Time-varying Transition Probabilities Research Articles

A Markov regime-switching framework to forecast El Niño Southern Oscillation patterns

The El Nino Southern Oscillation (ENSO) is an ocean–atmosphere phenomenon involving sustained sea surface temperature fluctuations in the Pacific Ocean, causing disruptions in the behavior of the ocean and atmosphere. We develop a Markov-switching autoregressive model to describe the Southern Oscillation Index (SOI), a variable that explains ENSO, using two autoregressive processes to describe the time evolution of SOI, each of which associated with a specific phase of ENSO. The switching between these two models is governed by a discrete-time Markov chain, with time-varying transition probabilities. Then, we extend the model using sinusoidal functions to forecast future values of SOI. The results can be used as a decision-making tool in the process of risk mitigation against weather- and climate-related disasters.

Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities

In this paper, problems of finite-time boundedness are investigated for a class of discrete-time switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities. The time-varying transition probabilities are described by a piecewise-constant matrix subject to a high-level average dwell time (ADT) switching. Sensor and actuator saturations are characterized by a vector-valued decomposition method and the stochastic nonlinearities are approximated by a statistical method. In general, not all trajectories originating from the admissible initial states could be stabilized in the mean square sense or sufficient conditions are too restrictive to yield feasible solutions. Therefore, the purpose of studying the problems addressed here is to design an output feedback controller via the ADT approach such that the resulting closed-loop systems are stochastically finite-time bounded and have a guaranteed disturbance attenuation capability. Simulation results demonstrate the potential and effectiveness of the theoretical results.

International Portfolio Flows and Exchange Rate Volatility for Emerging Markets

This paper investigates the effects of equity and bond portfolio inflows on exchange rate volatility, using monthly bilateral data for the US vis-a-vis eight Asian developing and emerging countries (India, Indonesia, South Korea, Pakistan, Hong Kong, Thailand, the Philippines, and Taiwan) over the period 1993:01-2012:11, and estimating a time-varying transition probability Markov-switching model. We find that net equity (bond) inflows drive the exchange rate to a high (low) volatility state. In particular, net bond inflows increase the probability of remaining in the low volatility state in the case of Pakistan, Thailand, and the Philippines, whilst they increase the probability of staying in the high volatility state in the case of Indonesia. Finally, net equity inflows from India, Indonesia, South Korea, Hong Kong, and Taiwan towards the US also increase the probability of staying in the high volatility state. These findings can be plausibly interpreted in terms of the return-chasing hypothesis and suggest that credit controls on portfolio flows could be an effective tool to stabilise the foreign exchange market.

The role of U.S. subprime mortgage-backed assets in propagating the crisis: Contagion or interdependence?

Though relatively small, the subprime mortgage-backed securities market is often identified as the source of the crisis that swept through the U.S. financial system from 2007 onwards. We investigate if its role in the propagation of the crisis was due to contagion or interdependence. Using a Markov-switching VAR with time-varying transition probabilities, we analyse the transmission of shocks across the financial system. We find little evidence of asset correlation changes between normal and crisis regimes and those that do occur are predominantly associated with liquidity variables. Otherwise, relationships are stable across market conditions, implying that the U.S. financial crisis was due to cross-market interdependencies rather than contagion. There is limited evidence that the deteriorating quality of the underlying assets can explain the transition from ‘normal’ market conditions to a high-volatility regime, although this is not consistent across model specifications.

The dynamic relationship between stock, bond and foreign exchange markets

This paper investigates whether the deviation of a currency from its fundamentally determined rate of return affects the relationship between interest rates and stock market yields. A time-varying transition probability, the Markov-switching vector autoregressive (MS-VAR) model, is utilized for this purpose. Wald and likelihood ratio tests are computed and used as model adequacy measures. In order to analyze the link between the variables, impulse–response functions are employed. A sticky price exchange rate model is used to show the fundamentally determined rate of return of currencies. States are defined as either overvalued or undervalued, depending on the position of the observed exchange rate compared to its fundamentally determined rate. The model is applied to four major currencies: the Australian Dollar, the Canadian Dollar, the Japanese Yen, and the British Pound. Transition between the states is linked to the risk-adjusted excess return (the Sharpe ratio) of the debt and equity markets of the respective currencies in order to understand whether over- and undervaluation is connected to the returns in these markets. The results provide evidence that the relationship between economic fundamentals and nominal exchange rates are subject to change depending on the over- or undervaluation of the currencies relative to their fundamentally determined rate of return. An extension of this result shows that the Sharpe ratios of debt and equity investments in the currencies influence the evolution of the transitional dynamics of the exchange rates’ deviation from their fundamental values.

The Effects of Oil Price Shocks on Transitional Dynamics of Turkish Business Cycle

In this study we investigated usefulness of oil price shocks in predicting switches between the growth phases of output in Turkey using monthly data for the period 1986-2014 by extending Markov Switching framework to include time-varying transition probabilities. We investigate the issue of whether the addition of various real oil price shocks to a univariate Markov Switching model for output can characterize the dynamics of business cycles better than the fixed transition probability version of Markov Switching model. The main results are summarized as follows. We find that although information about the lags of output growth and the information contained in transition probabilities combine to help identify which state of the economy has occurred in the TVTP model, oil price shocks are not the leading indicator of Turkish business cycle.

Impact of Global Shocks and Volatility on Herd Behavior in an Emerging Market: Evidence from Borsa Istanbul

This paper contributes to the literature on the financial integration in international stock markets by examining the dynamic relationship between global factors and herd behavior in an emerging market. Utilizing a time-varying transition probability Markov Switching model (TVTP-MS), we examine the role of global risk factors on investor behavior in Borsa Istanbul, dominated largely by foreign investors who hold a substantial share of the stocks traded in this market. Our tests yield three distinct market regimes - low, high, and extreme volatility - and evidence consistent with herd behavior during both the high and extreme volatility regimes. U.S. market related factors are found to dominate regime transitions and thus significantly contribute to herd behavior in all market sectors with the exception of industrials, suggesting that industrials are relatively immune from global shocks. Multivariate synchronization tests further suggest that herding regimes are perfectly synchronized across all market sectors, implying that none of the sectors can serve as a leading indicator for switching to (or from) the herding regimes.

A Tractable Framework for Analyzing a Class of Nonstationary Markov Models

We study a class of infinite-horizon nonlinear dynamic economic models in which preferences, technology and laws of motion for exogenous variables can change over time either deterministically or stochastically, according to a Markov process with time-varying transition probabilities, or both. The studied models are nonstationary in the sense that the decision and value functions are time-dependent, and they cannot be generally solved by conventional solution methods. We introduce a quantitative framework, called extended function path (EFP), for calibrating, solving, simulating and estimating such models. We apply EFP to analyze a collection of challenging applications that do not admit stationary Markov equilibria, including growth models with anticipated parameters shifts and drifts, unbalanced growth under capital augmenting technological progress, anticipated regime switches, deterministically time-varying volatility and seasonal fluctuations. Also, we show an example of estimation and calibration of parameters in an unbalanced growth model using data on the U.S. economy. Examples of MATLAB code are provided.

Effect of Global Shocks and Volatility on Herd Behavior in an Emerging Market: Evidence from Borsa Istanbul

ABSTRACTIn this article, we examine the dynamic relationship between global factors and herd behavior in an emerging market. Utilizing a time-varying transition probability Markov-switching model, we examine the role of global risk factors on investor behavior in Borsa Istanbul, which is dominated largely by foreign investors. Our tests yield three distinct market regimes (low, high, and extreme volatility) and evidence consistent with herd behavior during both the high- and extreme-volatility regimes. U.S. market–related factors are found to dominate regime transitions and thus significantly contribute to herd behavior in all market sectors with the exception of industrials, suggesting that industrials are relatively immune to global shocks. Multivariate synchronization tests further suggest that herding regimes are perfectly synchronized across all market sectors.

International Portfolio Flows and Exchange Rate Volatility for Emerging Markets

This paper investigates the effects of equity and bond portfolio inflows on exchange rate volatility, using monthly bilateral data for the US vis-a-vis eight Asian developing and emerging countries (India, Indonesia, South Korea, Pakistan, Hong Kong, Thailand, the Philippines, and Taiwan) over the period 1993:01-2012:11, and estimating a time-varying transition probability Markov-switching model. We find that net equity (bond) inflows drive the exchange rate to a high (low) volatility state. In particular, net bond inflows increase the probability of remaining in the low volatility state in the case of Pakistan, Thailand, and the Philippines, whilst they increase the probability of staying in the high volatility state in the case of Indonesia. Finally, net equity inflows from India, Indonesia, South Korea, Hong Kong, and Taiwan towards the US also increase the probability of staying in the high volatility state. These findings can be plausibly interpreted in terms of the return-chasing hypothesis and suggest that credit controls on portfolio flows could be an effective tool to stabilise the foreign exchange market.

Non‐fragile mixed ℋ ∞ / l 2 − l ∞ synchronisation control for complex networks with Markov jumping‐switching topology under unreliable communication links

This study is concerned with the non-fragile mixed ℋ∞/l 2 − l ∞ synchronisation control problem for discrete-time complex networks with Markov jumping-switching topology under unreliable communication links. The network topology under consideration is assumed to be governed by a Markov chain with time-varying transition probabilities (TPs). The variation of TPs is subject to a kind of slow switching signals; that is, the average dwell time (ADT) switching. The focus is on the design of non-fragile mixed mode-dependent/-independent controllers such that the underlying network reaches stochastic mean-square synchronisation with a mixed ℋ∞/l 2 − l ∞ performance level for an admissible switching signal with ADT. By using a new mixed ℋ∞/l 2 − l ∞ performance index, combined with the switched control method, the solutions to the considered problem are formulated. Finally, simulation results demonstrate the effectiveness of our proposed approach.

Time-varying expected momentum profits

This paper examines the time variations of expected momentum profits using a two-state Markov switching model with time-varying transition probabilities to evaluate the empirical relevance of recent rational theories of momentum profits. We find that in the expansion state the expected returns of winner stocks are more affected by aggregate economic conditions than those of loser stocks, while in the recession state the expected returns of loser stocks are more affected than those of winner stocks. Consequently, expected momentum profits display strong procyclical variations. We argue that the observed momentum profits are the realization of such expected returns and can be interpreted as the procyclicality premium. We provide a plausible explanation for time-varying momentum profits through the differential effect of leverage and growth options across business cycles.

Nonlinear effects of asset prices on fiscal policy: Evidence from the UK, Italy and Spain

We test for nonlinear effects of asset prices on the fiscal policy of three major European economies (the UK, Italy and Spain). We model primary government spending and government revenue as time-varying transition probability Markovian processes (TVPMS). We find that while in Italy fiscal policy is substantially neutral vis-a-vis asset price movements, fiscal authorities in the UK and Spain seem to track the dynamics of wealth. In particular, revenue-based fiscal policy interventions in the UK are particularly effective in counteracting shocks in the asset markets induced by sharp wealth fluctuations. Similarly, in Spain, the spending-side of the fiscal policy plays a dominant role in stabilizing stock and housing markets.

Business cycles synchronization in East Asia: A Markov-switching approach

This paper attempts to analyze the relationships between the ASEAN-5's business cycles. We examine the nature of business cycle synchronization trying to disentangle between intraregional and interregional synchronization by considering the important role of China, Japan and the US in synchronizing the activity within the ASEAN-5. We employ a time-varying transition probability Markov switching framework in order to allow the degree of synchronization to fluctuate across the phases of the business cycles. We provide evidence that the signals contained in some regional and global leading business cycles can impact the ASEAN-5's business cycles.

Finite-time [formula omitted] estimation for discrete-time Markov jump systems with time-varying transition probabilities subject to average dwell time switching

The time-varying character of transition probabilities is considered as finite piecewise homogeneous. This paper studies the problem of finite-time H∞ estimation for a class of discrete-time Markov jump systems with time-varying transition probabilities subject to average dwell time switching, sufficient conditions ensuring the Markov jump systems to be finite-time bounded and H∞ filtering finite-time boundness are established. Based on the results of finite-time boundness and average dwell time, the system trajectory stays within a prescribed bound. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.

Robust control for nonhomogeneous Markov jump processes: An application to DC motor device

This paper studies the problem of robust H∞ controller design for a class of uncertain Markov jump systems with time-varying transition probabilities, which follows nonhomogeneous jump processes. The time varying transition probability matrix is described as a polytope set. By Lyapunov function approach, under the designed controller, a sufficient condition is presented to ensure that the resulting closed-loop system is stochastically stable and that a prescribed H∞ performance index is satisfied. Finally, an application of a DC motor device is addressed to demonstrate the effectiveness of developed techniques.

Finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching

This paper investigates the problem of finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching. Another set of useful regime-switching models has been given for both fixed transition probability Markov switching models and time-varying transition probabilities. Based on the knowledge of average dwell time and multiple Lyapunov function, a novel sufficient condition for finite-time boundedness of H∞ filtering is derived and the system trajectory stays within a prescribed bound. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.

Robust control on saturated Markov jump systems with missing information

In this paper, a robust H∞ controller is designed for saturated Markov jump systems with uncertainties and time varying transition probabilities. The time-varying transition probability uncertainty is described as a polytope set. Stochastic stability is analyzed for the underlying systems by Lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed-loop system is stochastically stable and a prescribed H∞ performance is also achieved. Furthermore, the attraction domain of this Markov jump system is estimated and evaluated. A simulation example is given to show the effectiveness of the developed techniques.

The Credibility of Hong Kong's Currency Board System: Looking Through the Prism of MS-VAR Models with Time-Varying Transition Probabilities

The Credibility of Hong Kong's Currency Board System: Looking Through the Prism of MS-VAR Models with Time-Varying Transition Probabilities

Time Varying Transition Probabilities for Markov Regime Switching Models

Time Varying Transition Probabilities for Markov Regime Switching Models