Time-varying Transition Probabilities Research Articles

The relationship between renewable energy attention and volatility: A HAR model with markov time-varying transition probability

This study investigated whether a renewable energy attention (REA) index, based on natural language processing, Google search volume data, and dimensionality reduction methodology, can predict crude oil volatility. Considering the possible non-linear and time-varying effects, we adopted the time-varying transition probability Markov switching heterogeneous autoregressive-realized volatility (TVTP-MS-HAR-realized volatility (RV)) model. To further represent the impacts of REA, we developed an asymmetric TVTP-MS-HAR-RV model based on this model framework, i.e., the ASTVTP-MS-HAR-RV model. According to the results, the in-sample estimates indicated that West Texas Intermediate (WTI) volatility is more affected by negative REA shocks than by positive ones. Moreover, REA predicted WTI volatility better during low-volatility periods than in high ones. According to the out-of-sample findings, the ASTVTP-MS-HAR-RV-F model outperformed other competing models, indicating that time-varying transition probabilities and REA information can significantly improve volatility forecasting performance.

Flexible markov-switching models with evolving regime-specific parameters: an application to Brazilian business cycles

ABSTRACT 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.

Proportional-Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks.

This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

Generating and understanding human daily activity sequences using Time-Varying Markov Chain models

Human activity patterns have raised broad interests across fields and activity-based modeling has been applied to analyze travel behaviors, effects of policies, etc. In this paper, we examined daily activity sequences from large volumes of datasets collected in the Tokyo Metropolitan Area over thirty years. We show that, using a simple time-varying (inhomogeneous) Markov Chain model, activity sequences at the individual level can be generated with high accuracy. The predictive power of the model is comparable to neural network models when generating activity sequences for each administrative region. The results are surprising considering the huge number of potential activity sequences and the complicated process of activity planning. A fundamental relationship between time-varying Markov Chain models and Multinomial Logit models is recognized to understand the unexpected accuracy. A new mechanism is proposed on how people make daily activity plans from the perspective of cost and utility, where the probability of one plan being chosen is the same as the probability of it being generated by the Markov Chain model. From this perspective, the Markov process becomes a utility-based model. Furthermore, given the average time-varying transition probabilities over a large spatial and temporal scale, the Markov Chain model for any specific area is reconstructed with six parameters. The generation accuracy using the reconstructed model is examined. Moreover, the statistical characteristics of the costs assigned to the Markov Chain model are investigated.

Nonfragile observer-based event-triggered fuzzy tracking control for fast-sampling singularly perturbed systems with dual-layer switching mechanism and cyber-attacks

This paper investigates the problem of nonfragile observer-based tracking control for a class of fuzzy fast-sampling singularly perturbed systems (SPSs) with sensor saturation, which subject to event-triggered scheme and random cyber-attacks. The switching topology of the fast-sampling SPSs is dominated by a dual-layer switching mechanism, in this case, the Markov process in the underlying system is nonhomogeneous and its time-varying transition probabilities (TPs) are governed by a persistent dwell-time switching signal. First, in order to avoid asynchronous phenomenon of premise variable between the fuzzy fast-sampling SPSs and the fuzzy controller under network environments, the non-parallel distributed compensation (non-PDC) technique is applied to improve the design flexibility and reduce the conservativeness of the results. Furthermore, a novel fuzzy tracking control design scheme is proposed, in which integrating the fuzzy nonfragile observer and reference model signal into the synthetic design of the tracking controller can be expected to reduce the tracking error. Second, by constructing a well-designed time-delay and mode-dependent Lyapunov function, some sufficient conditions are derived such that the closed-loop system is mean-square exponential stable and with extended dissipative tracking performance. Finally, the effectiveness and applicability of the proposed control protocol are illustrated by two simulation examples.

Liquidity and realized volatility prediction in Chinese stock market: A time-varying transitional dynamic perspective

Basing on the features of emerging Chinese stock market, this article discusses whether sharply deteriorating liquidity propels the stock market into a “crisis” state and investigates the dynamic impacts of the market liquidity on volatility forecasting. We construct the Markov-switching (MS) liquidity-adjusted HAR models with liquidity from the perspective of time-varying transition probabilities (TVTP). Empirical evidence suggests that a sharp deterioration in liquidity increases the probability of a “crisis” state for China's stock market. Out-of-sample forecasting results demonstrate that our proposed TVTP-MS-HAR-CJ-LIQ model, combining TVTP and MS-HAR-CJ with liquidity, substantially improves the predictive performance. Considering liquidity's impact from the TVTP perspective is suggested for the emerging but attention-attracting Chinese stock market.

Exploring the nexus between monetary uncertainty and volatility in global crude oil: A contemporary approach of regime-switching

Understanding the complex relationship between global crude oil market volatility and monetary uncertainty motivates the study. Understanding crude oil's volatility is crucial because it affects the economy and geopolitics. Monetary uncertainty, caused by monetary policy decisions, exchange rate fluctuations, and global economic conditions, could affect crude oil markets. Thus, monetary uncertainty and crude oil volatility must be examined to understand the dynamics and inform policy. In this empirical work, we examine the effects of monetary uncertainty on global crude oil price volatility using a time-varying transition probabilities Markov regime-switching GARCH model (TVTP-MS-GARCH). Our approach differs from prior research by considering the potential nonlinearity and shifting patterns in the relationship between crude oil volatility and monetary uncertainty. Our in-sample analysis provides interesting evidence for regime changes between the two monetary variables. The results of our out-of-sample testing show that the asymmetric TVTP-MS-GARCH model outperforms the symmetric version in predicting crude oil volatility. This suggests that monetary uncertainty has an asymmetrical impact on crude oil price volatility. We perform several robustness tests to validate our findings, including alternate lag specifications of monetary uncertainty and varying estimation window sizes. These tests further reinforce the importance of considering the dynamic changes in monetary uncertainty when attempting to predict crude oil volatility. Overall, our research highlights the need for a more nuanced approach to understanding the relationship between crude oil prices and monetary uncertainty.

Disturbance-Observer-Based Finite-Time Antidisturbance Control for Markov Switched Descriptor Systems With Multi-Disturbances and Intermittent Measurements

This paper is concerned with the finite time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> composite anti-disturbance control problem for Markov switched descriptor systems with multiple disturbances and packet loss via a disturbance observer. Significantly, the switching topology of descriptor systems is controlled by nonhomogeneous Markov switching processes, whose time-varying transition probability is limited by a convex hull. Subsequently, a Bernoulli random variable is exploited to characterize the intermittent measurement mode behavior of controller-actuator packet loss. Furthermore, the stochastic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> finite time boundiness of the composite system and simultaneously suppression and rejection of external disturbances are established by resorting to disturbance observer-based robust control (DOBC) strategy and a new stochastic Lyapunov function technique. More importantly, a relaxed variable method is provided to eliminate the coupling between Lyapunov variables and the system matrix in the process of stability analysis, instead of eliminating the coupling by means of commonly-used traditional inequalities, which effectively increases the flexibility of the obtained stable results and greatly reduces the computational complexity of controller/observer in the existing works. Finally, the effectiveness and practicability of the developed results are verified by two practical engineering models.

Cost-Effectiveness Analysis of Siltuximab for Australian Public Investment in the Rare Condition Idiopathic Multicentric Castleman Disease.

This paper presents an Australian model that formed part of the health technology assessment for public investment in siltuximab for the rare condition of idiopathic Multicentric Castleman Disease (iMCD) in Australia. Two literature reviews were conducted to identify the appropriate comparator and model structure. Survival gain based on available clinical trial data were modelled using an Excel-based model semi-Markov model including time-varying transition probabilities, an adjustment for trial crossover and long-term data. A 20-year horizon was taken, and an Australian healthcare system perspective was adopted, with both benefits and costs discounted at 5%. The model was informed with an inclusive stakeholder approach that included a review of the model by an independent economist, Australian clinical expert opinion and feedback from the Pharmaceutical Benefits Advisory Committee (PBAC). The price used in the economic evaluation reflects a confidential discounted price, which wasagreed to with the PBAC. An incremental cost-effectiveness ratio of A$84,935 per quality-adjusted life-year (QALY) gained was estimated. At a willingness-to-pay threshold of A$100,000 per QALY, siltuximab has a 72.1% probability of being cost-effective compared with placebo and best supportive care. Sensitivity analyses results were most sensitive to the length of interval between administrations (from 3- to 6-weekly) and crossover adjustments. Within a collaborative and inclusive stakeholder framework, the model submitted to the Australian PBAC found siltuximab to be cost-effective for the treatment of iMCD.

Accelerating peak dating in a dynamic factor Markov-switching model

The dynamic factor Markov-switching (DFMS) model introduced by Diebold and Rudebusch (1996) has proven to be a powerful framework for measuring the business cycle. We extend the DFMS model by allowing for time-varying transition probabilities, intending to accelerate the real-time dating of business cycle peaks. Time-variation of the transition probabilities is brought about endogenously using the score-driven approach and exogenously using the term spread. In a real-time application using the four components of The Conference Board’s Coincident Economic Index for 1959–2020, we find that signaling power for recessions is significantly improved. We are able to date the 2001 and 2008 recession peaks four and two months after the peak date, which is four and ten months before the NBER.

Fiscal and monetary policy coordination and debt sustainability in the CEMAC zone: Evidence from a Markov regime-switching model

This paper investigates the nature of fiscal and monetary policy implemented in the Economic and Monetary Community of Central Africa (CEMAC) and its impact on long-run debt sustainability. The study employs a two-state Markov regime-switching model to the fiscal and monetary policy reaction functions of the six CEMAC countries using time series data from 1970 to 2020. The fiscal regime is regarded as active if the coefficient of debt is positive, while it is considered passive if the coefficient is negative and significant. Regarding monetary policy, an active regime is reported if the coefficient of inflation is positive; otherwise, the monetary policy regime is regarded as passive. In addition, the transition probability and time-varying transition probability are estimated to assess the nature of policy-mix coordination. The findings highlight unsustainable fiscal regimes in Equatorial Guinea and Chad, balanced results for Gabon and Congo, while Cameroon and the Central African Republic have sustainable fiscal regimes. Concerning monetary policy, a sustainable monetary regime is found for Cameroon and Equatorial Guinea, with balanced results for Congo, while evidence of an unsustainable monetary regime is found for the Central African Republic, Chad, and Gabon.

Output Feedback Control of Piecewise Homogeneous Semi-Markov Jump Systems

This brief addresses the output feedback control problem of semi-Markov jump systems with unfixed transition probabilities. A high level homogeneous Markov chain is employed to describe the variation of transition probabilities of the piecewise embedded homogeneous Markov chain. After studying the influence of transition probabilities on the system dynamics, and relaxing the requirement of Lyapunov function at jump instants, improved stability conditions are proposed which are tightly associated with the time-varying transition probabilities. Finally, a numerical example and an RLC circuit are presented to show the usefulness of incorporating the information of transition probabilities and to illustrate the effectiveness of the designed controllers.

Output-Feedback Control for Fuzzy Singularly Perturbed Systems: A Nonhomogeneous Stochastic Communication Protocol Approach.

In this study, the output-feedback control (OFC) strategy design problem is explored for a type of Takagi-Sugeno fuzzy singular perturbed system. To alleviate the communication load and improve the reliability of signal transmission, a novel stochastic communication protocol (SCP) is proposed. In particular, the SCP is scheduled based on a nonhomogeneous Markov chain, where the time-varying transition probability matrix is characterized by a polytope-structure-based set. Different from the existing homogeneous Markov SCP, a nonhomogeneous Markov SCP depicts the data transmission in a more reasonable manner. To detect the actual network mode, a hidden Markov process observer is addressed. By virtue of the hidden Markov model with partly unidentified detection probabilities, an asynchronous OFC law is formulated. By establishing a novel Lyapunov-Krasovskii functional with a singular perturbation parameter and a nonhomogeneous Markov process, a sufficient condition is exploited to guarantee the stochastic stability of the resulting system, and the solution for the asynchronous controller is portrayed. Eventually, the validity of the attained methodology is expressed through a practical example.

H∞ consensus for stochastic Markov jump multi-agent systems with imperfect time-varying transition probabilities and multiplicative noise

In this paper, the H∞ consensus control problem for Markov jump multi-agent systems with imperfect time-varying transition probabilities is studied. Both the transition probability matrix and the higher-level transition probability matrix are considered to be partly unknown. What’s more, the multiplicative noise is considered in the model to describe the factors from the changing environment. Sufficient conditions about state feedback controllers are derived by less linear matrix inequalities (LMIs) and are more convenient to program compared with the previous works. At last, the simulations are supplied to illustrate the effectiveness of the conclusions.

Extended Dissipative Sliding-Mode Control for Discrete-Time Piecewise Nonhomogeneous Markov Jump Nonlinear Systems.

This article analyzes the problem of the sliding-mode control (SMC) design for discrete-time piecewise nonhomogeneous Markov jump nonlinear systems (MJNSs) subject to an external disturbance with time-varying transition probabilities (TPs). A discrete-time asynchronous integral sliding surface is constructed, which yields matched-nonlinearity-free sliding-mode dynamics (SMDs). Then, by using the mode-dependent Lyapunov function technique, a sufficient condition is established for ensuring the stochastic stability of SMD with extended dissipation. The solution to designing controller gains is obtained. Moreover, an SMC law and an adaptive law are, respectively, derived for driving the system trajectories to move into a predetermined sliding-mode region with specified precision. Finally, the feasibility and effectiveness of the new design are verified and demonstrated by a simulation example.

Asymptotic properties of the maximum likelihood estimator in regime-switching models with time-varying transition probabilities

Summary Time-varying transition probability (TVTP) regime-switching models extend the constant regime transition probability in Markov-switching models to include information from observations. We show consistency and asymptotic normality of the maximum likelihood estimator (MLE) in general TVTP regime-switching models where the conditional distribution of $Y_t$ depends on lagged regimes. Consistency of the MLE is also shown under misspecification. The assumptions are verified in regime-switching autoregressive models with widely applied TVTP specifications. A simulation study examines the finite-sample distributions of the MLE and compares the asymptotic variance estimates constructed from the Hessian matrix and the outer product of the score. The simulation results favour the latter. As an empirical example, we compare three leading economic indicators in terms of describing U.S. industrial production.

Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme

This paper aims to design a robust observer-based dissipative controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems with nonhomogeneous Markov jumps through a non-parallel distributed compensation (non-PDC) scheme. Based on a mode-dependent nonquadratic Lyapunov function, the final form of the stabilization conditions is expressed as linear matrix inequalities in a less conservative manner. To be specific, this paper proposes a decoupling technique that can address the inherent nonconvex terms by extracting them from the stabilization conditions, where all slack variables are set to be fuzzy-basis-dependent for less conservative performance. Furthermore, the proposed stabilization method adopts a one-step design strategy that simultaneously designs the fuzzy observer and control gains without any iteration procedures by employing a positive tuning parameter. In particular, the time-varying transition probabilities included in the stabilization conditions are effectively removed using a modified relaxation technique that can avoid excessive use of free weighting matrices. Finally, based on four examples, the validity of the proposed method is verified through comparison with other studies.

Saturation control for fuzzy markovian switching systems with singularly perturbation and cyber-attacks

This paper is concerned with the issue of saturation control for discrete-time fuzzy Markov switching singularly perturbed systems. To describe the dynamic stochastic jumping behavior of system states, a novel nonhomogeneous Markov process is proposed, whose time-varying transition probabilities are orchestrated by a higher-level deterministic switching signal. Additionally, a novel control law is built by considering the random occurrence of cyber-attacks, and cyber-attacks rates are uncertain. Meanwhile, the saturation mechanism is adopted in designing an asynchronous controller, which is capable of eliminating the impact of cyber-attacks to a certain extent. In the end, two simulation results are provided to verify the effectiveness of the proposed methodology.

Dynamic asset allocation strategy using a state-dependent Markov model: Applications to international equity markets

This paper investigates the performance of an asset allocation strategy that relies on the state-dependent correlation between emerging and developed markets. We utilize a state-dependent Markov Model that employs a time-varying transition probability and uses the U.S. term spread differential as a market phase identifier. We show that by relying on the spillover effect of U.S. monetary policies on international equity markets, international investors can optimize returns on their investments by using a state-dependent model when diversifying their portfolios towards less volatile markets. Two states and optimal tangency portfolios reveal superior performance even after consideration of transaction costs. The effect of the U.S. term spread on equity returns is more apparent after the Global Financial Crisis; when positive (negative) term spread differentials are associated with an increased likelihood of being in a bull (bear) market.

The transmission of financial shocks and leverage of financial institutions: An endogenous regime switching framework

We conduct a novel empirical analysis of the role of leverage of financial institutions for the transmission of financial shocks to the macroeconomy. For that purpose we develop an endogenous regime-switching structural vector autoregressive model with time-varying transition probabilities that depend on the state of the economy. We propose new identification techniques for regime switching models. Recently developed theoretical models emphasize the role of bank balance sheets for the build-up of financial instabilities and the amplification of financial shocks. We build a market-based measure of leverage of financial institutions employing institution-level data and find empirical evidence that real effects of financial shocks are amplified by the leverage of financial institutions in the financial-constraint regime. We also find evidence of heterogeneity in how financial institutions, including depository financial institutions, global systemically important banks and selected nonbank financial institutions, affect the transmission of shocks to the macroeconomy. Our results confirm the leverage ratio as a useful indicator from a policy perspective.