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This research undertakes an examination of the Okun Model and re-evaluates its relationship within the context of the United States, spanning from January 1990 to May 2022. Employing the ARDL estimation, the study discerns that, over the long term, fiscal policy and trade policy exert upward pressure on the unemployment rate. Contrarily, the Consumer Price Index wields a statistically significant and detrimental influence on unemployment, driving it downwards. Furthermore, the results derived from the Markov-Switching Dynamic Regression analysis, when contemplating high-growth unemployment over the long term, illuminate noteworthy insights. Specifically, variables such as Gross Formation Capital Fixed multiplied by Capacity Utilization and Employment Level multiplied by Labour Force Participation are statistically significant with negative effects on unemployment. In contrast, Monetary Policy Uncertainty is linked to an anticipated increase in the unemployment rate. Therefore, this paper will be of interest to a wide range of labour market economic agents. As is known, investors' feelings on monetary policy and fiscal policy can shape US economic apprehension. [ABSTRACT FROM AUTHOR]

This study empirically explores the dynamic effect of MP and FP on the economic growth of Thailand from Q1:2003 to Q2:2024. In this study, data analysis was conducted using an advanced sequence of the econometric modeling approach to guarantee that the estimated results were more consistent and reliable. First, we used Bayesian additive regression trees (BART) and Bayesian variable selection (BASAD) methods to determine macro factors with the highest probabilities influencing growth, in addition to monetary and fiscal policy tools during the studied periods. Second, we used the time-varying coefficients seemingly unrelated equation (TVSURE) model to examine the economic impact of MP and FP. Last, we also employed the Markov switching regression (MSR) model not only to support the findings from the TVSURE model but also to propose policy recommendations based on regime durations and transitions tempted by MP and FP. The main results from both TVSURE and MSR reveal the following: (1) MP is more consistent with expected growth outcomes while FP is stronger when localized, (2) MP is more effective in sustaining long periods of high growth, (3) FP is significantly stronger in recovering from recessions, and (4) the coordination of MP and FP has a similar performance to MP alone but with shorter transition periods. This study makes an empirical contribution to the ongoing debate on the effectiveness of MP and FP in boosting growth and aiding in the recovery from recessions in the case of Thailand. In addition, this study not only acknowledged certain limitations but also recommended policies to sustain the Thai economy. [ABSTRACT FROM AUTHOR]

This paper focus on Mckean-Vlasov stochastic differential equations (SDEs) with two-time-scale Markov switching. These stochastic processes include the microcosmic location, the macrocosmic distribution of particles and the discrete event. Under appropriate conditions, by using martingale method, we prove that the original system will weakly converge to the corresponding limit system as ε → 0. Finally, an example is given to illustrate our results and the conclusion and future works are presented. [ABSTRACT FROM AUTHOR]

Due to the real applications, optimal consensus reinforcement learning with switching topology is still challenging due to the complexity of topological changes. This paper investigates the optimal consensus control problem for discrete multi-agent systems under Markov switching topologies. The goal is to design an appropriate algorithm to find the optimal control policies that minimize the performance index while achieving consensus among the agents. The concept of mean-square consensus is introduced, and the relationship between consensus error and tracking error to achieve mean-square consensus is studied. A performance function for each agent under switching topologies is established and a policy iteration algorithm using system data is proposed based on the Bellman optimality principle. The theoretical analysis shows that the consensus error realizes mean-square consensus and the performance function is optimized. The efficacy of the suggested approach is confirmed by numerical simulation using an actor–critic neural network. As a result, the value function is the optimum and the mean-square consensus can be reached using this technique. [ABSTRACT FROM AUTHOR]

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 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 , in other words, it indicates the long-term persistence of the disease. Finally, we investigate the related conditions of extinction. [ABSTRACT FROM AUTHOR]

Fault detecting is crucial for the safety of the lithium-ion battery. This is because thermal fault and sensor fault are the most common fault in battery, and it may be catastrophic. This study explores a novel fault detection scheme for the cylindrical lithium-ion battery. In this scheme, for the modeling simplicity and physical realism, an electrothermal model is adopted to describe the cell's thermal behaviors. Specifically, based on the uncertainties and mode switching, this scheme proposed an interval filter to estimate the surface temperature of cell. Furthermore, upper and lower bounds of surface temperature estimates are established using interval filters and information of uncertainty. In addition, an effective method based on L ∞ norm is proposed to measure the effect of uncertainty. Finally, we perform simulation studies on the proposed scheme, verifying the potential of our method in thermal fault detection. [ABSTRACT FROM AUTHOR]

Due to the increased availability of intensive longitudinal data, researchers have been able to specify increasingly complex dynamic latent variable models. However, these models present challenges related to overfitting, hierarchical features, non-linearity, and sample size requirements. There are further limitations to be addressed regarding the finite sample performance of priors, including bias, accuracy, and type I error inflation. Bayesian estimation provides the flexibility to treat these issues simultaneously through the use of regularizing priors. In this paper, we aim to compare several Bayesian regularizing priors (ridge, Bayesian Lasso, adaptive spike-and-slab Lasso, and regularized horseshoe). To achieve this, we introduce a multilevel dynamic latent variable model. We then conduct two simulation studies and a prior sensitivity analysis using empirical data. The results show that the ridge prior is able to provide sparse estimation while avoiding overshrinkage of relevant signals, in comparison to other Bayesian regularization priors. In addition, we find that the Lasso and heavy-tailed regularizing priors do not perform well compared to light-tailed priors for the logistic model. In the context of multilevel dynamic latent variable modeling, it is often attractive to diversify the choice of priors. However, we instead suggest prioritizing the choice of ridge priors without extreme shrinkage, which we show can handle the trade-off between informativeness and generality, compared to other priors with high concentration around zero and/or heavy tails. [ABSTRACT FROM AUTHOR]

This is the first empirical study that analyzes the nature of business cycles in India using quarterly GDP growth data from 1998Q1 to 2022Q4 and the Markov Switching Auto-regressive model. In order to capture the impact of exclusion and inclusion of post pandemic period data, it has developed two alternative models. Based on these models, the study provides the forecast of quarterly GDP growth and cumulative real output losses due to the pandemic. It also provides alternative scenarios and trajectories of the Indian economy towards the US$ 5 trillion milestone. It is our hope that these results will be useful to policymakers and other stakeholders to understand the business cycle issue in India and take appropriate strategies to overcome the problems associated with these cycles. [ABSTRACT FROM AUTHOR]

This study delves into an exploration of volatility spillover between financial stress, investor sentiment, and stock market index returns in the Gulf Cooperation Council (GCC) countries using the DCC-GARCH, wavelet coherence, and BEKK-GARCH models. A robustness check, applying Diebold and Yilmaz's (2012, 2014) methodology, verifies network measures across markets. Significant patterns in financial stress index were observed during crises, with strong co-movement between financial stress, investor sentiment, and stock returns, especially during COVID-19 pandemic. Volatility transmission from stock returns to investor sentiment and the financial stress index was notable in some markets. Additionally, we found a significant volatility transmission from the financial stress index to market returns during periods of bearish stress in Bahrain and Kuwait and bullish stress across all countries. These findings offer insights for investors and fund managers optimizing portfolios and managing risk exposure. [ABSTRACT FROM AUTHOR]

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.

Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat‐tailed and heteroscedastic with regime switching dynamic correlations. The conditional return distribution is modeled by an elliptical multi‐variate generalized hyperbolic distribution, allowing for fast parameter estimation via an expectation‐maximization algorithm, and a semi‐closed form of the risk contributions. A new method for efficient computation of non‐Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish–Fisher‐type approximations. Accounting for fat‐tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis or the COVID shock. While risk parity portfolios are rather robust to the misuse of the Gaussian distribution, a sophisticated time series model can improve risk‐adjusted returns, strongly reduces drawdowns during periods of market stress and enables to use a holistic risk model for portfolio and risk management. [ABSTRACT FROM AUTHOR]

We study two sources of heteroscedasticity in high-frequency financial data and estimate their contribution to overall volatility by means of a Markov switching (MS) structural VAR model. We achieve identification for all coefficients by assuming that the structural errors follow a GARCH-DCC process. Using transaction data of the EUR/USD interdealer market in 2016, we first detect three regimesof volatility. Then we show that both sources of volatility matter for the transmission of shocks, and that information is channeled to the market mostly through demand shocks. This suggests that, on the EUR/USD market, some liquidity takers (LTs) are better informed than both liquidity providers and those LTs who follow a feedback strategy. [ABSTRACT FROM AUTHOR]

This study employs the Bayesian Networks (BN) and the wavelet coherence approaches to invest the relationship between Bitcoin volatility and financial asset classes (MSCI world equity index, S&P Goldman Sachs Commodity Index [GSCI], US index and Investment Grade Corporate Bond Index ETF [PIMCO]) using daily data for the period from August 2011 to October 2021. The results show that the causal relationship between Bitcoin and other financial assets varies depending on the market states. During the low volatility periods, Bitcoin has a stronger impact on the GSCI, while during the stability periods, it has a direct effect on the US index and the MSCI world index. In contrast, during high volatility periods, Bitcoin has a direct impact on both the GSCI and PIMCO indices. The key findings enabled us to provide implications for US investors to promote asset allocation and risk management covering both Bitcoin and traditional financial markets. The results suggest that policymakers should watch Botcoin closely to preserve financial stability. [ABSTRACT FROM AUTHOR]

Infectious disease outbreaks have caused significant losses to populations worldwide in terms of morbidity, social and economic costs. This has prompted governments to seek suitable intervention policies to suppress the outbreaks. This paper aims to explore the intrinsic impact of intervention strategies and the psychological behavior of people on the spread of infectious diseases. Employing the finite state Markov chain, we formulate a new stochastic SIS epidemic model under regime switching by using the Beddington–DeAngelis transmission function, in the presence of some governmental control measures. The study of the model is centered on three different scenarios in terms of varying two control parameters. We analyze the deterministic system for the global dynamics in terms of basic reproductive number. Some new threshold parameters are defined to discuss the extinction and the persistence of the disease in the stochastic setting. Numerical assessments were undertaken to validate theoretical findings for the deterministic and stochastic systems. Our findings strongly suggest that heightened awareness among susceptible individuals contributes significantly to the eradication of infection and fosters a stable epidemiological situation. As levels of public awareness increase, particularly within the susceptible population, a discernible trend toward the eradication of the infection emerges, ultimately ensuring sustained stability within the epidemiological landscape. [ABSTRACT FROM AUTHOR]

We examine the relationship between gold prices and the U.S. dollar exchange rate, arguing that their interactions are state-dependent and asymmetric under different market conditions. State dependency hinges on different short-term interest rate zones. To prove this point, we determine three distinct levels or zones of the effective federal funds rate using SETAR(2,p) tests. Subsequently, we perform conditional least square estimations of log changes in gold prices as a function of log changes in the nominal broad U.S. dollar exchange rate index for each of the obtained zones. Their relationship is consistently inverse, suggesting that gold and the U.S. dollar are risk-hedging substitutes for normal market periods. This also implies that gold is a safe-haven asset against the U.S. dollar exchange rate risk against a broad range of currencies. The substitution is weaker in the low-interest rate zone, more robust in the intermediate zone, and very pronounced in the high zone. We also perform a Markov switching test on the double-log function of gold prices and the exchange rate. The tests show a pronounced inverse relationship, i.e., substitution between assets, at normal market conditions. The relationship becomes significantly positive during episodes of financial distress, indicating complementarity between gold and U.S. dollar assets. [ABSTRACT FROM AUTHOR]

Exchange rate modeling has always fascinated researchers because of its complex macroeconomic dynamics. This study documents the exchange rate dynamics of major emerging economies after accounting for their macroeconomic cycles and explores the Bayesian Vector Error Correction Model (VECM) Markov Regime switching model, which uses time‐varying transition probabilities. The main objective is to study the exchange rate dynamics of Brazil, Russia, India, China, and South Africa (BRICS) vis‐à‐vis the US dollar. The Bayesian setup uses two hierarchal shrinkage priors, the normal‐gamma (NG) prior and the Litterman prior, for parameters' estimation. These shrinkage priors allow for a more comprehensive assessment of the regime‐specific coefficients. The model performed well in differentiating between the two regimes for all currencies. The Russian ruble was identified to be the most depreciated currency, whereas the African Rand was the most appreciated. The evaluation of model features revealed that many regime‐specific coefficients differed significantly from their common mean. A forecasting exercise was then performed for the out‐of‐sample period to assess the model's performance. A significant improvement was observed over the basic random walk (RW) model and the linear Bayesian vector autoregression (BVAR) model. [ABSTRACT FROM AUTHOR]

To improve the dynamic assessment of risks of speculative assets, we apply a Markov switching MGARCH approach to portfolio risk forecasting. More specifically, we take advantage of the flexible Markov switching copula multivariate GARCH (MS‐C‐MGARCH) model of Fülle and Herwartz (2022). As an empirical illustration, we take the perspective of a risk‐averse agent and employ the suggested model for assessments of future risks of portfolios composed of a high‐yield equity index (S&P 500) and two safe‐haven investment instruments (i.e., Gold and US Treasury Bond Futures). We follow recent suggestions to employ the expected shortfall as a prime assessment of tail risks. To accurately evaluate the merits of the new model, we back‐test the risk forecasting for daily returns over 10 years for heterogeneous market environments including, for example, the COVID‐19 pandemic. We find that the MS‐C‐MGARCH model outperforms benchmark volatility models (MGARCH, C‐MGARCH) in predicting both value‐at‐risk and expected shortfall. The superiority of the MS‐C‐MGARCH model becomes stronger, when the share of comparably risky assets in the portfolio is relatively large. [ABSTRACT FROM AUTHOR]

This research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 χ 2 Markov chain. A discrete-time multiplicative approximation scheme was developed, and its convergence in Skorokhod topology to the continuous-time geometric Brownian motion with switching has been proved. Furthermore, in a financial market where the discounted asset price follows a geometric Brownian motion with drift switching, market incompleteness was established, and multiple equivalent martingale measures were constructed. [ABSTRACT FROM AUTHOR]

The article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria. [ABSTRACT FROM AUTHOR]

Summary: Bull and bear market identification generally focuses on a broad index of returns through a univariate analysis. This paper proposes a new approach to identify and forecast bull and bear markets through multivariate returns. The model assumes that all assets are directed by a common discrete state variable from a hierarchical Markov switching model. The hierarchical specification allows the cross‐section of state‐specific means and variances to differ over bull and bear markets. We investigate several empirically realistic specifications that permit feasible estimation even with 100 assets. Our results show that the multivariate framework provides competitive bull and bear regime identification and improves portfolio performance and density prediction compared with several benchmark models including univariate Markov switching models. [ABSTRACT FROM AUTHOR]

The present study aims to examine the impact of different types of income (oil and tax) and government expenditure (current and construction) shocks on inflation under varying inflationary conditions. To achieve this objective, quarterly data from the Iranian economy from 1369 to 1399 was utilized, and a regime switching structural vector autoregression model based on stochastic volatility was employed to analyze. In this approach, inflation was considered as a regime variable, and a threshold value of 21% was estimated for each season. Subsequently, regime switching impulse response functions were employed to explore the effects of shocks in oil and tax income, current and construction expenditures, exchange rate, liquidity, and GDP growth on inflation. The findings of the STVAR-SV model employed in this study demonstrated that the impact of shocks in government revenues (oil and tax) and expenditures (current and construction) on inflation is much stronger in the high inflation regime (inflation above 21% in each season) compared to the low inflation regime (inflation below 21% in each season). Notably, the effect of shocks in government construction expenditures and oil revenues is significant solely in the high inflation regime, while being nonsignificant in the low inflation regime. Conversely, shocks in current government expenditures and tax revenues have a positive and significant effect on inflation in both inflationary regimes.

Examining the structure of dependence between financial assets and the effects of their Co-movement is one of the important issues in financial markets. The corresponding copula is one of the most computationally convenient ways to describe the dependency structure. This paper examines regime change probability and the best copula model between Bitcoin and six other assets from 2018 to 2021. First, using the ARMA-GARCH model, the marginal distribution functions for all assets and residuals are calculated. Then, by using the obtained residuals, 11 models of copula and six models of combined Copula with Markov switching were implemented. The model that has the best function for constructing combined distribution functions is selected. Finally, the regime probabilities each time are calculated from the best-fitted model. The results show that in the study period, for Bitcoin-Ethereum, Bitcoin-Cardano, and Bitcoin-Gold pairs MS-CT, for Bitcoin-Binance coin and Bitcoin-Ripple pairs MS-CRG and MS-CN for Bitcoin-Oil pair have the best performance. Furthermore, the probabilities of regime change between each asset at each time were calculated and described. [ABSTRACT FROM AUTHOR]

Introduction: Iran is one of the ten countries with the most pollution, so research in this field is necessary. The goal of countries is high economic growth along with the non-emission of pollution. Environmental destruction and climate change are problems of all countries. Some people believe that economic growth leads to the destruction of the environment, and others do not accept this theory. Sustainable development means that today's generation must meet its own needs without compromising the next generation. Today, countries are trying to achieve sustainable development by minimizing environmental destruction in addition to economic growth. To achieve this goal, international treaties have been concluded between the countries of the world. Many environmental protection organizations were established. One of the long debates among economists is energy consumption. On the one hand, due to economic growth and the production of goods, energy consumption is needed, and on the other hand, the pollution caused by the consumption of this energy fuels environmental and non-climate pollution in countries. Because Iran is a country that sells oil and natural gas, it is a country that has a relative advantage in the field of fossil energy. Considering that Iran has a relative advantage in energy consumption, research in this field becomes necessary. Energy consumption can lead to more pollution.Materials and Methods: This research examines the factors affecting energy consumption and pollution emission in Iran using the Markov switching method, fully adjusted ordinary least squares and dynamic ordinary least squares, and Johansen's method for the period of 1994-2021. In most of the studies conducted on the relationship between energy consumption and major macroeconomic variables, the influence of factors affecting energy consumption, especially factors affecting energy consumption and pollution emission in Iran, has not been paid attention to.Results: According to the results of this research, the Kuznets curve was confirmed by the dynamic time series method and it means that economic growth leads to pollution in the beginning, but then it causes pollution to decrease. Energy consumption has had a positive and significant effect on carbon dioxide emissions. According to the research results, GDP, energy consumption, foreign direct investment has a positive and significant effect on carbon dioxide emissions. Trade liberalization affects energy consumption from its effect on the environment. The environment can be affected by trade liberalization through the three channels of scale effect, combination effect and technique effect. The scale effect is a change in economic growth, the combination effect is a change in the structure of the economy, and the technique effect is a change in the method and technology used in production. According to the results, trade has a negative and significant effect on carbon dioxide emissions. The LR test showed that the model is nonlinear and the Markov switching method was used to estimate the model.Discussion: Environmental issues are one of the most important concerns of countries and creating a clean environment is one of the important goals of countries. According to the research results, using the Markov switching MS-ARMA (3,1,0) method, there is a positive and significant relationship between trade, GDP, and energy consumption with a break in energy consumption. Due to the effect of Iran's composition in energy-intensive industries, it has gained a relative advantage and trade has a positive and significant effect on energy consumption.

This study empirically explores the dynamic effect of MP and FP on the economic growth of Thailand from Q1:2003 to Q2:2024. In this study, data analysis was conducted using an advanced sequence of the econometric modeling approach to guarantee that the estimated results were more consistent and reliable. First, we used Bayesian additive regression trees (BART) and Bayesian variable selection (BASAD) methods to determine macro factors with the highest probabilities influencing growth, in addition to monetary and fiscal policy tools during the studied periods. Second, we used the time-varying coefficients seemingly unrelated equation (TVSURE) model to examine the economic impact of MP and FP. Last, we also employed the Markov switching regression (MSR) model not only to support the findings from the TVSURE model but also to propose policy recommendations based on regime durations and transitions tempted by MP and FP. The main results from both TVSURE and MSR reveal the following: (1) MP is more consistent with expected growth outcomes while FP is stronger when localized, (2) MP is more effective in sustaining long periods of high growth, (3) FP is significantly stronger in recovering from recessions, and (4) the coordination of MP and FP has a similar performance to MP alone but with shorter transition periods. This study makes an empirical contribution to the ongoing debate on the effectiveness of MP and FP in boosting growth and aiding in the recovery from recessions in the case of Thailand. In addition, this study not only acknowledged certain limitations but also recommended policies to sustain the Thai economy.

Due to the real applications, optimal consensus reinforcement learning with switching topology is still challenging due to the complexity of topological changes. This paper investigates the optimal consensus control problem for discrete multi-agent systems under Markov switching topologies. The goal is to design an appropriate algorithm to find the optimal control policies that minimize the performance index while achieving consensus among the agents. The concept of mean-square consensus is introduced, and the relationship between consensus error and tracking error to achieve mean-square consensus is studied. A performance function for each agent under switching topologies is established and a policy iteration algorithm using system data is proposed based on the Bellman optimality principle. The theoretical analysis shows that the consensus error realizes mean-square consensus and the performance function is optimized. The efficacy of the suggested approach is confirmed by numerical simulation using an actor–critic neural network. As a result, the value function is the optimum and the mean-square consensus can be reached using this technique.

This work focuses on the convergence of the numerical invariant measure for a stochastic age-dependent population–toxicant model with Markov switching. Considering that Euler–Maruyama (EM) has the advantage of fast computation and low cost, explicit EM was used to discretize the time variable. With the help of the p-th moment boundedness of the analytical and numerical solutions of the model, the existence and uniqueness of the corresponding invariant measures were obtained. Under suitable assumptions, the conclusion that the numerical invariant measure converges to the invariant measure of the analytic solution was proven by defining the Wasserstein distance. A numerical simulation was performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article develops a flexible class of Markov-switching models in which the GDP growth rate is decomposed into a long-run growth trend and evolving regime-dependent means. The models can account for multiple regimes, breaks in the long-run trend, stochastic volatility, and time-varying transition probabilities. They can also handle data outliers that may arise from rare events, such as the COVID-19 crisis. We illustrate our methodology by modelling Brazilian GDP growth, which has exhibited complicated dynamics over the past four decades. Our results suggest two regimes, one long-run trend break, significant time variation in volatility, and the presence of outliers. Moreover, the selected model features time-varying transition probabilities driven by domestic variables (fiscal stance, reserves, and the real interest rate). Significantly, our findings indicate a marked decline in Brazil's long-run growth in recent years. [ABSTRACT FROM AUTHOR]

This research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 × 2 Markov chain. A discrete-time multiplicative approximation scheme was developed, and its convergence in Skorokhod topology to the continuous-time geometric Brownian motion with switching has been proved. Furthermore, in a financial market where the discounted asset price follows a geometric Brownian motion with drift switching, market incompleteness was established, and multiple equivalent martingale measures were constructed.

This paper presents a comparison of three different non-linear time series modelling approaches: NARMAX (Non-linear Autoregressive Moving Average with Exogenous Inputs), Beta-t-EGARCH (Beta t Exponential Generalized Autoregressive Conditional Heteroscedasticity), and Radial Basis Function Neural Networks (RBFNN) applied to weekly stock market index data. We will explain three types of models and compare their compositions and structures. Then, we will show which model gives better predictions. To study series data, the comparison involved analysing the structure of the model and its errors in various time series models and summarising their findings. We divide the data into two parts: training data to structure the time series and testing. The training data tests the model's predictions. Then, we can analyse the model with the errors and the best deterrence predictions. After selecting the NARMAX and Beta-t-EGARCH models, we test them with specific criteria. The best choice is finding the model with the lowest average errors. For this study, we analysed the weekly average closing of the Aramco 2222 index from 15 December 2019 to 16 July 2023 and made 187 observations.

Technological developments are followed in the form of speed and new products in the large finance ecosystem. Particularly, we can easily observe the increasing importance of both new products and speed in the cryptocurrency markets. Examining the liquidity in cryptocurrency markets, which are open 24 hours a day, 7 days a week, draws attention as an important issue. Liquidity, in simple terms, refers to the ease of converting a financial instrument into cash. Bid-ask spread of a financial instrument is also considered as a measure of liquidity. This study employs Markov switching GARCH (MSGARCH) models to investigate the intraday volatility of the liquidity of Bitcoin under low volatile and high volatile regime periods. The study analyses the 5 minutes’ intraday bid-ask spread by different types of MSGARCH models with different numbers of regimes. The analysed period 01.01.2019 – 06.29.2021 contains 52,548 observations. The first results of the study provide evidence that low and high volatility periods can be explained by different models such as MS EGARCH, MS TGARCH, and MS GJRGARCH. Secondly, the two-regime MSGARCH and MS GJR GARCH models are the best models for explaining low and high volatility periods of intra-day Bitcoin liquidity.

We examine the relationship between gold prices and the U.S. dollar exchange rate, arguing that their interactions are state-dependent and asymmetric under different market conditions. State dependency hinges on different short-term interest rate zones. To prove this point, we determine three distinct levels or zones of the effective federal funds rate using SETAR(2,p) tests. Subsequently, we perform conditional least square estimations of log changes in gold prices as a function of log changes in the nominal broad U.S. dollar exchange rate index for each of the obtained zones. Their relationship is consistently inverse, suggesting that gold and the U.S. dollar are risk-hedging substitutes for normal market periods. This also implies that gold is a safe-haven asset against the U.S. dollar exchange rate risk against a broad range of currencies. The substitution is weaker in the low-interest rate zone, more robust in the intermediate zone, and very pronounced in the high zone. We also perform a Markov switching test on the double-log function of gold prices and the exchange rate. The tests show a pronounced inverse relationship, i.e., substitution between assets, at normal market conditions. The relationship becomes significantly positive during episodes of financial distress, indicating complementarity between gold and U.S. dollar assets.

This article aims to investigate sufficient conditions for the stability of the trivial solution of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system. The novelty of this work is in the consideration of jump concentration points, which are not considered in classical works. The assumption of the existence of concentration points leads to additional constraints on jumps, jump times and relations between them.

From the perspective of prevention and treatment of dengue, it is important to minimize the number of infections within a limited time frame. That is, the study of finite time contraction stability (FTCS) of dengue system is a meaningful topic. This article proposes a dengue epidemic model with reaction-diffusion, impulse and Markov switching. By constructing an equivalent system, the well-posedness of the positive solution is proved. The main result is that sufficient conditions to guarantee the finite time contraction stability of the dengue model are acquired based on the average pulse interval method and the bounded pulse interval method. Furthermore, the numerical findings indicate the influences of impulse, control strategies and noise intensity on the FTCS.

The output gap, while inherently unobservable, plays a pivotal role in informing policymakers due to its significant implications for forecasting inflation rates and understanding the mechanisms of monetary policy transmission. Traditional filters frequently employed in estimating the output gap face criticism for being purely statistical and lacking economic theory. Conversely, estimates derived from Dynamic Stochastic General Equilibrium (DSGE) models encounter challenges stemming from the assumption of constant parameters over time. This study focuses on estimating the output gap for Brazil, employing a full specified DSGE model that incorporates Markov-Switching elements (MS-DSGE) to account for potential regime shifts. We introduce four model versions, some of which incorporate variations in volatilities and Taylor’s rule parameters. In order to compare our output gap estimate with other approaches, we perform prediction tests, both with the central bank’s reaction function and with the free price inflation Phillips curve. Our results in the first test indicate that the HP (Hodrick–Prescott) filter estimate performs better in the short and mid-term, but the MS-DSGE estimate presented better results in the long run. In the second exercise, no output gap series stands out among the approaches considered. In this context, the estimated output gap from the MS-DSGE framework emerges as a valuable asset within the arsenal available to policymakers, contributing meaningfully to their analytical toolkit.

A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier–Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier–Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier–Stokes equation with Markov switching. [ABSTRACT FROM AUTHOR]

AbstractThe study examines the stability of Indonesian Islamic Commercial Bank (ICB) and Islamic Rural Bank (IRB) by employing a Markov Switching Dynamic model of two regimes, stable (tranquil) and unstable (crisis). This study utilizes monthly data between December 2007 and April 2022. Findings show that both ICB and IRB have greater probabilities of remaining in the tranquil regime compared to the period of crisis. Even though ICB Z-scores have a wider range of volatility than IRB Z-scores, the ICB has been shown to recover from crises faster than the IRB. The differences in characteristics between ICB and IRB, as well as swings in the Z-score, do not provide resilience benefits. Thus, both ICB and IRB are equally vulnerable to the crisis. This study’s findings could be used to generate policy for the relevant stakeholders of Islamic banking industries.

The stochastic switching SIR epidemic model with saturated incidence and limited medical treatment is investigated in this paper. By using Lyapunov methods and Itô formula, we first prove that the system has a unique global positive solution with any positive initial value. Then combining inequality technique and the ergodic property of Markov switching, the sufficient conditions for extinction and persistence in the mean of the disease are established. The results demonstrate that increasing medical resources and improving supply efficiency can accelerate the transition from the persistent state to the extinct state. Meanwhile, the high incidence rate will slow down the extinction of the disease. Specially, the switching noise can induce the system to toggle between the extinct and persistent states. Finally, some numerical simulations are carried out to confirm the analytical results. [ABSTRACT FROM AUTHOR]

Objective Behavioral finance research delves into how investors' perceptions of the capital market and the decisions they make are influenced by psychological factors, ideas, and their willingness to take risks. In addition, it tries to identify the investors' decisions by investigating the psychological factors. The researchers have tried for several decades to explore the direct relationship between the sentiments and total index return by linear methods permanently. However, this research examines the asymmetrical relationship between investors' sentiments and fluctuations in the total index, categorized into recession and boom regimes. Generating instantaneous response functions based on regimes enables a comprehensive investigation of how investors' sentiments impact market fluctuations in distinct market conditions. Investors' perceptions of total index fluctuations revealed significant losses during various periods of market collapse. Consequently, this study explores the connection between the total index's behavior and investors' sentiments. Methods Four criteria were used in this research to assess the sentiments indirectly. First, the sentiments hybrid index was extracted in the 2011-2021 period using the main components analysis method. Then, the non-linear Markov switching model was used to investigate the asymmetric relationship between investors' sentiments and total index returns and fluctuations. Moreover, instantaneous response functions were used to investigate the effect of shocks on each research variable. Eviews12 and OxMetrics8 software types were used to estimate the research model. Results The findings affirm the presence of an asymmetric relationship between investors' sentiments, returns, and total index fluctuations during both recession and boom periods. Investors' reactions to market fluctuations were found to be positive and significant during the upward market trend of the capital market. However, investors' reactions to market fluctuations were negative during the downward market trend. Furthermore, the study revealed that an increase in returns during a bearish market trend elicited a negative response from investors, while in an upward market trend, it triggered a positive reaction. Moreover, extraction results of instantaneous response functions showed that the inserted shocks to the variables in recession and boom periods may lead to different reactions. Conclusion As per the research findings, the likelihood of market continuity stands at 41.54% during the boom regime and 58.46% during the recession regime. This shows the fact that the capital market's tendency to persist in the recession period is higher. Moreover, an examination of the derived instantaneous response functions from the model revealed that sentiment shocks can substantially alter stock market returns. The nature of these effects may vary depending on the prevailing market conditions (be it during a recession or a boom). The outcomes of this study enhance the understanding of investors and decisionmaking institutions regarding the impact of investor sentiments on capital market fluctuations and returns. This insight empowers decision-makers to formulate policies aimed at managing the impact of influential news and rumors, ultimately leading to heightened investor awareness and a reduction in market volatility. [ABSTRACT FROM AUTHOR]

This article aims to investigate suficient conditions for the stability of the trivial solution of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system. The novelty of this work is in the consideration of jump concentration points, which are not considered in classical works. The assumption of the existence of concentration points leads to additional constraints on jumps, jump times and relations between them. [ABSTRACT FROM AUTHOR]

In a national economy, are individual subnational regions business cycle takers or setters? We address this important regional policy question by investigating regional business cycles at NUTS-3 granularity in Poland (N = 73), using two metrics in parallel: GDP dynamics and unemployment. To extract the business cycle, we use a spatial Markov switching model that features both idiosyncratic business cycle fluctuations across regions (as a 2-state chain), as well as spatial interactions with other regions (as spatial autoregression). The posterior distribution of the parameters is simulated with a Metropolis-within-Gibbs procedure. We find a clear division into business cycle setters and takers, the latter being largely (but not only) non-metropolitan regions. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to understand and identify the cyclical fluctuations in cryptocurrency markets. To this end, we apply the Markov-Switching approach on daily prices of 17 selected digital currencies. This model allows us to capture the nonlinear structure in cryptocurrencies' prices. The empirical results clearly show potential difference(s) among digital currencies when they react to the varying levels of the pandemic's severity. The existence of two distinguishable states and each state seems to be characterized by different features of market cycle's phase for each cryptocurrency. So, the Covid19 pandemic affects asymmetrically the different market phases of digital currencies. Such findings can have insightful portfolios implications. [ABSTRACT FROM AUTHOR]

This contribution probes into ergodic stationary distribution for two stochastic SVELIT (susceptible-vaccinated-early latent-late latent-infective-treated) tuberculosis (TB) models to observe the impact of white noises and color noises on TB control in random environments. We first investigate the existence and uniqueness of ergodic stationary distribution (EUESD) for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions, and sufficient conditions on the extinction of disease are acquired. Next, sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established. Eventually, some numerical examples validate the theoretical findings. What's more, it has been observed that higher amplitude noises may lead to the eradication of TB, which is conducive to TB control. [ABSTRACT FROM AUTHOR]

COVID-19 adversely affected all market mechanisms, shocked economies, halted business operations, and disrupted supply chains. This study examines macroeconomic instability by assessing the commodities market in highly traded regimes using descriptive statistical analysis, the Economic Policy Uncertainty (EPU) Index, and Markov Regime Swapping (MRS) for data covering February 26 to November 30, 2020. The findings indicate that most commodities respond to stock values in both high and low-volatility regimes of supply and demand. Additionally, commodity prices are still in a low volatility regime due to COVID-19-related market uncertainty. The returns for oil, corn, gold, copper, natural gas, silver, and soybeans adapt to low macroeconomic uncertainty and variable rankings for COVID-19. In contrast, changes in COVID-19 deaths had no impact on natural gas or oil under any regime. As agricultural commodities and valuable metals have less negative feedback to exogenous variables than any other commodities, this model is useful for regulators and stockholders. The results suggest that in a global pandemic, portfolio managers and other stakeholders should use priceless metals like gold as a short-term hedge against systemic market risks to achieve macroeconomic stability and facilitate a rapid recovery in the green economy. [ABSTRACT FROM AUTHOR]