State Switching Issue and Application of Markov Switching Model

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2.3 State Switching Issue and Application of Markov Switching Model

In this part, some literatures about the issue of state switching and the evolution of Markov switching model will be reviewed.

Quandt (1958) begins time series modeling of regime shifts when he introduces the switching regression model. Goldfeld and Quandt (1973) extend the switching regression model and allow the regime shifts following Markov chain where the regime shifts is serially dependent. Their model is named Markov switching regression model. Based on Goldfeld and Quandt’s ideas, Hamilton (1989) establishes a similar approach but allows the regime shifts in dependent data and develops the Markov switching autoregressive model (MS-AR). In his model, the output mean growth rate depends on whether the economy is in a phase of expansion or in a phase of recession. He applies the technique to U.S. postwar data on real GNP. One possible outcome of maximum likelihood estimation of parameters might be the identification of long-term trends in the U.S. economy, which separates periods with faster growth from those with slower growth. His statistical estimates of the economy's growth state is very consistent with NBER dating of postwar recessions, and might be used as an alternative way for assigning business cycle dates.

The application of Markov regime switching model in identifying the state switching starts from Turner et al. (1989). They capture the regime shifts behavior in stock market using MS-AR model, and their study highlights the usefulness of Markov switching model allowing state shifts to happen in mean and variance and fitting the data adequately.

In Hamilton (1989)’s model, there is a discrete and unobservable variable named state variable or regime variable, which determines the state of the economy at each point of time. And the transition between states is governed by a constant-probability

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process which is not influenced by other macroeconomic forces.

Filardo (1994) extends the Markov-switching estimation method of Hamilton and incorporates the time-varying probabilities of transitions between the phases into Hamilton's model to examine differences in expansionary and contractionary phases of the business cycle. Filardo’s model is the time-varying transition probability Markov switching model (TVTP). The information variables he adds in the TVTP model as business-cycle predictors includes the Composite Index of Eleven Leading Indicators (CLI), the CLI's diffusion index, the Stock and Watson Experimental Index of Seven Leading Indicators, the term premium which is the 10-year less the 1-year constant maturity treasury interest rate, the Standard and Poor's Composite Stock Index, and the Federal Funds Rate. Using this technique and viewing monthly industrial production as a proxy for aggregate output, he presents the statistical significant empirical results that the output growth experiences one phase with a positive growth rate and another with a negative growth rate, and the former has higher persistence. He also finds in the TVTP specification, the Composite Index of Eleven Leading Indicators performs well as an information variable for the business cycle and turning points prediction.

Giot (2003) selects the time series data from January 3, 1992 to December 31, 2002 and uses a two-state Markov regime switching model applied to the observed daily VIX and VDAX implied volatility indices to find the volatility of both the U.S.

S&P100 index and German DAX index switched from a low-value state to a high-value state around the events of the Asian financial crisis in 1997. From July 1997, the volatility pattern reverses itself as both indices stay almost continuously in the high-volatility state for the next five years due to the successive events such as the Russian crisis and the LTCM collapse, the fall of the NASDAQ, the start of the bear market in the U.S. and Europe and the terrorists’ attacks on September 11, 2001.

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Moreover, market volatility has not reverted back to its initial low volatility state observed in the beginning of summer in 1997. He also shows that there has been a significant structural change in the asymmetric relationship between the stock index volatility and returns in both markets around the summer of 1997.

Ismail and Isa (2008) used a univariate two-regime Markov switching autoregressive model (MS-AR) to capture regime shifts behavior in both the mean and the variance and the nonlinear feature existed in Malaysian stock market in four monthly stock market indices of Bursa Malaysia, which are the Composite Index, the Industrial Index, the Financial Index and the Property index from 1974 to 2003. The MS-AR model is successful to capture the timing of regime shifts in the four indices and these regime shifts occurred because of global economic and financial crises such as the 1974 oil price shock, the 1987 stock market crash and the financial crisis in 1997. Therefore, they concluded that major economic events happened around the world have influence on the behavior of Malaysia stock market returns. According to the significant result of the likelihood ratio test, the use of nonlinear MS-AR(1) model is not only appropriate but rather superior to conventional linear AR(1) model.

Wasim and Bandi (2011) examine the regime switching behavior and seek for the existence of bull and bear regimes in the Indian stock market with daily data of two leading Indian stock market indices: NSE-Nifty and BSE-Sensex from February 7, 1997 to December 11, 2010. They use a two state Markov switching autoregressive model and adopt the appropriate lag as AR(2), and it predicts that the Indian stock market has a very high probability to remain under bull regime compared to bear regime. The results also identify the bear phases during all major global economic crises including recent US sub-prime (2008) and European debt crisis (2010).

Guo and Wohar (2006) examine multiple structural breaks in the mean level of market volatility measured by the VIX and VXO, and identify the dates of these mean

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shifts. The data series for VIX are from 1990 to 2003 and for VXO are from 1986 to 2003. They find evidence which indicates three distinct periods existed in the evolution of volatility index, including a pre-1992 period, a period from 1992 to 1997, and a post-1997 period. The average volatility and its standard deviation were lowest during the period from 1992 to 1997, and the means of market volatility proxied by the VIX and VXO are not stable during the sample periods. Their findings provide statistical evidence consistent with the idea that the average level of market volatility changes infrequently but significantly over time.

Romo (2012) presents a regime-switching framework to characterize the evolution of the VIX index that postulates the existence of two possible regimes: high volatility and low volatility, and assumes that the state variable governing the transition between the two regimes follows a Markov process. The specification accounts for deviations from normality due to the news about the economy or financial crisis, and exhibits persistent changes of the VIX index level.

To sum up, the issue about state switching in financial markets or economic business cycles motivates many researchers to study, and there are some literatures focusing on the state switching in VIX index. Moreover, this paper finds that Markov switching model is a common methodology using to study the issue of state shift.

Nevertheless, little literatures investigate the effects of TVTP model on identifying state switching in the VIX index. Therefore, this paper will use the TVTP model and incorporate some appropriate indicators generalized from past literatures to study the dynamics of VIX index, and investigate whether the TVTP model can also perform well in identifying state shifts. Finally, generalizing some useful indicators to help understanding the changes of VIX index is one of the purposes in this paper.

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