A Study of Nonlinear Dynamics in Equity Market Index: Evidence from Turkey

(ProQuest: ... denotes formulae omitted.)1. IntroductionSuccessful modeling of asset prices is very crucial for investors. It has been shown in a vast number of studies that asset prices exhibit non-linear structures (Hsieh, 1991; Lim and Brooks, 2011; Cariani, 2014). The non-linear dynamics in financial assets are of critical concern because they are inconsistent with market efficiency. In addition, using a linear model to price securities may result in an incorrect asset price and exploitable profit opportunities. Most of the recent empirical literature has focused mainly on discovering whether financial markets are characterized by non-linear behaviors. However, understanding the nature and function of non-linear dependence driving the market price has become increasingly more important in implementing a successful and accurate forecast leading to a profitable trade.The purpose of this study is to examine whether the Istanbul Stock Exchange (ISE) stock markets are governed by non-linear dynamics. The popularity of the ISE equity index has been increasing in proportion to the rapidly growing economy of Turkey. Approximately 60 percent of the securities traded in the ISE are owned by foreign investors. Therefore, the equity market in Turkey has become more important for global investors as well.This study aims to answer two important questions about the ISE index: First, is there a persistent dependency in the equities traded in the Istanbul Stock Exchange? Second, if the dependency persists in the ISE equity index, what is the form of the dependency? In other words, is the dependence due to linear, non-linear, or chaos dynamics? This paper evaluates the non-linear dynamics of the ISE 100 index using rich variety techniques, including the BDS test, the chaos test, the Markov Chain test, the time reversibility test, the and duration dependence test.There have been an extensive number of studies carried out to reveal non-linear structures in financial time series. In addition, some studies specifically analyzed the ISE for non-linear dependence and chaotic structures (Ozer and Ertokatli, 2010; Ozkaya and Ozkaya, 2012; Odabasi et.al., 2004). This study will make significant contributions to the current literature because none of the studies were as systematic and comprehensive as this study in analyzing dependence issues step by step. In the first step, a BDS test is applied to the log ISE index return series to diagnose for any form of dependency1. The BDS result reports evidence of dependence in the ISE returns. When several ARIMA models are fitted into the ISE time series and the residuals are tested again for dependence, dependence continues to persist. In the next step, some nonlinear models are employed to further investigate whether nonlinearity could possibly be one of the forms of dependency. When the ISE return is modelled as one significant GARCH term and one threshold order, the BDS test fails to reject the presence of dependency. Further K-map and Z-map analysis shows that the dependency in the ISE return is not caused by erratic and chaotic behavior in the Turkish equity market. A Markov chain test shows that the dependence is not a short-term dependence. A time reversibility test further provides supporting evidence that the dependence in the ISE 100 index is nonlinear and the non-linearity comes from the asymmetric innovations. Lastly, in accordance with the duration dependence test, the non-linear dependence evident in the ISE return is not consistent with the characteristic of a rational bubble.The remainder of the paper is organized as follows. In the next section, we review the literature for nonlinear dependency in security prices. This section also provides a comprehensive review of stock returns behavior in Turkey. Section 3 describes our data and summarizes the descriptive statistics of the ISE 100 index and three macro-economic variables including Turkish Lira/$ exchange rate, interbank overnight rate, and inflation in Turkey. …