Markov Switching Research Articles

Conditions for extinction and ergodicity of a stochastic Mycobacterium tuberculosis model with Markov switching

<p>This paper is concerned with a stochastic Mycobacterium tuberculosis model, which is perturbed by both white noise and colored noise. First, we prove that the stochastic model has a unique global positive solution. Second, we derive an important condition $ R_0^* $ depending on environmental noise for this stochastic model. We construct an appropriate Lyapunov function, and show that the model possesses a unique ergodic stationary distribution when $ R_0^* < 0 $, in other words, it indicates the long-term persistence of the disease. Finally, we investigate the related conditions of extinction.</p>

Weak convergence of Mckean-Vlasov stochastic differential equations with two-time-scale Markov switching

Weak convergence of Mckean-Vlasov stochastic differential equations with two-time-scale Markov switching

Multiscale non-linear tale risk spillover effect from oil to stocks – The case of East European emerging markets

This paper investigates the multiscale non-linear risk transmission effect from Brent oil to eleven European emerging stock markets. Dynamic extreme risk time series are created using the FIAPARCH-CVaR approach. The MODWT transformation is applied to make three wavelet details that represent different time horizons. In the final step, the MODWT time series are fitted into the Markov switching model to examine the spillover phenomenon. The results indicate that the Czech and Hungarian stock markets endure the spillover effect in crisis regime in the short term, probably because these markets are among the most efficient emerging European markets. On the other hand, a relatively high spillover effect is found in a peaceful rather than a crisis regime in the case of Poland. This is probably because the Polish index lists almost 300 stocks, which means that oil shocks disperse to a large number of different industry sectors. In small and less developed markets, such as Estonia, Slovenia, Bulgaria, and Croatia, a high spillover effect exists in a tranquil regime because these countries have high oil consumption per capita. Lithuania and Latvia do not report the spillover effect in the short run, while this is true for all time horizons in the case of Slovakia.

Yield rate in the Warsaw office market and its determinants. Further studies

This article is a continuation and extension of a previous study which, to the best of the author’s knowledge, was the first scientific attempt to identify determinants of the yield rate in the Warsaw office market. The paper is based on the Gordon growth model. In this approach, the yield rate of buildings offering office space to let is a function of the risk-free interest rate, the risk premium and a constant rate of growth of generated cash flows. In the article, five different elements of the risk premium were identified (term structure, alternative investments’, market (country) specific, monetary and local office market capacity risk premium). The Error Correction Model was formulated based on quarterly time series data from 2007Q1 to 2021Q2. Most investors in the office market in Poland are financial institutions representing foreign capital. Therefore, the innovation of the paper and its main goal was to define which factors play key roles in determining yield rates in the Warsaw office space market – national or regional/international. However, the selected group of Polish determinants were indicated as having prevailing an impact on the yield rate in the Warsaw office market than the corresponding determinants from the European Monetary Union and the USA. Based on the model, the lead-lag, as well as asymmetric relations, were depicted. Moreover, the use of dummy variables checks, the Chow test and the Markov switching model indicated the presence of structural breaks and the existence of the two regimes in the model.

Comparative stability analysis of Indonesian banks: Markov Switching-Dynamic Regression for Islamic and conventional sectors.

The banking industry necessitates implementing an early warning system to effectively identify the factors that impact bank managers and enable them to make informed decisions, thereby mitigating systemic risk. Identifying factors that influence banks in times of stability and crisis is crucial, as it ultimately contributes to developing an improved early warning system. This study undertakes a comparative analysis of the stability of Indonesian Islamic and conventional banking across distinct economic regimes-crisis and stability. We analyze monthly banking data from December 2007 to November 2022 using the Markov Switching Dynamic Regression technique. The study focuses on conducting a comparative analysis between Islamic banks, represented by Islamic Commercial Bank (ICB) and Islamic Rural Bank (IRB), and conventional banks, represented by the Conventional Commercial Bank (CCB) and Conventional Rural Bank (CRB). The findings reveal that both Islamic and conventional banks exhibit a higher probability of being in a stable regime than a crisis regime. Notably, Islamic banks demonstrate a greater propensity to remain in a stable regime than their conventional counterparts. However, in a crisis regime, the likelihood of recovery for Sharia-compliant institutions is lower than for conventional banks. Furthermore, our analysis indicates that larger banks exhibit higher stability than their smaller counterparts regarding assets and size. This study pioneers a comprehensive comparison of the Z-score, employed as a proxy for stability, between two distinct classifications of Indonesian banks: Sharia (ICB and IRB) and conventional (CCB and CRB). The result is expected to improve our awareness of the elements that affect the stability of Islamic and conventional banking in Indonesia, leading to a deeper comprehension of their dynamics.

Regional COVID-19 cases and Bitcoin volatility: Assessment through the Markov switching prism

The 21st century has become the century of technology, which has spread to the currency market, presenting the international economic system with a new challenge – the challenge created by digital currency, which has determined a change in the rules of operation in the market. The main property of cryptocurrencies in general, and Bitcoin in particular, is constant volatility and mutual sensitivity to each other. This article aims to analyze the cryptocurrency market landscape from both short-term and long-term perspectives. Additionally, the article seeks to quantitatively assess the contradictions, trends, and patterns of price volatility in Bitcoin by employing the framework of Markov switching during the period spanning from 2020 to 2022. The Markov switching model was used in the study. In this study, the factors influencing volatility on different modes of the Markov switch are the COVID-19 pandemic and the Pearson correlation statistical method. The Chisquared test was estimated to identify the connection between Bitcoin volatility switching modes and the COVID-19 pandemic spread. This analysis enables international investors to diversify with maximum efficiency and returns using available hedging tools. However, several open questions remain for future research. Future studies can analyze different cryptocurrencies’ volatility. This research helps to assess the nature of the relationship of cryptocurrencies in statistics (the correlation of cryptocurrencies as of December 1, 2021, when no significant events in the financial market and political upheavals were recorded) and dynamics (the Markov switching models for the postpandemic period of 2020–2022). The article contributes to understanding the interdependence and sensitivity of different cryptocurrencies in relation to each other.

Inflation: Demand Pull or Cost Push? A Markov Switching Approach

Inflation: Demand Pull or Cost Push? A Markov Switching Approach

A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies.

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.

$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control

<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.</p></abstract>

Conditional macroeconomic and stock market volatility under regime switching: Empirical evidence from Africa

<abstract> <p>We used the Markov switching regression model to establish a relationship between the conditional stock market returns and macroeconomic volatilities. Monthly data from thirteen (13) African stock markets and macroeconomic variables (exchange rate, inflation, interest rate, money supply, and crude oil price) from 2003 to 2022 were employed. We confirmed the existence of two distinct regimes: An economic expansion or a "tranquil" state with less volatility and an economic decline or a "crisis" state with high volatility. Our findings indicated that macroeconomic variables significantly affect both expansion and crisis periods. However, the estimated coefficients were more significant in a tranquil than in a crisis state. The findings of the study were consistent with macroeconomic theory and pointed out policy implications.</p> </abstract>

Large-deviation principles of switching Markov processes via Hamilton-Jacobi equations

Large-deviation principles of switching Markov processes via Hamilton-Jacobi equations

Adaptive Neural Consensus of Unknown Non-Linear Multi-Agent Systems with Communication Noises under Markov Switching Topologies

In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-linear multi-agent systems is designed. It consists of the local interfered relative information and the estimation of the unknown dynamic. The Radial Basis Function networks (RBFNNs) approximate the nonlinear dynamic, and the estimated weight matrix is updated by utilizing the measurable state information. Then, using the stochastic Lyapunov analysis method, conditions for attaining consensus are derived on the consensus gain and the weight of RBFNNs. The main findings of this paper are as follows: the consensus control of multi-agent systems under more complicated and practical circumstances, including unknown nonlinear dynamic, Markov switching topologies and communication noises, is discussed; the nonlinear dynamic is approximated based on the RBFNNs and the local interfered relative information; the consensus gain k must to be small to guarantee the consensus performance; and the proposed algorithm is validated by the numerical simulations finally.

Practical finite-time and fixed-time containment for second-order nonlinear multi-agent systems with IDAs and Markov switching topology

In this article, the finite-time containment problem and the fixed-time containment problem accompanied by injection and deception attacks (IDAs) and Markov switching topology for second-order nonlinear multi-agent systems (MASs) are investigated, respectively. By introducing a radial basis function neural network (RBFNN), the approximation property of radial basis neural networks is used to solve the unmeasurable difficulties of nonlinear functions and injection attacks. Finite-time and fixed-time distributed control protocols are proposed for switching topologies and attack-induced state deception and control injection, and finite-time and fixed-time containment as well as obtaining their corresponding sufficient conditions are achieved, respectively. Correspondingly, two examples are shown to demonstrate the feasibility of the control protocols.

A matrix unified framework for deriving various impulse responses in Markov switching VAR: Evidence from oil and gas markets

We propose a new method to compute various impulse response functions (IRF) for a Markov switching VAR model in terms of neat matrix expressions in closed form. The key is to derive a suitable closed form representation for Markov switching VAR models using a state-space representation. By this representation, the IRF analysis can be processed with respect to either an asymmetric discrete or a symmetric continuous shocks. A simulation study demonstrates the actual advantages of the proposed matrix methodology. To illustrate the feasibility and the usefulness of our approach, we present empirical applications to oil and natural gas markets showing the relevance of accommodating asymmetries in the relationship between their price shocks and economic activities.

Threshold dynamics of stochastic H7N9 model with Markov switching and hybrid strategy

This article aims to study the impact of different environmental states on the transmission dynamics of avian influenza A (H7N9) for poultry by using an epidemic model with general incidence rate and Markov switching. The model couples the essential roles of quarantine and hybrid strategy of vaccination and elimination. By establishing the basic reproduction number R0 as a sharp threshold for the spread of H7N9. When R0<1, the disease almost surely dies out exponentially. We use the compactness of space to prove that when R0>1, the disease almost surely persistent, and this method can be applied to other infectious disease models considering vaccination. In addition, under a mild extra condition, the ergodicity of the Markov process is proved. Our research indicates that: (i) theoretical results and sensitivity analysis show that implementing hybrid strategy is an effective method to control H7N9 propagation; (ii) under the influence of environmental switching, numerical simulations find that the transmission state of H7N9 will neutralize multiple regimes, leading to the possibility of multi wave transmission. This can be used to explain the multiple outbreaks of H7N9 in China.

The effect of gas and oil prices on economic confidence: An empirical analysis for euro area

Energy prices are determinants of economic confidence by directly affecting production, consumption, and transportation costs. Nevertheless, countries’ energy policies and macroeconomic and geopolitical developments may moderate the impact of energy prices on economic confidence. This study analyzes the effects of oil and gas prices on business and confidence in the Euro Area over the period 1994–2023. We employ non-linear correlation and regression models to investigate the spillover relationship between the variables. For this purpose, the Markov Switching Regression (MSR) model is employed to analyze the spillover effect of oil and gas prices on both consumer and business confidence. The empirical results show that oil and gas prices harm consumer confidence in all regimes. Oil prices have a positive effect on business confidence in a volatility regime. However, oil prices negatively affect business confidence in low volatility, but this effect is insignificant. The effect of gas prices on the business confidence index is negative and statistically significant during periods of high volatility. Besides, gas prices positively affect business confidence for low volatility.

Another look at the asymmetric relationship between stock returns and trading volume: evidence from the Markov-switching model

PurposeThe purpose of this paper is to bridge the gap between the existing theoretical and empirical studies by examining the asymmetric return–volume relationship. Indeed, the authors aim to shed light on the return–volume linkages for French-listed small and medium-sized enterprises (SMEs) compared to blue chips across different market regimes.Design/methodology/approachThis study includes both large capitalizations included in the CAC 40 index and listed SMEs included in the Euronext Growth All Share index. The Markov-switching (MS) approach is applied to understand the asymmetric relationship between trading volume and stock returns. The study investigates also the causal impact between stock returns and trading volume using regime-dependent Granger causality tests.FindingsAsymmetric contemporaneous and lagged relationships between stock returns and trading volume are found for both large capitalizations and listed SMEs. However, the causality investigation reveals some differences between large capitalizations and SMEs. Indeed, causal relationships depend on market conditions and the size of the market.Research limitations/implicationsThis paper explains the asymmetric return–volume relationship for both large capitalizations and listed SMEs by incorporating several psychological biases, such as the disposition effect, investor overconfidence and self-attribution bias. Future research needs to deepen the analysis especially for SMEs as most of the literature focuses on large capitalizations.Practical implicationsThis empirical study has fundamental implications for portfolio management. The findings provide a deeper understanding of how trading activity impact current returns and vice versa. The authors’ results constitute an important input to build and control trading strategies.Originality/valueThis paper fills the literature gap on the asymmetric return–volume relationship across different regimes. To the best of the authors’ knowledge, the present study is the first empirical attempt to test the asymmetric return–volume relationship for listed SMEs by using an accurate MS framework.

Measuring fiscal policy sustainability in developing Asia: what does the Markov Switching Augmented Dickey-Fuller Test tell us?

This paper measures fiscal sustainability in 22 developing Asian countries for the period 1999–2017. Previous literature generates conflicting results: one paper applies the usual stationarity and cointegration tests and finds that fiscal policy is sustainable but in weak form. Another paper employs a fiscal reaction function and finds that fiscal policy is unsustainable. This paper uses an expanded version of the Markov Switching Augmented Dickey-Fuller test (MS-ADF), which remedies the shortcomings of conventional stationarity tests to provide more statistical power in the presence of nonlinearities and structural breaks. The MS-ADF has never been applied to this set of countries. Results show that the majority of the countries have “uncertain” debt trajectories, not definitively sustainable or unsustainable but somewhere in-between. This is a more nuanced picture of the debt trajectories in the region relative to what is obtained using the established methods. A more nuanced assessment could lead to more suitable policy corrections.

Modeling Corporate CDS Spreads Using Markov Switching Regressions

Abstract This paper investigates the determinants of the European iTraxx corporate CDS index considering a large set of explanatory variables within a Markov switching model framework. The influence of financial and economic variables on CDS spreads are compared using linear, two, three, and four-regime models in a sample post-subprime financial crisis up to the COVID-19 pandemic. Results indicate that four regimes are necessary to model the CDS spreads. The fourth regime was activated during the COVID-19 pandemic and in high volatility periods. Further, the effect of the covariates differs significantly across regimes. Brent and term structure factors became relevant after the outbreak of the COVID-19 pandemic.

Approximating Botswana's financial cycle: Expanding the macroprudential toolkit

AbstractThis study estimates the financial cycle for Botswana using the Christiano–Fitzgerald band‐pass filter, unobserved components approach and a Markov switching dynamic factor model. Using real credit and equity prices, together with several macroeconomic variables from 2001Q1 to 2021Q4, we find that the domestic financial cycle generally captures movements along the business cycle, with peaks reflecting the cumulative build‐up of risks during the boom that ultimately burst, coinciding with periods of financial distress. These findings shed light on the implications of financial fluctuations on domestic financial stability, hence, inform effective calibration of macroprudential tools, while also providing traction for implementation of the recently approved macroprudential policy framework for Botswana.