See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/24070987 Seasonality as an unobservable component: The case of Kuwait stock market Article in Applied Financial Economics · February 2006 DOI: 10.1080/09603100500414636 · Source: RePEc CITATIONS READS 5 17 1 author: Talla M. Al-Deehani Kuwait University 22 PUBLICATIONS 173 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Islamic banking and economic crisis View project KSE Optimization View project All content following this page was uploaded by Talla M. Al-Deehani on 07 November 2016. The user has requested enhancement of the downloaded file. Applied Financial Economics ISSN: 0960-3107 (Print) 1466-4305 (Online) Journal homepage: http://www.tandfonline.com/loi/rafe20 Seasonality as an unobservable component: the case of Kuwait stock market Talla M. Al-Deehani To cite this article: Talla M. Al-Deehani (2006) Seasonality as an unobservable component: the case of Kuwait stock market, Applied Financial Economics, 16:6, 471-478, DOI: 10.1080/09603100500414636 To link to this article: http://dx.doi.org/10.1080/09603100500414636 Published online: 23 Aug 2006. Submit your article to this journal Article views: 63 View related articles Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=rafe20 Download by: [Kuwait University] Date: 07 November 2016, At: 00:34 Applied Financial Economics, 2006, 16, 471–478 Seasonality as an unobservable component: the case of Kuwait stock market Talla M. Al-Deehani Department of Finance & Financial Institutions, College of Business Administration, Kuwait University, PO Box 5486, Safat 13055, Kuwait E-mail: talla@cba.edu.kw This paper uses structural time series methodology to investigate seasonality factors for the returns of Kuwait stock market and its various sectors. The results indicate the existence of positive pre-summer seasonal factors for the market and most of the sectors, which can be explained by the summer holiday effect. Significant seasonal factors are found to be stochastic rather than deterministic, which cannot be handled by traditional time series models that assume deterministic seasonality. I. Introduction Research in finance and economics has provided evidence of return anomalies in stock markets that are related to seasonal movements. The January effect is now an established hypothesis that has been confirmed by many empirical studies in most developed stock markets. The most widely accepted interpretation of this phenomenon is tax saving. In order to claim realized capital losses, investors tend to sell their stocks before the end of the calendar year, causing prices to go down. To return to their previous position, they usually buy back stocks during the first week of January, causing prices to go up. For emerging markets, limited evidence on seasonal effects is available. This may be due to the fact that many of these markets are relatively new with short histories and limited historical data. However, some emerging markets (such as the Kuwait stock market) do provide sufficient data. Most of the studies on developed and emerging markets consider the seasonality of the stock market as a whole and disregard the nature of seasonality of the different sectors comprising the markets. The assumption that all sectors of the same market realize the same seasonality pattern as the market as a whole is yet to be tested. Therefore, this paper strives to contribute to the very limited literature on sector monthly seasonal effects in emerging markets. In particular, it examines the nature of seasonality in the monthly stock returns using the market and sectors indices. II. Review of the Relevant Literature Ever since the preliminary observations of Wachtel (1942), investigations of various seasonal effects for developed and non-developed stock markets have been conducted. Rozeff and Kinney (1976) were the first to confirm Wachtel’s observations with regard to the January effect. January returns were found to be significantly higher than those of the other months. Other empirical studies reached similar conclusions (see for example Jones and Wilson, 1989; Musto, 1997). Further studies found that small cap companies realize higher January returns when compared to large cap companies (see for example Roll, 1983; Keim, 1983; and Reinganum, 1983). The stock market seasonality in 13 major industrialized countries was examined by Gultekin and Gultekin (1983). They provided evidence of strong seasonalities Applied Financial Economics ISSN 0960–3107 print/ISSN 1466–4305 online ß 2006 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/09603100500414636 471 T. M. Al-Deehani 472 that appear to be caused by the disproportionately large January returns in most countries and April returns in the UK. However, they argued that the cause of the seasonality could not be ascertained. Other empirical studies provided explanations for the January effect other than the need to save tax payments at the end of the year. Constantinides (1984) simulated three trading policies and the buyand-hold policy for a large sample of stocks listed on the New York Stock Exchange and the American Stock Exchange over the period 1962–1977. He concluded that tax trading does not explain the small-firm anomaly but does predict a seasonal pattern in trading volume. Similar conclusions were reached by Chan (1986), Ritter (1988), Brauer and Chang (1990) and Peavy (1995). Sias and Starks (1997) evaluated the tax-loss selling hypothesis and the window dressing hypothesis as explanations for the turn of the year effect. They found that stocks with a greater percentage of individual ownership outperform stocks with a greater percentage of institutional ownership at the turn of the year, consistent with the tax-loss selling explanation. Their results were later refuted by Johnston et al. (2000) in their re-examination of the issue after adjusting for risk and controlling more closely for share price differences. There are some empirical studies that investigated seasonality in less developed and emerging markets. Chan et al. (1996) used daily returns to identify seasonality on the Kuala Lumpur Stock Exchange (KLSE), the Bombay Stock Exchange (BSE), the Stock Exchange of Singapore (SES) and the Stock Exchange of Thailand (SET). Month-of-the-year effects were found to exist on the KLSE and the SES, but not on the SET or the BSE. Using nonparametric and ordinary regression techniques, Ayadi et al. (1998) found some evidence on the January effect in low-income equity markets of Africa. Mills et al. (2000) studied calendar effects for each of the constituent stocks of the Athens Stock Exchange general index for the period from October 1986 to April 1997 and found substantial evidence of monthly effects. The results indicated that the calendar regularities vary significantly across the constituent shares of the General Index and that aggregation introduced considerable bias in unravelling these regularities. Pandey (2002) investigated the existence of seasonality in Malaysia’s stock market and found some evidence for February and December positive effects. Cheung and Coutts (1999) investigated the presence of the January effect, or other monthly seasonalities in the Hong Kong Stock Exchange Hang Seng Index and found no evidence for a January effect or any other monthly seasonality. For the Kuwait stock market, only two empirical studies investigated stock returns anomalies using the Global Investment House Company Index. By using non-parametric and ordinary regression techniques, Al-Loughani (2003) realized mixed results. Al-Saad and Moosa (2005) used conventional regression and structural time series techniques to provide evidence for a positive July effect. This is an interesting study because it uses structural time series analysis to account for the possibility of stochastic seasonality, which is important because seasonality effects are not always deterministic. Therefore, I choose to use structural time series analysis for this re-examination of seasonality in the Kuwait stock market. III. Data and Methodology The data used in this study cover the period from January 1996 to December 2004. Monthly average indices for the market and its nine sectors are used. These are prices-weighted indices prepared by the Kuwait Stock Exchange (KSE) on a daily basis. The sectors are: banking, investments, insurance, real estate, services, food, non-Kuwaiti and funds. The reason for using sector data as well as the market data is that the evidence based on the market index (as provided by most of the studies) is based on the implicit assumption of the homogeneity of components (that is, all sectors comprising the market will observe the same effect). Heterogeneity is a possible result of aggregation that is occasionally overlooked by researchers. This topic was recently surveyed by Blundell and Stoker (2005) who showed how concerns faced by empirical researchers regarding aggregation can be addressed. Therefore, homogeneity of sectors returns is not assumed in this paper. I argue that because each sector operates differently from the others, it is not expected for all sectors to have the seasonality effect as that of the market. To capture unobserved components of the time series, including seasonal effects, structural time series modelling is employed to determine the seasonal factors for the market as a whole and for each sector in isolation. Structural time series analysis involves the decomposition of a series into unobserved components that have a direct interpretation. Usually, four components are considered: a trend, a cyclical component, a seasonal component and an irregular component. As demonstrated by Harvey and Scott (1994), a stochastic seasonal component can be included in a dynamic regression model. Seasonality as an unobservable component 473 They have shown that seasonality evolves relatively slowly and that a model exhibiting these characteristics appears to fit most economic time series when included as a component in a structural time series model. This paper follows the structural time series model proposed by Harvey (1989, 1997) and used by Al-Saad and Moosa (2005). The model is estimated by maximum likelihood using the Kalman filter, which is a set of vector and matrix recursions computing one-step ahead predictions of observation and state vectors and the corresponding mean square errors (for detailed statistical treatment of the Kalman filter see Koopman et al., 1999). This model may be written as Rt ¼ Tt þ Ct þ St þ "t ð1Þ where Rt is the rate of return calculated as the first log difference of the price index, Tt is the trend component, St is the seasonal component, and "t is the irregular component which is assumed to be a white noise. Tt represents the long-run movements in the series which is specified as Tt ¼ Tt
1 þ
t
1 þ t t  NIDð0, 2 Þ
t ¼
t
1 þ t t  ð3Þ where
t is the slope of the trend. The irregular "t, the level disturbance t and the slope disturbance t are mutually uncorrelated. Equations 2 and 3 encompass various specifications. For example, when 2 ¼ 2 ¼ 0, the trend is deterministic and linear. When 2 ¼ 0 while 2 6¼ 0, then the process will have a smooth stochastic trend. The specification of the cyclical component is given by Ct ¼ a cos t þ b sin t such that C0 ¼ a and C0 ¼ b. !t and !t are two mutually uncorrelated NID disturbances with zero means and common variances !2 and !2  .  is a damping factor and  is the frequency of the cycle (in radians). It is more useful to present the frequency in terms of period as Cp ¼ 2  ð6Þ As for the seasonal components, a ‘dummy seasonal’ specification is employed as a form of stochastic seasonality, which is given by St ¼
n
1 X St
j þ t t  NIDð0, 2 Þ where n is the number of seasons (12 months) in one year. ð4Þ IV. Model Estimation and Analysis of the Results Before analysing the results of the estimated model a closer look at the correlation matrix of market and sectors’ returns should provide a sign of what should we expect with regard to heterogeneous seasonality of the sectors. Table 1 shows the investment sector has the highest correlation with the market followed by the services sector and the industrial sector. The insurance sector has the lowest correlation with the market as a whole, then the nonKuwaiti sector. These observations indicate the presence of variation in the relation between the Table 1. Correlation matrix Market Bank Inve Insu Real Indu Serv Food Nkuw Fund ð7Þ j¼1 ð2Þ with NIDð0, 2 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where a2 þ b2 represents the amplitude of the cycle. A stochastic representation of the cycle may be obtained by        Ct
1 !t Ct cos  sin  ¼ þ ð5Þ Ct !t
sin  cos  Ct
1 Market Bank Inve Insu Real Indu Serv Food Nkuw Fund 1.000 0.935 0.987 0.786 0.871 0.986 0.986 0.961 0.866 0.930 1.000 0.899 0.667 0.725 0.962 0.940 0.979 0.659 0.956 1.000 0.833 0.918 0.961 0.951 0.933 0.882 0.9896 1.000 0.956 0.739 0.712 0.749 0.699 0.705 1.000 0.818 0.798 0.796 0.813 0.764 1.000 0.984 0.967 0.798 0.944 1.000 0.959 0.831 0.929 1.000 0.723 0.946 1.000 0.705 1.000 T. M. Al-Deehani 474 market returns and the returns of the different sectors, which might lead to statistical evidence suffering from an aggregation problem if only the market index is used. The results of estimating the complete structural time series model that includes the trend, cycles and seasonal components are presented in Table 2. The table reports the final state vector, including the estimated components with their t-statistics in parentheses. Also reported are two diagnostics for serial correlation and two measures of the goodness-of-fit. Starting with the diagnostics and the goodness-of fitmeasures placed at the end of the table, the tests indicate that the model is well determined. We can observe no serial correlation problem as indicated by DW and Q. The Q statistic is distributed as 2 ðn þ 1
kÞ where n is the number of autocorrelation coefficients and k is the number of estimated parameters. For seasonal data with a trend, R2s is the modified coefficient of determination, which is more Table 2. Results of estimating the structural time series model Coef/test Market 0.033 (2.10) Tt Cycle 1 Ct Ct  0.005 (0.23) 0.0003 (0.01) Bank Inve Insu Real 0.017 (1.26) 0.027 (1.43) 0.021 (1.29) 0.027 (1.46) 0.006 (0.25) 0.001 (0.03) 0.006 (0.17) 0.063 0.024 (3.18) (1.99) 0.011 –0.01 (0.31) (–0.84) 6.0 9.0 Pera Cycle 2 Ct 0.014 (0.76) –0.019 (–1.41) –0.010 (–0.67) Ct Pera 2 2 C1 2 C2 2 S1t S2t S3t S4t S5t S6t S7t S8t S9t S10t S11t Q(11,6) DW R2 R2s 7.18e–5 6.38e–5 0.00012 5.45e–5 0.00010 0.00012 1.77e–5 6.55e–5 –0.005 (–0.28) –0.023 (–1.50) –0.008 (–0.53) 0.0004 (0.03) –0.002 (–0.14) –0.023 (–1.50) 0.041 (2.67) –0.005 (–0.35) 0.043 (2.81) –0.017 (–1.12) –0.014 (–0.88) 10.58 1.88 0.32 0.22 4.65e–5 0.001 (0.29) –0.022 (–1.45) –0.006 (–0.42) 0.0003 (0.02) 0.009 (0.60) –0.015 (–0.98) 0.040 (2.72) –0.012 (–0.78) 0.019 (1.31) 0.000 (0.01) –0.008 (–0.57) 9.76 1.90 0.23 0.31 0.00010 –0.003 (–0.16) –0.044 (–2.38) –0.003 (–0.14) –0.004 (–0.19) –0.009 (–0.48) –0.027 (–1.47) 0.050 (2.66) 0.011 (0.61) 0.041 (2.18) –0.024 (–1.27) –0.001 (–0.03) 5.74 1.90 0.28 0.25 0.00000 0.002 (0.14) –0.007 (–0.53) –0.015 (–1.18) –0.001 (–0.11) –0.005 (–0.40) –0.013 (–1.03) 0.017 (1.36) 0.023 (1.84) –0.020 (–1.54) –0.005 (–0.36) 0.005 (0.41) 7.66 1.76 0.24 0.20 0.00011 –0.013 (–0.71) –0.024 (–1.39) –0.016 (–0.94) 0.013 (0.75) –0.009 (–0.51) –0.020 (–1.18) 0.048 (2.75) –0.009 (–0.52) 0.057 (3.28) –0.018 (–1.06) –0.019 (–1.12) 1.65b 1.95 0.33 0.29 Indu 0.029 (2.02) Serv  –0.017 (–0.75) –0.019 (–0.56) Food  Fund  0.036 (1.68) 0.018 (1.25) 0.043 (2.49) 0.013 (0.73) –0.022 (–1.12) 0.019 (1.02) 0.018 (0.96) 0.029 (0.99) 0.017 (0.48) –0.008 (–0.46) –0.045 (–2.37) 4.8 2.21e–5 0.00020 0.00011 –0.005 (–0.23) 0.007 (0.37) –0.020 (–1.12) 0.005 (0.26) 0.009 (0.51) –0.030 (–1.64) 0.034 (1.89) –0.005 (–0.14) 0.042 (2.32) –0.026 (–1.45) –0.025 (–1.36) 6.37 1.95 0.18 0.23 Nkuw 4.81e–5 0.00015 –0.019 (–0.93) –0.015 (–0.77) –0.004 (–0.21) –0.011 (–0.56) 0.003 (0.14) –0.021 (–1.08) 0.068 (3.55) –0.035 (–1.82) 0.061 (3.20) –0.002 (–0.08) –0.038 (–2.01) 9.48b 2.04 0.35 0.28 0.013 (0.90) –0.016 (–3.22) 0.001 (0.10) 6.6 0.027 (1.19) 0.007 (0.26) 2.31e–5 5.08e–5 3.80e–5 0.00000 6.46e–5 0.021 (0.87) –0.035 (–1.47) 0.002 (0.09) 0.008 (0.33) –0.007 (–0.29) –0.016 (–0.68) 0.031 (1.71) –0.013 (–0.55) 0.038 (1.61) –0.029 (–1.21) –0.010 (–0.43) 5.78b 1.97 0.18 0.28 0.00000 0.017 (0.83) –0.031 (–1.56) –0.018 (–0.91) 0.012 (0.59) 0.005 (0.26) –0.015 (–0.77) 0.014 (0.71) 0.018 (0.88) 0.015 (0.74) –0.030 (–1.47) –0.008 (–0.41) 8.01 2.01 0.35 0.39 0.00000 –0.010 (–0.80) –0.005 (–0.38) 0.002 (0.17) –0.004 (–0.33) –0.008 (–0.65) –0.008 (–0.64) –0.009 (–0.75) 0.013 (1.06) 0.009 (0.73) 0.027 (2.18) 0.001 (0.07) 2.99 1.80 0.13 0.38 Notes:  ,  and  indicate significance at the 1%, 5% and 10% levels respectively. a cycle period in months, blag ¼ 14. Numbers in parentheses represent t-statistic values (Harvey, 1989). Seasonality as an unobservable component 475 suitable than the conventional R2 (see Koopman et al., 1999 for detailed properties). The table reports the seasonal factors S1 , S2 , . . . , S11 , which correspond to December, November, . . . , February. The seasonal factor corresponding to January can be calculated as in Equation 7 or by re-estimating the model by deleting the last observation (December 2004). In any case it turns out to be statistically insignificant, thus refuting the presence of a January effect. Statistically seasonal factors can be observed for the market and all the sectors except the non-Kuwaiti sector. The fact that seasonality effects are not the same for all sectors compared to that of the market confirms our concern with regard to the heterogeneity as a result of aggregation. In general terms, the results confirm 0.15 RMARK the positive relationship between correlation and homogeneity. Sectors that are highly correlated with the market seem to have similar seasonality effects and vice versa. A positive and significant coefficient of trend, Tt, for stock returns can be detected for the market index and the indices of only three sectors, namely; industrial, services and non-Kuwaiti-companies sectors. The level variances, 2 , for the returns of the market index and the indices of these three sectors are not equal to zero indicating a stochastic trend confirming the need to cater for unobservable components represented by the trend which the ordinary least squares regression cannot handle. Stochastic trend of market returns is illustrated in Fig. 1. Figure 2 shows how the unobservable Trend_RMARK 0.10 0.05 0.00 −0.05 −0.10 1997 1998 1999 2000 2001 2002 2003 2004 2005 2003 2004 2005 Fig. 1. Market returns and trend 0.15 RMARK TrendCyc1_RMARK 0.10 0.05 0.00 −0.05 −0.10 1997 1998 1999 2000 2001 2002 Fig. 2. Market returns and trend plus cycle T. M. Al-Deehani 476 0.04 Seas_RMARK 0.03 0.02 0.01 0.00 −0.01 −0.02 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 3. Seasonal factor of market returns components of trend plus cycle can provide a better fit of the actual returns. Seasonality of market return is shown by Fig. 3. A significant cyclical component can be detected for the insurance, real estate, services and funds sectors, with cycle periods of 6, 9, 4.8 and 6.6 months for these sectors respectively. Of these four sectors only the mutual fund sector seems to have 2 , is a deterministic cycle as the cycle variance, C1 equal to zero. Although the focus of this paper is on seasonal effects, the results on the unobservable component of business cycles seem to affect the specification of the model. The problem of serial correlation was overcome by including one cycle or two for some of the sectors confirming the importance of including such unobservable components in the model. Pre-summer holiday seasonality is positively and significantly evident for the returns of the market index and the indices of all other Kuwaiti companies sectors. The only sector that does not seem to have a seasonal effect is the sector of non-Kuwaiti companies. This is logical as those companies do not operate in Kuwait but rather within their original countries where major operating factors such as the weekend holidays come into effect. Significant and positive April and June effects appear in the returns of the market index and the indices of the investment, real estate, industrial and services sectors. The general homogeneity between the market returns and the returns of these sectors is understandable, as they are closely correlated. The investment sector reveals an additional significant and negative November effect. A reasonable explanation for this result is that the Islamic month of Ramadan has been overlapping with the month of November for the past seven years. The fact that the stocks of the investment sector are heavily traded makes them vulnerable to the slowdown phenomenon in November. A positive seasonal factor significant at the 10% level appears to exist in May for the insurance sector confirming the pre-summer holiday assumption. The services sector reveals a negative February effect (significant at the 5% level). Similar to November, the month of February can be characterized as a slow month due to the many holidays. This month witnesses the midterm two weeks educational holiday, during which many of the wealthy families travel abroad. The liberation and national holidays are on the 25th and 26th of this month. The result indicates that the services sector is the most affected by this slowdown. This is logical as many of the companies of which this sector consists are closely related to services delivered to people on the ground. If they leave the country, business will slow down. Educational institutions and communication companies are examples of such services companies. Another negative effect but less significant (at the 10% level) appears to exist in May. The mutual fund sector indicates a significant and positive March effect that is earlier than that of the other sectors. A possible interpretation of this result is that after the slow month of February, investors tend to re-establish their trading positions with caution by investing in the securities managed by professionals such as mutual funds. Seasonality as an unobservable component V. Conclusion From the reviewed literature, evidence on seasonality is still controversial and the results appear to differ with different markets, economic environment, data used and methodology employed. The results of research on more developed markets by using the traditional regression methodology provide evidence of seasonal factors based on deterministic assumptions, disregarding the possibility that seasonal factors may change over time. Moreover, the problem of aggregation is often overlooked by researchers who provide general conclusions that might suffer from heterogeneity problems among data components. To bridge the gap in the literature for emerging markets, the Kuwait stock market was chosen for this study. The problem of aggregation was overcome by investigating the seasonal factor of the market returns as well as the seasonal factors of its nine sectors. To establish a better fit and capture the unobservable components of the series (including trends, seasonal factors and cycles), structural time series methodology was used. The results show that trends, seasonal factors and cycles are important components of the underlying time series and that they are not always deterministic. The results also indicate that positive significant seasonal effects corresponding to April/June are evident when using market index data. This same effect does not exist for three of its sectors, confirming the concern regarding the aggregation problem. The existence of the April/June (and to a lesser extent, May) seasonal factors for the aggregate market and most of the sectors can be explained by the summer holiday effect. That is, because of the extreme hot weather during the summer, most people in Kuwait leave the country throughout the months of July and August for their summer holiday. Therefore, investors tend to trade heavily to establish good trading positions, hence the increase in trading volumes and prices before the summer holiday. The investment sector was found to have a negative seasonal effect corresponding to November, which was explained by the fact that the Islamic month of Ramadan (when the market slows down) has been overlapping with the month of November for the past seven years. As the investment sector is characterized by active trading, it is believed to suffer the most. There are two main implications of this study. The first is theoretical concerning the modelling of time series. It is strongly believed that structural time series analysis is a better methodology as it explicitly accounts for the unobservable components of trends, seasonal factors and cycles, which traditional OLS is 477 not meant to handle. The second concerns investors’ decisions and to what extent they can take advantage of positive and negative seasonalities to beat the market. It is believed that any advantageous move cannot last for long as the market adjusts. References Al-Loughani, N. 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