A Bayesian Markov Regime-Switching Model of Stock Return Volatility: Evidence from the Moroccan All Shares Index
This repository includes the code used in one of the master's projects "A Bayesian Markov Regime-Switching Model of Stock Return Volatility: Evidence from the Moroccan All Shares Index" by Khalil Belghouat.
In this project, a Bayesian Markov regime-switching approach is followed in order to describe and predict the volatility of the Moroccan All Shares Index returns.
The R programming language, version 4.1.1, and its statistical and machine learning libraries were used to build all applied models. The R script packages.R in the packages folder installs and loads all necessary R packages.
All operations, from data preprocessing to model estimation, were carried out on the Google Colaboratory platform.
So far in the literature, two models have been developed that capture this time-varying autocorrelated volatility process: the stochastic volatility model and that of GARCH (Generalized Autoregressive Conditional Heterscedasticity). In the stochastic volatility model, the variance is modeled as a latent component that follows a stochastic process. While GARCH models define time-varying variance as a deterministic function of past squared innovations and lagged conditional variances. Multiple extensions of GARCH's sedastic function have been proposed to capture additional stylized facts observed in financial and economic time series, such as non-linearities, asymmetries, and long memory properties. GARCH-type models are, until now, widely used to model various financial phenomena such as risk management of futures contracts, estimation of the volatility of yield spreads, and portfolio optimization. However, various studies have shown that one of the most problematic features of these models is the excessive persistence attributed to the volatility of financial variables. This suggests that conditional variance shocks that arose in the distant past continue to have sizeable effects on the present value. This long-lasting persistence is in fact the reason attributed to the relatively poor forecasts of the GARCH models. A number of researchers have observed that the high persistence of GARCH models and therefore poor forecasting performance could be related to structural changes in the data generating process. And pointed out that GARCH models may be limited in their ability to model the volatility of financial time series if structural breaks, caused by some dramatic events such as financial crises, recessions or changes in government policies, are present. Therefore, Markov-switching GARCH models, as introduced by Hamilton and several other econometers, were advanced and found to be useful in solving this problem. These models allow the conditional volatility process to switch between a discrete number of states, the transitions between states being governed by a Markov chain of hidden and finite order. More often than not, such a structure has been found to improve the forecasting of volatility and risk. The Markov regime-switching model and its variants have found application in the analysis of the fluctuation of interest rates and exchange rates, forecasting business cycles, and portfolio management for hedging against financial risks. In this paper, we conduct an empirical analysis of the MASI index using the Bayesian Markov regime-switching GJR-GARCH model. We also study its forecasting performance in estimating VaR.
The parameter estimates indicate that the evolution of the volatility process is heterogeneous between the two regimes. Indeed, we first notice that the two regimes report different levels of unconditional volatility: 10.69 % in the first regime and 26.70 % in the second. As well as different reactions to past negative returns: 0.2171 versus 0.3364. In addition, the persistence of volatility in the two regimes is different. The first regime yields 0.65835 while the second regime yields 0.7333. In summary, the first regime is characterized by: (i) low unconditional volatility, (ii) lower volatility response to past negative returns, and (iii) relatively low persistence of the volatility process. Differently, the second regime is characterized by: (i) high unconditional volatility, (ii) a higher volatility response to past negative returns, and (iii) relatively high persistence of the volatility process. The posterior mean stable probabilities indicate that the probability of being in the first regime is 63.99 %, while being in the second is 36.01 %. Regarding the subsequent distribution of unconditional volatility in each regime. The first regime registers, on average, about 7.34 % per annum. While the second registers 54.30 %. The Bayesian approach provides 95% confidence intervals which are respectively [4.08 %, 14.60 %] and [24.78 %, 134.60 %]. Additionally, the results from backtesting VaR at 5% risk confirm that the two-regime Bayesian Markov-switching GARCH model outperforms its single-regime counterpart. This study, therefore, provides an empirical evidence supporting the ability of the latter to improve MASI’s volatility forecasting.
The data, a financial time series, is organized in a table containing 7 columns and 2501 rows. The first column contains the date, the following 4 columns contain the closing, opening, high and low prices of the MASI index, while the remaining columns contain the index's trading volumes and daily variations.
The two-regime Markov-switching GARCH model and its single-regime counterpart were both built using the MSGARCH package. The estimation procedure was done via Bayesian Markov chain Monte Carlo (MCMC) technique generating draws from the posterior distribution. These draws are used to characterize the distribution of the parameters.