Comparison of Time Domain and Frequency Domain Analysis in Forecasting Sri Lankan Share Market Returns
International Journal of Management and Applied Science, ISSN: 2394-7926 Volume-1, Issue-9, Oct.-2015 COMPARISON OF TIME DOMAIN AND FREQUENCY DOMAIN ANALYSIS IN FORECASTING SRI LANKAN SHARE MARKET RETURNS
1W.G. S. KONARASINGHE, 2N. R. ABEYNAYAKE, 3L.H.P.GUNARATNE
1Postgraduate Institute of Agriculture, University of Peradeniya, Sri Lanka. 2Faculty of Agriculture and Plantation Management, Wayamba University of Sri Lanka, Makandura, Gonawila (NWP), Sri Lanka. 3Department of Agricultural Economics and Business Management Faculty of Agriculture, University of Peradeniya, Peradeniya, Sri Lanka. E mail: [email protected], [email protected], [email protected]
Abstract- Time domain analysis and frequency domain analysis are two approaches for analyzing a financial time series. Time domain analysis is widely used in that respect but the latter is applied less. Literature revealed that both approaches have not been applied much in sri lankan context. Also it revealed a knowledge gap in forecasting sri lankan stock market returns. Therefore this study aimed to compare the forecasting ability of time domain and frequency domain in forecasting sri lankan stock returns. Two time domain models: auto regressive integrated moving average (arima) and auto distributed lag model (adlm) were compared with fourier transformation based analysis. Data collection period was year 2011 to 2014. Monthly total market returns and returns of random sample of four business sectors were analyzed. Model assumptions were tested by residual plots, anderson darling test and durbin watson test. Model assessment was based on mean square error (mse). Results revealed that arima and fourier transformation based analysis are suitable in forecasting but adlm is not. Based on the results, it was concluded that frequency domain approach is better than time domain approach in forecasting sri lankan stock market returns.
Keywords- Time domain, Frequency Domain.
INTRODUCTION Literature revealed that ADLM are suitable in forecasting stock returns. Some of the studies based A continuous set of observations that are ordered in on ADLM are: Timothy (1992), Chordia and equally spaced intervals is known as a time series Swaminathan (2000) and Jianping, Olesya and (Stephen, 1998). Traditional approach of analyzing a Lubomir (2002). But such studies were limited in Sri time series is known as the time domain approach. Lankan context. Konarasinghe & Abeynayake (2014- The time domain is a record of what happens to a b) has shown that Sri Lankan stock market returns parameter of the system versus time or space. An follow wave like patterns. A wave can be viewed in alternative approach for time domain analysis is the either time domain or frequency domain. On view of frequency domain analysis. This approach is known the above, this study was focused on comparing time as Spectral Analysis or Fourier analysis. domain and frequency domain approaches in Spectral analysis was initially established in natural forecasting Sri Lankan stock market returns. sciences such as physics, engineering, geophysics, oceanography, atmospheric science, astronomy etc. MATERIAL & METHODS and not much used in the field of economics. As Granger (1964) emphasis, frequency domain Auto Regressive Integrated Moving Average approach was less popular in economic time series (ARIMA) model and Auto Distributed Lag Model analysis, due to the complexity. (ADLM) were tested in the study. Auto Regressive Integrated Moving Average (ARIMA) method is a PROBLEM STATEMENT widely applied univariate forecasting technique in many fields. Auto Distributed Lag Model (ADLM) is Forecasting asset returns in Sri Lankan share market a multivariate regression model which includes has been an immense interest in past few decades. current values as well as lagged (past) values of Literature revealed that Nimal (1997), Samarakoon explanatory variables. (1997), Pathirawasam, C. (2009), Konarasinghe & Pathirawasam (2013) Rathnayaka, Seneviratna, & Tested Univariate Adlm Is Given In Equation (1) n Nagahawatta, (2014), Konarasinghe & Abeynayake (1) (2014-a), Konarasinghe, Abeynayake & Gunaratne R t i R t i t i 1 (2015) and many others have attempted to identify patterns and trends in stock returns of Sri Lankan ARIMA model is given in equation (3): stock market. But forecasting ability of suggested (B)d Y (B) methods are still in debate. p t q t (2)
Comparison Of Time Domain And Frequency Domain Analysis In Forecasting Sri Lankan Share Market Returns
16 International Journal of Management and Applied Science, ISSN: 2394-7926 Volume-1, Issue-9, Oct.-2015 where, Rt is the return on day t, Vt is the trading , volume on day t and B is the back shift operator. uncorr Fourier transformation is used to transform a time elated L& (a) 0.594 0.0% series of returns Rt into a series of trigonometric functions as: P n (b) 0.830 0.0% (3) MF (a) 0.038 1.4% Residu Rt ak coskt bk sin kt G als k1 normal 2f , Where: uncorr N elated n/2; if n is even (b) 0.101 1.1% k MT (a) 0.547 0.0% (n -1)/2; if n is odd R (b) 0.835 0.0%
ak and bk are amplitudes, f= number of peaks/ troughs P values of models (a) and (b) of total market, sectors of series, N= number of observations in the series, n= L&P, MFG, and MTR are greater than 0.05. It reveals number of observations per season (12 month that there is no linear relationship between variables seasonality in this analysis) and k is the harmonic of of those models. P values of models (a) and (b) of ω (Stephen, 1998). Multiple Regression analysis was sector DIV are less than the significance level, but used to estimate the amplitudes. adjusted R2 of both models were very small. Therefore ADLM models are not suitable for Random sample of four business sectors of Colombo forecasting Sri Lankan stock market returns. Stock Exchange (CSE) were selected and monthly Table 2 is the summary of ARIMA model testing and returns were calculated by using sector indices. Fourier analysis based models. Residuals of all the Monthly returns of total market were calculated by fitted models were normally distributed and using All Share Price Index. Data collection period uncorrelated. was year 1994- 2014. Model assumptions were tested by residual plots, Anderson Darling test and Durbin Table 2: Summary of ARIMA model testing and Watson test. Model assessment was based on Mean Fourier analysis Outputs Square Error (MSE). Total Secto Secto Secto Sector Marke r r r MTR RESULTS AND DISCUSSION t DIV L&P MFG ARIMA 35.81 51.35 73.42 45.14 63.02 Univariate ADLM models were tested on total market :MSE in returns and returns of four business sectors of CSE. model fitting Summary of results are given in Table 1: ARIMA 77.89 44.58 62.04 73.83 63.80 :MSE in Table 1: Summary of ADLM analysis model Sec Models Tested P Adju Comm verificatio tor value sted ents n of R2 Fourier: 34.43 54.7 31.9 41.9 Model regre MSE in was not ssion model significan Tot 0.375 0.0% fitting t al (a) Fourier: 17.23 37.2 37.43 42.2 MSE in mar R R ket t 0 1 t1 model verificatio (b) 0.381 0.0% n Table 2 clearly shows that MSE of Fourier analysis Rt 0 1Rt1 based models are less than ARIMA models in both model fitting and verification. DI (a) 0.000 12.9 Residu V % als CONCLUSIONS normal
, uncorr This study was focused on comparison of time elated domain and frequency domain approaches in (b) 0.000 13.6 Residu forecasting Sri Lankan stock market returns. Results % als revealed that ADLM approach is a failure. Both normal ARIMA models and Fourier analysis based models
Comparison Of Time Domain And Frequency Domain Analysis In Forecasting Sri Lankan Share Market Returns
17 International Journal of Management and Applied Science, ISSN: 2394-7926 Volume-1, Issue-9, Oct.-2015 are suitable in forecasting, but Fourier analysis is Colombo Stock Exchange. Sri Lankan Journal of better than ARIMA. It was concluded that frequency Management. Vol. 18, Nos. 3 & 4, July - December, 2013 domain approach is better than time domain approach [4] Konarasinghe, W.G.S. & Abeynayake, N.R., (2014-b). in forecasting Sri Lankan stock market returns. Time Series Patterns of Sri Lankan Stock Returns. Proceedings of Doctoral Consortium, 11th International However, MSE of Fourier analysis based models also Conference in Business & Management, University of Sri Jayewardenepura, Sri Lanka, pp.78-95. not satisfactory. It is recommended to test Fourier [5] Konarasinghe, W.G.S., & Abeynayake, N.R., analysis on individual company returns of Sri Lankan Gunaratne, L.H.P. (2015), ARIMA Models on stock market and try to find out techniques for error Forecasting Sri Lankan Share Market Returns. reduction. International Journal of Novel Research in Physics, Chemistry & Mathematics, Vol.2, Issue 1: pp 6-12. www.noveltyjournals.com REFERENCES [6] Samarakoon, M. P.(1997)/” The Cross Section of Expected Stock Returns of Sri Lanka”. Sri Lankan [1] Granger, (1964). Spectral Analysis of Economic Time Journal of Management, 2(3). Series, Princeton University Press, Princeton, New [7] Stephen, A., D., (1998). Forecasting Principles and Jersey. Applications. First Edition. Irwin McGraw-Hill, USA [2] Konarasinghe, W.G.S. & Abeynayake, N.R.(2014- [8] Timothy, S.M. (1992). Portfolio returns autocorrelation. a).Modeling Stock Returns of Individual Companies of Journal of Financial Economics, 34,307-344 Colombo Stock Exchange. Conference Proceedings of [9] Chordia, T., Swaminathan, B., (2000). Trading Volume the 1st International Forum for Mathematical Modeling and Cross Auto-correlations in Stock Returns. Journal 2014, Department of Mathematics, University of of Finance, Volume. LV (2). Colombo, Sri Lanka, 111. [10] Jianping, M., Olesya V.G., Lubomir.P. L.,(2002). [3] Konarasinghe, W.G.S., Pathirawasam, C. (2013). Measuring Private Information Trading in Emerging Modeling Stock Returns and Trading Volume of Markets. New York University
Comparison Of Time Domain And Frequency Domain Analysis In Forecasting Sri Lankan Share Market Returns
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