Multi-Scaling Analysis of the S&P500 under Different Regimes in Wavelet Domain

Multi-Scaling Analysis of the S&P500 under Different Regimes in Wavelet Domain

Salim Lahmiri
Copyright: © 2014 |Pages: 13
DOI: 10.4018/ijsds.2014040104
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In this article, the authors investigate the multi-scale structure of the S&P500 minute-by-minute time series. The authors attempt to find the answer to the following question: Are upward and downward regimes in the S&P500 time series exhibit different long-range power-law correlations? To answer this question, the authors apply the discrete wavelet transform (DWT) to the original time series for de-noising purpose. Then, the authors apply the generalized Hurst exponent (GHE) to the de-noised data to characterize the multi-scaling complexity of the signal (time series) under each regime and using different q-order moments. The authors found that S&P500 intra-day time series show long-range power-law correlations. In addition, this behavior varies depending on the stock market regime. This finding should be taken into account in active investment management.
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1. Introduction

During the last two decades, scholars have come to rely upon various types of statistical and intelligent systems to forecast financial markets (Davalos et al., 2009; Sun, 2010; Joseph & Mazouz, 2010; Hammami & Boujelbene, 2012; Lai & Joseph, 2012; Strang, 2012, Lahmiri, 2013). And, lately the scaling concept which is widely applied in physics receives an increasing attention in finance to find the existence of scaling laws (Dimatteo et al., 2005; Qi et al., 2011; Domino, 2011). The goal is to search for patterns that are repeated at different time scales in stock prices. Therefore, understanding their temporal dynamics is important to assess the potential impacts of their variations on wealth; and consequently to determine the optimal investment strategy. Investigating the dynamic behavior of stock prices has been an attractive topic in the literature during a relatively long time span. In particular, multi-scaling processes have been used in many studies to account for the time-scale dependence of the statistical properties of financial time series. For instance, it was found that stock prices reveal different properties such long-term correlation or memory dependence (Dimatteo et al., 2005), and fractals/multifractals (Qi et al., 2011; Domino, 2011). Indeed, many empirical studies are concerned with the market multifractality formation, and it is found that there are two major sources of it: fat-tailed probability distribution and nonlinear temporal correlation (Kwapien et al., 2005; Du & Ning, 2008).

In recent years, the multifractal analysis has become an important technique to examine the intermittency observed in financial time series; including stock market prices (Alvarez-Ramirez et al.,2008; Suárez-García & Gómez-Ullate, 2008; Mariani et al., 2010; Wang et al., 2010a; Alvarez-Ramirez et al., 2012; Ma et al., 2013; Reboredo et al., 2013), trading volume (Bolgorian & Raei, 2011, Alvarez-Ramírez & Rodríguez, 2012; Yuan et al., 2012; Wang et al., 2013), and volatility (Wang et al., 2010b; Lin et al., 2011), commodities (He et al., 2010; Siqueira et al., 2010; Kim et al., 2011; Wang et al., 2011a, 2011b, Lu et al., 2013; Liu, 2014), and exchange rate (Norouzzadeh & Rahmani, 2006; Abounoori et al., 2012; Cao et al., 2012). A review of recent works on multifractal analysis of stock market follows.

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