CBN JAS Article: Markov Regime-Switching Autoregressive Model of Stock Market Returns in Nigeria

CBN Journal of Applied Statistics Vol. 11 No. 2 (December 2020)

65-83

Markov Regime-Switching Autoregressive Model of Stock Market Returns in Nigeria

Oluwasegun A. Adejumo,1 Seno Albert1, and Omorogbe J. Asemota2

This study is designed to model and forecast Nigeria's stock market using the All Share Index (ASI) as a proxy. By employing the Markov regime-switching autoregressive (MS-AR) model with data from April 2005 to September 2019, the study analyzes the stock market volatility in three distinct regimes (accumulation or distribution - regime 1; big-move - regime 2; and excess or panic phases - regime 3) of the bull and bear periods. Six MS-AR candidate models are estimated and based on the minimum AIC value, MS(3)-AR(2) is returned as the optimal model among the six candidate models. The MS(3)-AR(2) analysis provides evidence of regime-switching behaviour in the stock market. The study also shows that only extreme events can switch the ASI returns from regime 1 to regime 2 and to regime 3, or vice versa. It further specifies an average duration period of 9, 3 and 4 weeks for the accumu- lation/distribution, big-move and excess/panic regimes respectively which is an evidence of favorable market for investors to trade. Based on Root Mean Square Error and Mean Absolute Error, the fitted MS-AR model is adjudged the most appropriate ASI returns forecasting model. The study recommends investments in stock across the regimes that are switching between accumulation/distribution and big-move phases for promising returns.

Keywords: All share index, Markov process, regime switching, stock market, volatility

JEL Classification: C13, C22, C52, C58

DOI: 10.33429/Cjas.11220.3/8

1. Introduction

The modelling of volatility and the forecast of financial markets has attracted the attention of investment analysts, exchange and security analysts and risk managers (Poon & Granger, 2003). While modelling the stock market volatility, most financial analysts are specifically interested in obtaining worthy estimates of the conditional variance (a distinctive feature of volatility) in order to enhance portfolio shares or its risk management. Over the years, a series of models have been established to evaluate the conditional volatility of stock markets. The Engle (1982) generalized autoregressive conditional heteroscedastic (GARCH) models are

• Department of Statistics, University of Abuja. Corresponding Author: [e-mail]
  2Research Department, National Institute for Legislative and Democratic Studies, Abuja.

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Markov Regime-Switching Autoregressive Model of Stock Market
Returns in Nigeria	Adejumo et al.

the commonly used models for volatility forecast in stock markets. Thus, accurate measure and forecast of volatility are applied to asset-pricing models as a simple risk measure as well as derivative pricing theories and trading (Andersen & Bollerslev, 1998; Barndorff-Nielsen & Shephard, 2002). It must be pointed out that prior to the introduction of conditional volatility models, there were the Box-Jenkins (1976) models, specifically, the Autoregressive Integrated Moving Average (ARIMA) models. However, ARIMA models are based on the inaccurate assumptions of constant variance for the time series of stock market returns (Goldfeld

• Quandt, 1976; Hamilton, 1989; Shamsuddeen et al., 2015). This shortcoming of ARIMA models has led to the emergence of various types of Engle-like models (examples are Tule, Dogo & Uzonwanne, 2018; Maqsood et al. 2017; Yaya, Akinlana & Shittu, 2016; Bala
• Asemota 2013; Wang, 2006; Longmore-Robinson, 2004; Brooks & Burke, 1998; Tse & Tsui 1997; McKenzie, 1997; Jorion, 1995; Pesaran-Robinson, 1993; Lastrapes, 1989; Hsieh, 1989; Taylor, 1987; Milhoj, 1987; Meese & Rogoff, 1983). These new methods adopted var- ious extensions of the GARCH models like the GARCH-M, IGARCH, EGARCH, TGARCH and PARCH which take into consideration the possibility of variations in the stock market.

A further example of stock market volatility models is the regime-switching model, which was developed by Hamilton (1989). This model has become very prevalent in applied re- search. Regime-switching model has gained the attention of many scholars like Calvet and Fisher (2004), Masoud, Hamidreza and Safael (2012), Beckmann and Czudaj (2013), Lux, Morales-Arias and Sattarho (2014), Nguyen and Walid (2014), Aliyu and Wambai (2018). They have documented the distinctiveness and forecasting capabilities of Markov regime- switching against the commonly used GARCH models. Additionally, the Markov regime- switching method of volatility analysis has recorded some advantages over time.

According to Dow theory, it is recognized that the bull and bear markets of stock market returns are primarily and distinctly characterized by three regimes or phases: the bull market has the accumulation, big-move (public participation) and excess regimes while the bear market has the distribution, big-move and panic (despair) regimes (Adam, 2020), Markov regime-switching method has proven to be more reliable in this aspect in that it models all observed structures of the stock market returns. The observed eras characterized in the series such as bull and bear markets as well as interventions can be modeled in different regimes of the Markov regime-switching model. An innovative feature of the Markov regime-switching

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CBN Journal of Applied Statistics Vol. 11 No. 2 (December 2020)

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is that the mechanism of switching is determined by an unobservable regime variable which follows first order Markov-Chain (Hamilton, 1989). Interestingly, while the application of the Markov regime-switching method has increased in other parts of the world and despite the attractiveness and unique features of the model in analyzing financial market volatility, yet to the best of our knowledge, no evidence of Markov three regimes-switching model have been used to model the three distinct phases of Nigeria's stock market eras (bull or bear). Close studies are Aliyu and Wambai (2018), and Yahaya and Adeoye (2020). Both studies examined the volatility of Nigeria's stock market using Markov two regime-switching to model the bull and bear markets. However, both studies did not consider the three distinct phases (the accumulation or distribution, big-move and excess or panic regimes) of the stock market eras (bull and bear) as identified by Dow theory and the investors. As described by Adam (2020), the three distinct phases serve as indicators for investors to guide in allocation of stocks, also to know when to invest and sell. Hence, it is against this background that this study seeks to analyze Nigeria's stock market volatility in three distinct phases namely: the accumulation or distribution, big-move and excess or panic regimes.

This study models Nigeria's stock market returns using the Markov three-regime switching model. Specifically, the study analyzes the Nigeria stock market volatility in the accumulation or distribution, big-move and excess or panic regimes; estimates the transition probabilities of each of the regimes; estimates the expected durations of each of the regimes; and to forecast Nigeria's stock market volatility.

The rest of this paper is ordered as follows. Section 2 provides a brief description of theoretical and empirical literatures, Section 3 presents the research methodologies. Data analysis and results are discussed in Section 4. Section 5 provides conclusion and policy recommen- dations.

2. Literature Review

2.1 Theoretical Literature

The application of regime switching models has ranged over wide areas of research, such as modeling the swings in exchange rate, inflation rate, interest rate, stock prices, and the changes in government policy. The modeling of swings, known as regime switching in the financial market, started far back in 1958 when Quandt introduced the switching regression model (Aliyu & Wambai, 2018). Subsequently, Goldfeld and Quandt (1976) extended the

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Markov Regime-Switching Autoregressive Model of Stock Market
Returns in Nigeria	Adejumo et al.

switching regression model to tolerate the shifting of regimes to follow Markov process. Afterwards, Hamilton (1989 and 1990) built on Goldfeld and Quandt (1976) studies. Hamil- ton examined the shifts of regimes in dependent observations and developed the branded Markov regime-switching model. The Markov regime-switching model was developed to arrest swift shifts in time-series with the assumption that regime is an unobservable stochastic process, that is movement within regimes are distinct. Additionally, more than accommodating the regimes, frequently, the identified regimes, using econometric procedure are intrinsically linked to different eras in policy, regulation and other variations. Also, the Markov regime-switching model estimates the transition probabilities and the expected duration of the regimes.

2.2 Empirical Literature

Masoud et al. (2012) assessed the dynamic behaviors of Iran's exchange rate using the Markov regime-switching model and other five different modeling approaches. The six models were compared based on their performances (using their AIC and BIC values) in capturing the dynamic behavior of exchange rate, their results identified the Markov regime-switching model as the best fit model among the six modeling approaches to evaluate the dynamic behavior of Iran's exchange rate. They observed a dramatic jump in the early part of 2002 which coincided with the change in exchange rate regime. Also, Beckmann and Czudaj (2013) examined the inter-relationship between oil prices and dollar exchange rates such as the nonlinear adjustment dynamics, using a Markov-switching vector error correction model. Their results showed that the error-correction of the series short-run follows Markov regime- switching, entrenched within a long-run linear cointegrating relationship. In the same way, Zhu-Zhu (2013) examined the surplus returns of the US stock market. They modeled the stock market returns using 15 financial variables as predictors of the surplus returns. They utilized the regime-switching combination process to model uncertainty in 3-dimensions. Their finding depicted 2-regimes that were connected to the US business cycle. The depreciation regime was connected to economic growth while the appreciation regime was related to economic decline, which implies that surplus returns are more predictable during economic recession and less predictable when the economy booms.

Moreover, Nguyen and Walid (2014) investigated the dynamic relationships between stock market and exchange rate returns of Brazil, China, India, Russia and South-Africa. They

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utilized the Markov regime-switching model. Their findings revealed that the stock market returns of these countries evolved based on low variance and high variance regimes. Also, the Markov regime-switching models provide evidence that stock markets in these countries have an effect on exchange rates during both bear and bull eras. Lux et al. (2015) applied the markov-switching multifractal model and the GARCH-type models to estimate oil price volatility. Based on the superior predictive ability (SPA) test and six loss functions, their forecasting performance were evaluated and compared at short and long horizons. The empirical results revealed that the new Markov-switching multifractal model came out as the model that cannot be outperformed by other models across the forecasting horizons and subsam- ples. Aikaterini (2016) investigated the forecast power of Markov regime-switching models for the returns of Canadian, UK and US daily stock markets. Aikaterini's findings revealed that the regime's transition probabilities were very small, which implies the probability of regime changes is low. Hence, Aikaterini's model is a single regime model since the transition probabilities are very low. The expected duration of regimes staying in the appreciation era is high compared to the depreciation era, however the impacts were significantly strong in the depreciation era.

Recently, Aliyu and Wambai (2018) examined the spillover volatility between the Nigeria's stock market and exchange rate using the Markov regime-switching model. Their approach tolerated regime-shift in the series' mean and variance. The results revealed that the exchange rate and stock market returns were not normally distributed and had ARCH effects and unit root. Also, the evidence from two-regimes estimation established higher transition probabilities in the depreciation era compared to the appreciation era. Afterwards, they studied the spillover volatility between the stock market and exchange rate. Moreover, Korkpoe and Howard (2019) examined the volatility model for Botswana, Ghana, Kenya and Nigeria equity markets using the Markov regime-switching Bayesian method. They adopted Markov two regime-switching models to select the best models that describe the markets' returns, they found heterogeneity in the evolution of volatility across the equity markets and the Markov two regime-switching described better the heteroscedastic returns generating pro- cesses. Also, Yahaya and Adeoye (2020) examined the Nigeria's stock market volatility by comparing different lags of Markov two regime-switching models. They found that over the years, investors had been exposed to certain risks and the financial crisis among others was the major cause of stock market volatility. However, while the literature on Markov

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