Electronic copy available at: http://ssrn.com/abstract=1811786 International Journal of Computer Information Systems, Vol. 2, No. 3, 2011 GARCH -Monte-Carlo Simulation Models with Wavelets Decomposition Algorithm for Stock Returns Prediction Eleftherios Giovanis Department of Economics Royal Holloway University of London Egham, England Eleftherios.Giovanis.2010@live.rhul.ac.uk Abstract— In this paper we examine four different approaches in trading rules for stock returns. More specifically we examine the popular procedures in technical analysis, which are the moving average and the Moving Average Convergence-Divergence (MACD) oscillator. The third approach is the simple random walk autoregressive model and the fourth model we propose is a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) regression with wavelets decomposition and Monte- Carlo simulations algorithm developed in MATLAB. We examine five major stock market index returns for a testing forecasting period of 10 days ahead. We conclude that moving average and MACD might lead to net profits, but not in all cases, therefore are not consistent procedures. Furthermore, moving average 1-30 provides the best results. On the other hand random walk autoregressive model leads in all cases to net losses. Finally, the model we propose not only leads always to net profits, but also to significant higher profits in three stock indices than the respective conventional technical analysis tools. Keywords- Forecasting; MACD; MATLAB; Moving Average; Stock Returns; Random Walk I. INTRODUCTION Two of the most used and popular trading rules used by financial traders and fund managers are the moving average and the MACD oscillator. Moving average is one method of technical analysis among others, which during the last years has gained a significant increase of interest in the academic world too. Some empirical studies like among others [1]-[3] provide evidences of profitability by using technical trading rules. Many other applications have been developed in technical analysis and trading rules modeling, as Fibonacci retracement, candlesticks, various oscillators and momentum indicators among others [4]. Since the decade of 1990 and especially the last years new approaches have been applied with superior results than the traditional technical analysis tools and traditional statistic and econometric approaches [5]-[11]. Some of them are neural networks, fuzzy logic, and genetic algorithms and wavelets analysis. In this paper we propose a computation model where the full programming routine written in MATLAB software is available and provided in the appendix, which combines the well know GARCH model with Monte-Carlo simulation and wavelet decomposition. The structure of this paper is: The second section presents a brief description on the methodology of the four approaches we examine. In the third section the data sample is provided. In the fourth section the empirical results are reported and finally, in section five we discuss the main conclusions of our findings. II. METHODOLOGY A. Moving average The simple moving average is defined as:      1 0 ) / 1 ( L i i t t p L SMA (1) Eq. (1) can be used as a trading rule, which generates a buy signal when the current stock price is higher or above the moving average and a sell signal when it is below. Eq. (1) is the simple moving average, while there are also additional modifications in moving average, as the exponential, the square root weighted, the weighted or the linear moving average. We examine all the mentioned possible modifications of moving average, but we present only the results of the simple moving average as the conclusions are the same, as also many financial traders claim that. We examine three possible moving averages. The 1-30, 1-50 and 1-200, where the short period is 1 day and the long periods are respectively 30, 50 and 200 days. We should mention that we refer to days, March Issue Page 29 of 69 ISSN 2229 5208