Markov Switching Research Articles

Stationary distribution of periodic stochastic differential equations with Markov switching

Periodic stochastic differential equations (SDEs) with Markov switching are widely applied to describe various financial and biological phenomena in the real world and hence have been receiving intensive attention. One of the essential dynamical behaviours researchers are interested in is the asymptotic stability in distribution. However, related work on periodic SDEs is quite little. This paper aims to fill the gap. Technical challenges including time-inhomogeneity and periodicity of SDEs make this a challenging and non-trivial work. The main results are finally demonstrated by an example. Our theory can be easily implemented to different application scenarios.

Practical finite‐time and fixed‐time multigroup consensus for second‐order nonlinear multi‐agent systems with Markov switching topology

AbstractPractical finite‐time and fixed‐time multigroup consensus questions for second‐order nonlinear multi‐agent systems (MASs) with Markov switching topologies are investigated in this article. Based on the topology of switching, each agent will appear to switch between different groups, and by setting up group switching signal variables embedded in error variables for each agent, finite‐time and fixed‐time control protocols are proposed, respectively, such that the conditions that must be satisfied for all agents to achieve practical finite‐time multigroup consensus and practical fixed‐time multigroup consensus can be obtained, respectively. For unknown nonlinear functions in the dynamical system, a radial basis function neural network (RBFNN) fit is used for approximation. Correspondingly, two examples are provided to verify the control effects of the control protocols.

Stability for Markov switching stochastic delay systems binding event-triggered mechanism to activate multi-impulse jumps

This paper focuses on the pth moment exponentially stability for Markov switching and multi-impulse jumps stochastic time-varying delay system, where the switching behavior among subsystems of the target system is determined by Markov chains, and the occurrence of impulsive jumps is decided according to event-triggered impulsive mechanism when certain well-designed conditions are satisfied. By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria are provided to assure the system stability and get rid of Zeno phenomenon. It is worth pointing out that the multi-impulse jumps are our research aim and the range of delays considered is relatively wide, i.e., the daily bounded delay τ(t)∈[0,1) and the unupper bound delay τ(t)∈[1,∞). Subsequently, two diverse event trigger mechanism about impulsive jumps are proposed for such two types of delays, namely the defined event-triggered impulsive mechanism with delay. Finally, the validity and feasibility of the developed theoretical results are verified by two numerical simulations.

Interactive influence of house prices and the repo rate on household debt in South Africa

<p><big>The recent interest rate policy decisions of the South African Reserve Bank have been criticized significantly by left-leaning political parties and civic society organisations for being anti-poor, anti-labour, and pro-capital because of their implications for household debt. Existing literature has established that interest rates and house prices are insignificant determinants of household debt dynamics in South Africa. Taking advantage of additional data for the period 2013-2022, and contrary to the previous studies, the paper maintains that house prices and the central bank policy rate play a crucial role in household debt dynamics. Applying a Markov Switching regression to quarterly data for the period 1981Q1 to 2022Q1, the paper finds that house prices and the policy rate have a significant influence on household debt dynamics. It establishes the existence of a ‘house price boom, low policy rate burden’ regime and a ‘high policy rate burden, low house price’ regime. The coexistence of the ‘house price boom’ and the ‘low policy rate’ explains the debt euphoria characterised by significant household leveraging.</big></p>

Examining the effect of global energy reserves to production ratio on carbon emission in the USA

A salient perspective to the global net zero emission aspiration that has yet received sparse attention is the unabating conventional energy reserves to production ratio. Considering the both the energy and energy-related emission profiles of the United States, this study considers the outlook of the country's carbon neutral 2050 with reference to the coal, natural gas, and oil energy reserves to production ratios for the period 1970 to 2040. The investigation implied a number of relevant results after employing the Markov switching, cointegration, and causality approaches. The result revealed that both oil and natural gas reserves to production ratio on global scale exert a significantly and positive influence on emission of carbon dioxide in the USA while coal has negative significant effect on carbon dioxide (CO2) emission in two different regimes. From the Wavelet coherence, both in phase and anti-phase relationship, CO2 and oil reserves-production ratio display strong interdependence while a mixed result in the short run (in phase) and medium run (anti phase) is established for CO2 and coal reserves-production ratio. In both short and medium run, natural gas reserves-production ratio leads CO2, and the reverse is also true. Additionally, from the frequency domain causality result, we found causality from oil reserves-production ratio to CO2 while there is bidirectional causality between CO2 and gas reserves-production ratio. The relevance of this study is that it offers insight into the seriousness of the carbon global goal amidst the dimension of energy reserves and production.

Agricultural commodities market reaction to COVID-19

This study examines the volatility transmission mechanism in agricultural futures returns during crisis periods, with a specific focus on the COVID-19 pandemic. The research employs the Markov Switching model to analyze the market dynamics of key agricultural commodities—cotton, sugar, rice, wheat, and corn. The study period is divided into three phases: Pre-COVID, COVID, and Post-COVID, allowing for a comprehensive analysis of market trends and shifts in response to the pandemic. Key findings reveal significant disruptions and heightened volatility in these markets during the COVID-19 period, with notable deviations from traditional market behaviors. The research reveals how various macroeconomic factors, such as the S&P 500, US 10-year Treasury bills, Brent crude oil prices, and the US Dollar Index, distinctly affect these commodity markets. Crucially, it sheds light on the dual nature of these markets, demonstrating both their resilience and susceptibility to worldwide disruptions, along with their recovery patterns following the pandemic. The policy implications of these findings are crucial for investors and policymakers. The study provides insights into managing and mitigating the impacts of global crises on essential commodities, emphasizing the need for robust strategies to navigate future market uncertainties. Additionally, the research contributes to the broader discourse on the interplay between macroeconomic conditions and agricultural market dynamics, offering valuable perspectives for informed decision-making in these sectors.

Almost sure exponential stabilization of impulsive Markov switching systems via discrete-time stochastic feedback control

It is well known that noise can stabilize an unstable Markov switching system (MSS). However, given an unstable impulsive Markov switching system (IMSS), can it be stabilized by noise? To the best of the author’s knowledge, this question has been rarely explored. If the stochastic feedback controller is observed in discrete time, the research is more difficult. In this paper, a comparative method is used to establish a noise stabilization strategy based on discrete-time state and mode observations for IMSSs. In addition, we use the stationary distribution of the ergodic Markov chain instead of the M-matrix technique to obtain the pth moment estimation on the gap between the discrete-time observed controlled system’s states and the auxiliary system’s states, so that the control strategy can be applied to a wider class of IMSSs. Finally, we applied the proposed control scheme to impulsive neural networks with Markovian switching (INNs-MS) and impulsive boost converter systems (IBCSs). Through an example and several simulations, we validated the effectiveness and feasibility of this control scheme.

Global oil price and stock markets in oil exporting and European countries: Evidence during the Covid-19 and the Russia-Ukraine war

The relationship between oil price movements and stock markets during the COVID-19 pandemic and the geopolitical crisis like the ongoing Russian-Ukraine war is yet unexplored extensively. This study therefore examines the return-correlation effects of oil prices on stock markets and their spillover effects in oil-exporting and European countries using daily closing data. After estimating the GARCH process, we employ the static and dynamic Markov Switching model that allow the relationship between oil price and stock market to switch between two regimes coined the COVID-19 and the Russia-Ukraine war periods. The static model shows stock price returns to respond positively and significantly to oil price returns in Italy, Germany and the US during the Covid-19 period while the response is significantly positive only for US in the Russia-Ukraine war period. As regards the volatility spillover, significant spillover is found from stock to oil market for Nigeria, vice versa for Saudi Arabia and bi-directional volatility spillover found for the US, Italy and Germany during the COVID-19 period. The policy implication is that Nigeria and Saudi Arabia should prioritize financial policy and energy policy respectively while US, Italy and Germany should adopt policy coordination to stabilize oil-stock market volatility during low oil price period like the COVID-19 period.

Beyond the numbers: unveiling the environmental impacts of international tourism and the role of renewable energy transition

ABSTRACT In pursuit of Saudi Arabia's Vision 2030 objectives for a sustainable and low-carbon future, this study examines the intricate dynamics between carbon emissions and key variables crucial to the nation's decarbonisation strategy. Grounded in the Triple Bottom Line (TBL) Theory, the chosen variables – sustainable tourism, renewable energy demand, and natural resource management – take centre stage. Applying Markov switching regime regression to data spanning 1990–2022, our findings reveal a positive association between international tourism and carbon emissions, aligning with the Tourism-induced Environmental Impact theory. Incorporating the Environmental Kuznets Curve (EKC), our results illustrate a U-shaped relationship. Renewable energy consumption (REC) exhibits a negative impact, supporting EKC's premise that economic development and cleaner energy adoption mitigate environmental degradation. Identified as influential factors affecting carbon emissions, Economic growth and natural resource capital find theoretical backing. The second power of economic expansion positively influences carbon emissions, while the square of natural resources has a negative impact, aligning with resource scarcity theories. Granger causality estimates validate Tourism-led Growth, Resource Capital, and Emissions-led Growth hypotheses. Integrating insights from the Community-Based Tourism (CBT) and stakeholder theory, this study provides actionable insights for policymakers steering Saudi Arabia toward a sustainable, low-carbon future.

An EM/MCMC Markov-Switching GARCH Behavioral Algorithm for Random-Length Lumber Futures Trading

This paper tests using two-regime Markov-switching models with asymmetric, time-varying exponential generalized autoregressive conditional heteroskedasticity (MS-EGARCH) variances in random-length lumber futures trading. By assuming a two-regime context (a low s=1 and high s=2 volatility), a trading algorithm was simulated with the following trading rule: invest in lumber futures if the probability of being in the high-volatility regime s=2 is lower or equal to 50%, or invest in the 3-month U.S. Treasury bills (TBills) otherwise. The rationale tested in this paper was that using a two-regime Markov-switching (MS) algorithm leads to an overperformance against a buy-and-hold strategy in lumber futures. To extend the current literature in MS trading algorithms, two location parameter scenarios were simulated. The first uses an unconditional mean or expected value (no factors), and the second incorporates market and behavioral factors. With weekly simulations form 2 January 1994 to 28 July 2023, the results suggest that using MS-EGARCH models in a no-factors scenario is appropriate for active lumber futures trading with an accumulated return of 158.33%. Also, the results suggest that it is not useful to add market and behavioral factors in the MS-GARCH estimation because it leads to a lower performance.

Pth Moment Exponential Synchronization for Delayed Multi-Agent Systems With Lévy Noise and Markov Switching

<i>P</i>th Moment Exponential Synchronization for Delayed Multi-Agent Systems With Lévy Noise and Markov Switching

Do shipping freight markets impact commodity markets?

The Baltic Dry Index (BDI) is mostly perceived as the leading indicator of shipping freight market and economic activity. In this study, we investigate the dependence structure and distributional predictability between BDI and nineteen major commodity investable indices to offer insights on the predictive ability of BDI for commodity assets. In addition, we explore the effects of policy uncertainty and geopolitical risk on the dynamic dependence structure between BDI and commodities futures. To this end, we apply time-varying Markov switching copula models and non-parametric causality in quantile approach to daily closed price indices of commodities futures running from 23rd May 2006 to 20th November 2020. We provide for the first-time empirical evidence of time-varying Markov tail dependence structure dynamics between marine activities and commodities futures. The nature of the dependence is positives except for petroleum, all metals, livestock wheat, cattle and softs markets. Furthermore, we show the significant effects of global uncertainties, policy uncertainty and geopolitical risk on the dependence between sea transport and commodity assets. Finally, we note from the causality-in-mean and causality-in-variance analysis that the daily change of BDI is an efficient predictor (informational efficiency) of the daily changes of most of the commodity indices. Finally, we show that markets.

Regime Tracking in Markets with Markov Switching

The object of the investigation is a model of the incomplete financial market. It includes a bank deposit with a known interest rate and basic risky securities. The instant interest rate and volatility are governed by a hidden market regime, represented by some finite-state Markov jump process. The paper presents a solution to two problems. The first one consists of the characterization of the derivatives based on the existing market securities, which are valid to complete the considered market. It is determined that for the market completion, it is sufficient to add the number of derivatives equal to the number of possible market regimes. A generalization of the classic Black–Scholes equation, describing the evolution of the fair derivative price, is obtained along with the structure of a self-financing portfolio, replicating an arbitrary contingent claim in the market. The second problem consists of the online estimation of the market regime, given the observations of both the underlying and derivative prices. The available observations are either a combination of the time-discretized risky security prices or some high-frequency multivariate point processes associated with these prices. The paper presents the numerical algorithms of the market regime tracking for both observation types. The comparative numerical experiments illustrate the high quality of the proposed estimates.

Foreign investor portfolio flow and monetary policy response in the Indonesian stock market considering the COVID-19 pandemic

Foreign portfolio investment in developing countries, including Indonesia, plays a crucial role in the economy, where this fund flow can influence exchange rates and stimulate price increases in the stock market. During the COVID-19 pandemic, the volatility of foreign portfolio flows by investors has significantly increased. To anticipate these conditions, the monetary authorities in Indonesia have implemented various monetary policies to address the possibility of more adverse situations. This study examines the impact of the inflow or outflow of foreign portfolio investments and the monetary policies reflected in the 7-day repo rate of Bank Indonesia on the Indonesian stock market. The data were collected from April 4, 2016, to March 18, 2022. The research methodology involves the Non-Linear Autoregressive Distributed Lag and the Markov Switching Regression (MSR) model. The findings indicate that foreign investor portfolio flows influence the Jakarta Composite Index. There is a tendency for domestic investors to analyze the habits of foreign investors. The study also found that monetary policy is not proven to affect the Jakarta Composite Index, while the USD/IDR exchange rate has an impact on the Indonesian stock market. This indicates many companies listed on the Indonesia Stock Exchange have debt in dollars or are paid in US dollars, making them vulnerable to exchange rate fluctuations.

Examining the business cycle of the tourism industry in Mexico at the state level using the Markov Switching Model (1992 to 2017)

Despite being a popular tourist destination, state-level research on the business cycle in Mexico's tourism industry is lacking. This study aims to answer three research questions: Are the growth stages of the international tourism market similar across states? Are the growth stages of the domestic tourism market similar among entities? Is there a relation between the economic cycle of the international tourism market and the domestic market? We use the Markov Switching Model to estimate the business cycle of the tourism industry in each Mexican state from 1992 to 2017. We identify the most attractive states for international and domestic tourists. Notably, eleven of the coefficients belong to the economic cycle of the foreign tourist market, indicating a greater economic impact compared to the domestic market. The results show that each state has its own business cycle, requiring individual projections for each market. This information is relevant for tourism planners and policymakers to address the challenges posed by the SDGs.

Asymmetric and Nonlinear Foreign Debt–Inflation Nexus in Brazil: Evidence from NARDL and Markov Regime Switching Approaches

This paper augments the sparse literature on the inflationary impact of foreign debt in Brazil while addressing methodological caveats in previous studies. We depart from the linearity assumption and employ two nonlinear techniques: the nonlinear autoregressive distributed lag (NARDL) model and a Markov Switching Regression (MSR) to investigate the connection between foreign debt and inflation within a multivariate framework. The analyses consider the presence of structural breaks via assessing variable stationarity using the Zivot and Andrew unit root test and incorporating a residual-based cointegration test proposed by Gregory and Hansen. Additionally, we apply a multiple structural breakpoints test by Bai and Perron to determine the presence of structural breaks in the impact of foreign debt on inflation. Our findings robustly indicate that the domestic money supply has a statistically significant positive effect, while the nominal effective exchange rate has a negative effect on inflation in both the short and long run. The NARDL model reveals that only positive changes in foreign debt have a statistically significant negative effect on inflation in the short run, whereas both positive and negative foreign debt changes significantly affect inflation in the long run. The results from the MSR model are generally consistent with those of the NARDL model.

Stability and rate of decay for solutions to stochastic differential equations with Markov switching

In this article, we present the almost sure asymptotic stability and a general rate of decay for solutions to stochastic differential equations (SDEs) with Markov switching. By establishing a suitable Lyapunov function and using an exponential Martingale inequality and the Borel-Cantelli theorem, we give sufficient conditions for the asymptotic stability. Also, we obtain sufficient conditions for the construction of two kinds of Lyapunov functions. Finally give two examples to illustrate the validity of our results. For more information see https://ejde.math.txstate.edu/Volumes/2024/01/abstr.html

Exchange rate expectations and exchange rate behaviour in the South African context

The literature maintains that exchange rate movements are largely dependent on expectations formed by economic agents. The study attempts to understand the impact of exchange rate expectations on the behaviour of the exchange rates. We use the Markov Switch Model to estimate the probability of the exchange rates transitioning from regime-to-regime. The study finds that the exchange rate movement is asymmetric to its expectations.

The Effects of External Debt on the Economic Growth of India during Various Crisis Periods: A Markov- Switching GARCH Model Approach

This article seeks to investigate the impact of the volatility of the external debt burden on the economic growth of India. The MS (Markov - Switching) - GARCH model is the cornerstone in studying the effects of external debt on the economic growth that is simulated herein. This article applies a MS - GARCH model that allows not only unobserved variables within an observed model but also uses a robust algorithm to reach strong optimization (convergence) through iteration in a dynamic system in the estimation procedure. This article considers the period from Q2 2004 to Q4 2022 with 74 sample observations. Considering various crises like the global financial crisis, the Euro crisis, and the COVID-19 pandemic that occurred during the study period, the results identify two regimes based on conditional volatility. One is the global financial recession period (regime-1) and another is the post-global financial recession period (regime-2). The findings show that the conditional volatility as well as the variance in the volatility of economic growth due to the external debt of India is much stronger in the global financial recession period (regime-1) than in the post-global financial recession period (regime-2). It implies that the Euro crisis and the COVID-19 pandemic are having less impact on external debts in India. The transition matrix indicates the greater probability of the economic growth rate settling down in regime 2 when it is already in regime 2, as it is considered to be a much calmer period. Finally, the results of the stable probabilities suggest that the economic growth rate of India is much more stable in regime 2 than in regime 1. This article puts forward relevant policy implications for coming out from the debt overhang scenario in India.

Proportional-Integral Observer-Based State Estimation for Markov Memristive Neural Networks With Sensor Saturations.

This article investigates the resilient proportional-integral observer (PIO) problem for Markov switching memristive neural networks (MSMNNs) with randomly occurring sensor saturation within a finite-time interval. The Markov switching of memristive neural networks is regulated by a higher level deterministic switching signal, whose transition probabilities are piecewise time-varying and can be depicted by the average dwell-time strategy. Meanwhile, a Bernoulli stochastic process associated with an uncertain packet arriving rate is adopted to describe the randomly occurring sensor saturation. The aim is to design a resilient PIO such that the augmented dynamic has the property of stochastic finite-time boundedness while meeting the desired performance index. By applying the Lyapunov method and the average dwell-time scheme, sufficient criteria are established for MSMNNs, and a unified design method is presented for the existence of the PIO. Lastly, the attained theoretical results are validated via a numerical simulation.