains, prompt a sell-off.

Turn-of-the-month effect

The Turn-of-the-Month Effect is described as a temporary increase in stock prices during the last few days and the first few days of each month. Some analysts credit the turn of the month effect to distributions from pension funds and other retirement accounts that the pensioners immediately reinvest in the stock market.

Updated: May 19, 2021
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Time series analysis. (2019, Nov 14). Retrieved from https://studymoose.com/time-series-analysis-essay

Time series analysis essay
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