FORECASTING STOCK MARKET OF BANK USING BROWNIAN MOTION

In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.

Download Full-text

Fuzzy Time Series and Geometric Brownian Motion in Forecasting Stock Prices in Bursa Malaysia

Jurnal Intelek ◽

10.24191/ji.v14i2.241 ◽

2019 ◽

Vol 14 (2) ◽

pp. 240-250

Author(s):

Nor Hayati Shafii ◽

Nur Ezzati Dayana Mohd Ramli ◽

Rohana Alias ◽

Nur Fatihah Fauzi

Keyword(s):

Time Series ◽

Brownian Motion ◽

Stock Market ◽

Stock Prices ◽

Stock Exchange ◽

Investment Decisions ◽

Geometric Brownian Motion ◽

Fuzzy Time Series ◽

Good Information ◽

The Mean

Every country has its own stock market exchange, which is a platform to raise capital and is a place where shares of listed company are traded. Bursa Malaysia is a stock exchange of Malaysia and it is previously known as Kuala Lumpur Stock Exchange. All over the world, including Malaysia, it is common for investors or traders to face some loss due to wrong investment decisions. According to the conventional financial theory, there are so many reasons that can lead to bad investment decisions. One of them is confirmation bias where an investor has a preconceived notion about an investment without a good information and knowledge. In this paper, we study the best way to provide good information for investors in helping them make the right decisions and not to fall prey to this behavioral miscue. Two models for forecasting stock prices data are employed, namely, Fuzzy Time Series (FTS) and Geometric Brownian Motion (GBM). This study used a secondary data consisting of AirAsia Berhad daily stock prices for a duration of 20 weeks from January 2015 to May 2015. The 16-weeks data from January to April 2015 was used to forecast the stock prices for the 4-weeks of May 2015. The results showed that FTS has the lowest values of the Mean Absolute Percentage Error (MAPE) and the Mean Square Error (MSE), which are 1.11% and MYR20.0011, respectively. For comparison, for GBM, the MAPE is 1.53% and the MSE is MYR2 0.0017. The findings imply that the FTS model provides a more accurate forecast of stock prices. Keywords: Forecasted values, stock market, Fuzzy Time Series, Geometric Brownian Motion

Download Full-text