Markov Switching GARCH Models Research Articles

Analyzing Composite Stock Price Index Volatility in Response to Changes in Data Structure Using Bayesian Markov-Switching GARCH

Rapid economic growth was observed to have motivated economic actors and investors to maximize business performance using different methods. An example of these are stocks or shares securities showing that a person or entity has a stake in a company. Investors are primarily drawn to stocks due to their potential for substantial profits closely tied to the volatility in the stock market. The prevalence of this volatility has long been addressed using the ARCH/GARCH model, but it is not ideal for datasets experiencing structural changes. Therefore, a model was developed using the Bayesian Markov-switching GARCH approach to effectively capture the heteroscedastic component and structural changes in data and mitigate certain limitations, especially those associated with a small sample size. This study adopted the composite stock price index (CSI) data from March 2020 to April 2021 to model and understand the volatility. The results showed that the Bayesian Markov-switching GARCH model with the most negligible variance provided the best fit. It was also discovered that a more minor error variance corresponded to lower data volatility. Moreover, the concept of value at risk was used to assess the investment risk based on the criterion that a decrease in the CSI investments led to a reduction in the level of risk faced by the investors.

Number of Volatility Regimes in the Muscat Securities Market Index in Oman Using Markov-Switching GARCH Models

The predominant approach for studying volatility is through various GARCH specifications, which are widely utilized in model-based analyses. This study focuses on assessing the predictive performance of specific GARCH models, particularly the Markov-Switching GARCH (MS-GARCH). The primary objective is to determine the optimal number of regimes within the MS-GARCH framework that effectively captures the conditional variance of the Muscat Securities Market Index (MSMI). To achieve this, we employ the Akaike Information Criterion (AIC) to compare different MS-GARCH models, estimated via Maximum Likelihood Estimation (MLE). Our findings indicate that the chosen models consistently exhibit at least two regimes across various GARCH specifications. Furthermore, a validation using the Value at Risk (VaR) confirms the accuracy of volatility forecasts generated by the selected models.

The functional central limit theorem for Markov-switching GARCH model

In this paper we consider the Markov Switching GARCH model suggested by Haas, Mittnik, and Paolella(2004). We show under proper assumptions that the functional central limit theorems hold for the process, the square of the process, and regime variances. The functional central limit theorem for a linear combination of regime variances is also obtained.

Supplementary Material: Forecasting VaR and ES through Markov Switching GARCH Models: Does the Specification Matter?

Supplementary Material: Forecasting VaR and ES through Markov Switching GARCH Models: Does the Specification Matter?

The impact of news about COVID-19 on the dynamics of the Russian stock market

Subject. The article addresses the Russian stock market during the COVID-19 pandemic. Objectives. The study aims at empirical substantiation of the influence of tonality of news about COVID-19 published in official sources and social networks, on the Russian stock market. Methods. We employ a set of methods and procedures to assess the sentiment of downloaded news texts and tweets and to model the dynamics of general and sectoral stock indices (bag-of-words method, Markov-switching GARCH models, evaluation of text tonality using EcSentiThemeLex dictionary). Results. The paper reveals the influence of the tone of coverage of events related to COVID-19 pandemic in news sources and social networks on changes in stock prices of Russian companies. We substantiated the existence of industry specifics in terms of the degree of influence of the tone of news and tweets on stock price dynamics. The findings can be used by investors and issuers to model and predict changes in securities prices, and complement the theory, by underpinning the significance of the tonality of messages in the news and social networks for the dynamics of the Russian stock market. Conclusions. Changes in the emotional tonality of news and social media posts about COVID-19 impacted the stock market of the Russian Federation. The models enabled to prove that in a volatile economy, not only the information published about the coronavirus is significant for the stock market, but also the dynamics of the number of cases.

Indian start-ups going public: return and volatility of stocks during bear and bull regimes

PurposeStart-ups are successful in receiving valuation in billions of US dollars prior to initial public offering (IPO). However, to sustain higher valuation, the stocks need to perform consistently after the IPO. Short-run stock performance of India-based start-ups during the first year of IPO listing from March 2021 to March 2022 is analysed.Design/methodology/approachThe paper deals with the new generation start-ups' stock performance in emerging market in terms of total and abnormal return generated in comparison to the market (NIFTY-200). Further, the volatility of returns during bear and bull regimes is analysed through a family of Markov-switching GARCH models using both normal and skewed distributions.FindingsThe results suggest that start-up stocks are more volatile during bear regime than in the bull run in market-based economies where price limit policy does not apply. Besides, the cumulative abnormal return over the market return was lower for majority of start-up IPO stocks.Social implicationsThough negative returns of the start-up stocks during the first year of IPO need not be surprising, higher volatility during bear regime is a matter of concern as it could severely impact retail investors and founders. The results hold implication for IPO regulation in emerging markets and for retail investors desirous of investing in start-up stocks.Originality/valueVolatility of return is examined using a state-space model during the first year of the start-up IPO listing. The study contributes to the emerging market IPO literature by examining IPO performance in market-based economy. Previous IPO performance studies in emerging markets are predominantly based on ecosystems where start-ups are subjected to price limit policy, and it does not reflect the true nature of IPO performance across emerging markets.

How Vulnerable is the Turkish Stock Market to the Credit Default Swap? Evidence from the Markov Switching GARCH Model

How Vulnerable is the Turkish Stock Market to the Credit Default Swap? Evidence from the Markov Switching GARCH Model

Estimating MS-BLGARCH Models Using Recursive Method

In this paper a new class of models is proposed for modeling nonlinear and stationary time series. This new class of models is referred to as the Markov-switching bilinear GARCH (MS-BLGARCH) models. In these models, the parameters are allowed to depend on an unobservable time-homogeneous and stationary Markov chain with finite state space. The statistical inference for these models is rather difficult due to the dependence on the whole regime path. We propose a recursive algorithm for parameter estimation in MS − BLGARCH. The proposed method is useful for long time series as well as for data available in real time. The main idea is to use the maximum likelihood estimation (MLE) method and from this develop a recursive Expectation-Maximization (EM) algorithm.

Bayesian Nonparametric Panel Markov-Switching GARCH Models

This article proposes Bayesian nonparametric inference for panel Markov-switching GARCH models. The model incorporates series-specific hidden Markov chain processes that drive the GARCH parameters. To cope with the high-dimensionality of the parameter space, the article assumes soft parameter pooling through a hierarchical prior distribution and introduces cross sectional clustering through a Bayesian nonparametric prior distribution. An MCMC posterior approximation algorithm is developed and its efficiency is studied in simulations under alternative settings. An empirical application to financial returns data in the United States is offered with a portfolio performance exercise based on forecasts. A comparison shows that the Bayesian nonparametric panel Markov-switching GARCH model provides good forecasting performances and economic gains in optimal asset allocation.

The Bitcoin Halving Cycle Volatility Dynamics and Safe Haven-Hedge Properties: A MSGARCH Approach

This paper introduces a unique perspective towards Bitcoin safe haven and hedge properties through the Bitcoin halving cycle. The Bitcoin halving cycle suggests that Bitcoin price movement follows specific sequences, and Bitcoin price movement is independent of other assets. This has significant implications for Bitcoin properties, encompassing its risk profile, volatility dynamics, safe haven properties, and hedge properties. Bitcoin’s institutional and industrial adoption gained traction in 2021, while recent studies suggest that gold lost its safe haven properties against the S&P500 in 2021 amid signs of funds flowing out of gold into Bitcoin. Amid multiple forces at play (COVID-19, halving cycle, institutional adoption), the potential existence of regime changes should be considered when examining volatility dynamics. Therefore, the objective of this study is twofold. The first objective is to examine gold and Bitcoin safe haven and hedge properties against three US stock indices before and after the stock market selloff in March 2020. The second objective is to examine the potential regime changes and the symmetric properties of the Bitcoin volatility profile during the halving cycle. The Markov Switching GARCH model was used in this study to elucidate regime changes in the GARCH volatility dynamics of Bitcoin and its halving cycle. Results show that gold did not exhibit safe haven and hedge properties against three US stock indices after the COVID-19 outbreak, while Bitcoin did not exhibit safe haven or hedge properties against the US stock market indices before or after the COVID-19 pandemic market crash. Furthermore, this study also found that the regime changes are associated with low and high volatility periods rather than specific stages of a Bitcoin halving cycle and are asymmetric. Bitcoin may yet exhibit safe haven and hedge properties as, at the time of writing, these properties may manifest through sustained adoption growth.

Stock Market Liquidity during Periods of Distress and its Implications: Evidence from International Financial Markets

Traditional market pricing models assume frictionless markets with abundant liquidity. This traditional models also incorporate stock market liquidity as an exogenous cost. However, this paradigm has many shortcomings due to its inability to explain some of the problems associated with security market illiquidity. The aim of this study was to explore the concept of stock market liquidity during periods of financial distress. A Markov switching GARCH model was used to investigate market liquidity in the CAC 40, DAX, JSE, Nasdaq Index and the Nikkei-225 during the 2007-2008 financial crisis and the Covid-19 pandemic. The sample period was January 1, 2020 to December 31, 2021 and December 1, 2007 to June 30, 2009. From the findings, some financial markets where still liquid despite the financial crisis with the exception of the Nasdaq index. Conversely, all the financial markets under consideration displayed strong illiquidity during the covid-19 pandemic. In essence, the level of market depth has significantly decreased from the financial crisis to the covid-19 pandemic which may be attributed to increasing margin requirements and information asymmetry as well as price restrictions. There is an urgent need for regulatory authorities to review some of the trading regulations during financial distress.

An analysis of East African tea crop prices using the MCMC approach to estimate volatility and forecast the in-sample value-at-risk

In Eastern African countries, agriculture contributes significantly to the national economy. However, the prices of the essential crops fluctuate considerably due to climate change, the economic crisis, and surging food and fuel costs in the region. This paper aims to capture the dynamic volatility of tea crop prices, one of the region's most important cash crops. We applied the Markov-switching GARCH (MS-GARCH)-type specifications with different scedastic functions and error distributions to estimate volatility and forecast the in-sample value-at-risk (VaR) of tea price returns. This paper analyses monthly tea auction prices (i.e., Mombasa auction) in USD from January 1980 to June 2022. The parameters of the MS-GARCH model are estimated in a Bayesian framework via the MCMC approach. The findings evidenced that the EGARCH skewed Student-t model with three regimes was superior in estimating volatility. In terms of VaR evaluation, there is no superior method, but considering scedastic functions, fat tails, asymmetry, and regime switching is more effective. To manage volatility and risk in the East African tea sector, investors should consider regime switching GARCH models.

The network of commodity risk

In this paper, we investigate the interconnections among and within the Energy, Agricultural, and Metal commodities, operating in a risk management framework with a twofold goal. First, we estimate the Value-at-Risk (VaR) employing GARCH and Markov-switching GARCH models with different error term distributions. The use of such models allows us to take into account well-known stylized facts shown in the time series of commodities as well as possible regime changes in their conditional variance dynamics. We rely on backtesting procedures to select the best model for each commodity. Second, we estimate the sparse Gaussian Graphical model of commodities exploiting the Graphical LASSO (GLASSO) methodology to detect the most relevant conditional dependence structure among and within the sectors. A novel feature of our framework is that GLASSO estimation is achieved exploring the precision matrix of the multivariate Gaussian distribution obtained using a Gaussian copula with marginals given by the residuals of the aforementioned selected models. We apply our approach to the sample of twenty-four series of commodity futures prices over the years 2005–2022. We find that Soybean Oil, Cotton, and Coffee represent the major sources of propagation of financial distress in commodity markets while Gold, Natural Gas UK, and Heating Oil are depicted as safe-haven commodities. The impact of Covid-19 is reflected in increased heterogeneity, as captured by the strongest relationships between commodities belonging to the same commodity sector and by weakened inter-sectorial connections. This finding suggests that connectedness does not always increase in response to crisis events.

Detecting Financial Crisis in Nigerian Capital Markets Using Markov Switching Generalized Autoregressive Conditional Heteroscedasticity

Financial crisis is often a thing of major concern in many countries. It has led so many experts to be interested in identifying the causes and the general statistical pattern associated with them. Based on the causes, pattern and characteristics exhibited by the financial crisis, it is expected that experts should be able to develop a model to detect the financial crisis. The financial crisis in Nigerian stock markets can be observed as a macro-economic indicator. Therefore, the aim of this study is to develop a model using a macro-economic indicator (All share index) that can explain the combined nature of volatility and switching characteristics associated with Nigerian capital markets. The data used for the study is the All Share Index (ASI) of Nigerian stock markets spanned from the month of January, 1985 – January 2021. The series is fitted to conditionally compound monthly return and the result obtained was used in fitting volatility and Markov switching GARCH models. Based on the AIC and SIC, the EGARCH model was found to be the appropriate model for modeling Nigerian stock markets. However, structural changes in the model were tested using the Chow breakpoint test. The results obtained based on the test of structural changes, found that there was a structural change in the real exchange rate in the period between February 1998 and July 2010. For MSGARCH (3,1.1), the results show that the conditional probability of surviving in the high volatility state in the next period is 0.984. Also, the conditional probability of surviving in a medium volatility state in the next period is 0.617 and the conditional probability of surviving in a low volatility state in the next period is 0.410. The results showed that the MSGARCH (3,1,1) model could explain that the period from February 1997 until July 2020 had probability values of more than 0.6. This reveals high volatility confirming the occurrence of a crisis

On the volatility of cryptocurrencies

We perform a large-scale analysis to evaluate the performance of traditional and Markov-switching GARCH models for the volatility of 292 cryptocurrencies. For each cryptocurrency, we estimate a total of 27 alternative GARCH specifications. We consider models that allow up to three different regimes. First, the models are compared in terms of goodness-of-fit using the Deviance Information Criterion and the Bayesian Predictive Information Criterion. Next, we evaluate the ability of the models in forecasting one-day ahead conditional volatility and Value-at-Risk. The results indicate that for a wide range of cryptocurrencies, time-varying models outperform traditional ones.

Performance of a Novel Hybrid Model Through Simulation and Historical Financial Data

It is thoroughly acknowledged that the historical financial time series is not linear, exhibits structural changes, and is volatile. It has been noticed in the current literature that because of the existence of structural breaks in the historical time series, the GARCH family models provide misleading results and poor forecasts. Thus, it is unavoidable to incorporate models with nonlinearity in the conditional mean and conditional variance to capture volatility dynamics more precisely than the existing models. Therefore, inspiring in this matter, this study proposes a novel hybrid model of exponential autoregressive (ExpAR) with a Markov-switching GARCH (MSGARCH) model. This study also examines volatility dynamics and performances through simulation and real-world financial data. Moreover, this study investigates downside risk management performances using 5% VaR (Value-at-Risk) back-testing. The empirical findings showed that the proposed model outperforms the benchmark model for both simulation and real-world time series data. The VaR results also showed that the proposed model captures downside risk more meticulously than the benchmark model.

Empirical Pricing Kernel and Option-Implied Risk Aversion in China 50 ETF

ABSTRACT Based on an analysis of the China 50 ETF options and their underlying assets, we measure the empirical pricing kernel and implied risk aversion. By employing a Markov-switching GARCH model, the estimated results show a monotonically decreasing pricing kernel under a high-volatility regime and a U-shaped pricing kernel under a low-volatility regime. The implied risk aversion is inversely S-shaped under both high- and low-volatility regimes. However, the implied risk aversion under the low-volatility regime has a wide range. Investors’ risk aversion perspective helps explain patterns of pricing kernels and risk aversion estimates. Finally, we find that implied risk aversion is predictive of short-term (excess) market returns based on in-sample and out-of-sample tests.

Bayesian Switching Volatility Models for Analysing Stock Returns in Ghana

Abstract The goal of this research was to use Bayesian switching volatility models to model the stock returns of the GCB, bank in Ghana. Monthly stock prices of GCB bank for the period of 138 months were used for the study. The two-state Markov-Switching GARCH models were used in the study to determine the best model for modelling and forecasting the stock returns. The Deviance Information Criteria was considered when selecting the best model. Based on the Deviance Information Criteria, E-GARCH variance specification with skewed student-t innovation was shown to be appropriate for modelling the stock returns. The estimates of the best model showed the first regime to exhibit the features of “turbulent market conditions” while the second regime exhibits “tranquil market conditions”. The risk analysis finds the best model to generally perform better in estimating both Value-at-Risk and Expected Shortfall at 1% rather than 5%. The study advises investors to invest in GCB bank because of the high returns connected with the stock and the fact that when “turbulent market conditions” arise, the recovery rate for these stocks is faster.

Spectral analysis of Markov switching GARCH models with statistical inference

AbstractWe derive matrix expressions in closed form for the autocovariance function and the spectral density of Markov switching GARCH models and their powers. For this, we apply the Riesz–Fischer theorem which defines the spectral representation as the Fourier transform of the autocovariance function. Under suitable assumptions, we prove that the sample estimator of the spectral density is consistent and asymptotically normally distributed. Further statistical implications in terms of order identification and parameter estimation are discussed. A simulation study confirms the validity of the asymptotic properties. These methods are also well suited for financial market applications, and in particular for the analysis of time series in the frequency domain, as shown in some proposed real‐world examples.

Testing an Algorithm with Asymmetric Markov-Switching GARCH Models in US Stock Trading

In the present paper, we extend the current literature in algorithmic trading with Markov-switching models with generalized autoregressive conditional heteroskedastic (MS-GARCH) models. We performed this by using asymmetric log-likelihood functions (LLF) and variance models. From 2 January 2004 to 19 March 2021, we simulated 36 institutional investor’s portfolios. These used homogenous (either symmetric or asymmetric) Gaussian, Student’s t-distribution, or generalized error distribution (GED) and (symmetric or asymmetric) GARCH variance models. By including the impact of stock trading fees and taxes, we found that an institutional investor could outperform the S&P 500 stock index (SP500) if they used the suggested trading algorithm with symmetric homogeneous GED LLF and an asymmetric E-GARCH variance model. The trading algorithm had a simple rule, that is, to invest in the SP500 if the forecast probability of being in a calm or normal regime at t + 1 is higher than 50%. With this configuration in the MS-GARCH model, the simulated portfolios achieved a 324.43% accumulated return, of which the algorithm generated 168.48%. Our results contribute to the discussion on using MS-GARCH models in algorithmic trading with a combination of either symmetric or asymmetric pdfs and variance models.