Time-varying Transition Probabilities Research Articles

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.

Protocol-based filtering for fuzzy Markov affine systems with switching chain

This paper investigates the reduced-order filter design method for fuzzy Markov jump affine systems with dynamic event-triggered protocol and uncertain packet dropouts. Aiming at approximating the nonlinearities with high accuracy and broadening practical application, the fuzzy Markov jump affine systems associated with mode-dependent operating regions are developed. A novel nonhomogeneous Markov process is proposed to describe the generalized stochastic jumping among subsystems, whose time-varying transition probabilities are orchestrated by a higher-level deterministic switching signal. Compared with the conventional Markov process with arbitrary switchings, the average dwell-time strategy is adopted in the novel nonhomogeneous Markov process to improve the dynamic performance. A dynamic event-triggered protocol is provided to alleviate the network transmission burden by elongating the interval between any two consecutive events. Based on the variation of state-space partitions, nonsynchronous reduced-order generalized filters are considered. Under this framework, sufficient criteria are attained to ensure stochastic stability and prescribed l2−l∞ performance for the filtering error systems. Eventually, the theoretical findings are verified by two simulation examples.

Jointly forecasting the value-at-risk and expected shortfall of Bitcoin with a regime-switching CAViaR model

We explore the dynamic tail risk in the Bitcoin market by jointly estimating value-at-risk (VaR) and expected shortfall (ES) using the conditional autoregressive value-at-risk (CAViaR) model. To enable more accurate measurement, we construct a Markov regime-switching (MS) model in which the time-varying transition probability is driven by the information contained in asset price bubbles. This is motivated by prior evidence that bubbles are a key indicator of the economic cycle and contain important information on systemic risk. Using daily Bitcoin data from 2013 to 2021, the results provide strong evidence of a form of regime change in Bitcoin’s VaR and ES. Furthermore, the bubble index has a significant impact on tail risk and improves the model’s ability to estimate and predict VaR and ES.

Examining the long term relationships between energy commodities prices and carbon prices on electricity prices using Markov Switching Regression

The present work aims to quantitatively measure the relationships between the price of energy commodities, coal, gas natural, fuel oil, carbon prices and the price of wholesale electricity in the Iberian Electricity Market, using 2018 daily data. To examine this relationship, we considered both techniques, Markov-Switching Dynamic Regression and Markov-Switching Autoregressive Regression, and proposed two equations with electricity price and coal price as dependent variables. According to the parameters estimated in the model, coal and gas affect the cost of electricity moderately at times in the day that are highly recessive. During the 2018 daily periods analysed, the relative changes in gas and coal prices led to a loss of competitiveness of natural gas, increased by the moderate evolution of carbon prices, and therefore the cost of coal fell sharply in the recent past. The evolution of both time-varying transition probabilities and energy commodities prices variables is informative. The transition probabilities of staying in the same state change throughout our sample of energy commodities and wholesale electricity prices.

Impact of financial instability on international crude oil volatility: New sight from a regime-switching framework

In this paper, we investigate the dynamic impact of financial stress on crude oil volatility by employing a time-varying transition probabilities Markov regime-switching GARCH model (TVTP-MS-GARCH). Different from the existing work, we mainly consider the possible nonlinearity and regime changes among crude oil volatility and financial stress. First, the in-sample results strongly support the existence of the potential regime switches among the two financial fundamentals. Second, compared with the symmetric TVTP-MS-GARCH model, the model based on an asymmetric framework shows a better predictive performance in the out-of-sample findings. It implies that the dynamic impact of financial stress on crude oil exhibits an asymmetric feature. Finally, our findings are robust to several alternative checks, including other lags of financial stress and estimated window size. Thus, it is necessary to focus on the dynamic changes of financial stress for accurately predicting crude oil volatility.

Multiple epidemic waves as the outcome of stochastic SIR epidemics with behavioral responses: a hybrid modeling approach.

In the behavioral epidemiology (BE) of infectious diseases, little theoretical effort seems to have been devoted to understand the possible effects of individuals’ behavioral responses during an epidemic outbreak in small populations. To fill this gap, here we first build general, behavior implicit, SIR epidemic models including behavioral responses and set them within the framework of nonlinear feedback control theory. Second, we provide a thorough investigation of the effects of different types of agents’ behavioral responses for the dynamics of hybrid stochastic SIR outbreak models. In the proposed model, the stochastic discrete dynamics of infection spread is combined with a continuous model describing the agents’ delayed behavioral response. The delay reflects the memory mechanisms with which individuals enact protective behavior based on past data on the epidemic course. This results in a stochastic hybrid system with time-varying transition probabilities. To simulate such system, we extend Gillespie’s classic stochastic simulation algorithm by developing analytical formulas valid for our classes of models. The algorithm is used to simulate a number of stochastic behavioral models and to classify the effects of different types of agents’ behavioral responses. In particular this work focuses on the effects of the structure of the response function and of the form of the temporal distribution of such response. Among the various results, we stress the appearance of multiple, stochastic epidemic waves triggered by the delayed behavioral response of individuals.

Predictability of bull and bear markets: A new look at forecasting stock market regimes (and returns) in the US

The empirical literature of stock market predictability mainly suffers from model uncertainty and parameter instability. To meet this challenge, we propose a novel approach that combines dimensionality reduction, regime-switching models, and forecast combination to predict excess returns on the S&P 500. First, we aggregate the weekly information of 146 popular macroeconomic and financial variables using different principal component analysis techniques. Second, we estimate Markov-switching models with time-varying transition probabilities using the principal components as predictors. Third, we pool the models in forecast clusters to hedge against model risk and to evaluate the usefulness of different specifications. Our weekly forecasts respond to regime changes in a timely manner to participate in recoveries or to prevent losses. This is also reflected in an improvement of risk-adjusted performance measures as compared to several benchmarks. However, when considering stock market returns, our forecasts do not outperform common benchmarks. Nevertheless, they do add statistical and, in particular, economic value during recessions or in declining markets.

Markov switching quantile regression models with time-varying transition probabilities

Markov switching quantile regression models with time-varying transition probabilities

The Impact of Global Economic Policy Uncertainty, Geopolitical Risk and Oil Price on Stock Market: Evidence From Asean Countries

Using monthly data from January 1997 to July 2020, this study examines the impact of Global Economic Policy Uncertainty (GEPU), Geopolitical Risk (GPR), and oil price (WTI) on ASEAN stock exchanges such as the Jakarta Stock Exchange (JSE), Kuala Lumpur Composite Index (KLCI), Philippine Stock Exchange (PSI), Stock Exchange of Thailand (SET), and Vietnam Stock Index (VNI). We use a two-stage Markov switching model to model market returns as a time-varying transition probability Markovian process. The findings reveal some fascinating new information, such as the fact that global policy uncertainty has a strong negative impact on the bulk of ASEAN stock returns during periods of high volatility. Another finding shows that, contrary to assumptions, geopolitical concerns had no effect across all samples. We also discovered that, in both the low and high volatility regimes, oil price changes have a considerable impact on all ASEAN stock markets.

Structural breaks, macroeconomic fundamentals and cross hedge ratio

This paper proposes a new specification to estimate and evaluate the optimal hedge ratio. Due to the concern of structural breaks, we consider a time-varying transition probability regime switching model, which transition probability is driven by lower frequency macroeconomic fundamental variable, namely global policy uncertainty index. Based on the measure of variance reduction and expected utility gain, our model outperforms the specifications with fixed hedge ratio and OLS strategy with regime switching structural. Hence, it pays off to consider structural breaks and macroeconomic fundamental information. The excellent performance of the RS-TVTP-MIDAS model hinges on the ability to adjust strategies flexibly according to financial events.

On Stability of Network Control Systems with Switching Transmission Probabilities

The paper addresses modeling, stability analysis, and control of a class of networked control systems, in which the communication network, and thus the probability for successful transmission of sensor data, varies over time. This variation is modeled probabilistically by Markov chains with time-varying transition probabilities. The offline synthesis of output feedback controllers for this system class is addressed with focus on criteria for mean square stability.

Market Instability, Investor Sentiment, and Probability Judgment Error in Index Option Prices

In a natural experiment with index option prices, we study how probability judgment error, and probabilistic risk attitudes, characterize investors’ sentiment about the ranking of index option attractiveness, the weight they place on each rank, and their ability to discriminate between prices. We introduce a novel behavioral process that (1) characterizes investor sentiment about tail events in index option prices over time and probability ranks, (2) provides early warning signals of market instability, and (3) crash probability estimates from a closed form expression for the time varying transition probability that a seemingly stable market state will become unstable and crash.

The asymmetric impacts of international portfolio flows on Australian dollar returns

ABSTRACT This study investigates how equity portfolio flows affect the transition processes of exchange rate returns in Australia by employing a Markov-switching AR-GARCH-Jump model with time-varying transition probabilities. Three interesting findings are observed. Firstly, both GARCH and jump effects are totally different in the high-volatility and low-volatility states. Secondly, the net equity portfolio inflows increase exchange rate market fluctuations. Thirdly, the marginal effect of net equity flows is stronger in low-volatility state than in high-volatile state.

Robust Static Output-Feedback Control for MJLS with Non-Homogeneous Markov Chains: A Comparative Study Considering a Wireless Sensor Network with Time-Varying PER.

This paper deals with the problem of control through a semi-reliable communication channel, such as wireless sensor networks (WSN). Particularly, the case investigated is the one where the packet loss rate of the network is time-varying due to, for instance, variation in the distance between the nodes. Considering this practical motivation, the control system is modeled using a formulation based on discrete-time Markov jump linear systems (MJLS) with non-homogeneous Markov chains (time-varying transition probabilities). New control design conditions based on parameter-dependent linear matrix inequalities are proposed in order to solve this problem. The purpose is to demonstrate that this strategy is suitable to handle the networked control problem by comparing the temporal behavior of the closed-loop system with the Markovian controller and a standard proportional-integral-derivative (PID) controller. The case study presented in the paper considers the problem of the remote control of a Vertical Take-Off and Landing (VTOL) vehicle through a wireless communication channel. The network packet loss model employed in the case study is based on data collected on a wireless network workbench, which was previously developed and validated by the authors.

An adaptive approach for estimation of transition probability matrix in the interacting multiple model filter

The traditional Interacting Multiple Model (IMM) filters usually consider that the Transition Probability Matrix (TPM) is known, however, when the IMM is associated with time-varying or inaccurate transition probabilities the estimation of system states may not be predicted adequately. The main methodological contribution of this paper is an approach based on the IMM filter and retention models to determine the TPM adaptively and automatically with relatively low computational cost and no need for complex operations or storing the measurement history. The proposed method is compared to the traditional IMM filter, IMM with Bayesian Network (BNs) and a state-of-the-art Adaptive TPM-based parallel IMM (ATPM-PIMM) algorithm. The experiments were carried out in an artificial numerical example as well as in two real-world health monitoring applications: the PRONOSTIA platform and the Li-ion batteries data set provided by NASA. The Retention Interacting Multiple Model (R-IMM) results indicate that a better prediction performance can be obtained when the TPM is not properly adjusted or not precisely known.

HEDOS—a computational tool to assess radiation dose to circulating blood cells during external beam radiotherapy based on whole-body blood flow simulations

We have developed a time-dependent computational framework, hematological dose (HEDOS), to estimate dose to circulating blood cells from radiation therapy treatment fields for any treatment site. Two independent dynamic models were implemented in HEDOS: one describing the spatiotemporal distribution of blood particles (BPs) in organs and the second describing the time-dependent radiation field delivery. A whole-body blood flow network based on blood volumes and flow rates from ICRP Publication 89 was simulated to produce the spatiotemporal distribution of BPs in organs across the entire body using a discrete-time Markov process. Constant or time-varying transition probabilities were applied and their impact on transition time was investigated. The impact of treatment time and anatomical site were investigated using imaging data and dose distributions from a liver cancer and a brain cancer patient. The simulations revealed different dose levels to the circulating blood for brain irradiation compared to liver irradiation even for similar field sizes due to the different blood flow properties of the two organs. The volume of blood receiving any dose (V >0 Gy) after a single radiation fraction increases from 1.2% for a 1 s delivery time to 20.9% for 120 s delivery time for the brain cancer treatment, and from 10% (1 s) to 48.7% (120 s) for a liver cancer treatment. Other measures of the low-dose bath to the circulating blood such as the dose to small volumes of blood (D 2%) decreases with longer delivery time. Furthermore, we demonstrate that the blood dose-volume histogram is highly sensitive to changes in the treatment time, indicating that dynamic modeling of blood flow and radiation fields is necessary to evaluate dose to circulating blood cells for the assessment of radiation-induced lymphopenia. HEDOS is publicly available and allows for the estimation of patient-specific dose to circulating blood cells based on organ DVHs, thus enabling the study of the impact of different treatment plans, dose rates, and fractionation schemes.

Do U.S. and Japanese uncertainty shocks play important roles in affecting transition mechanisms of Japanese stock market?

This research investigates the impacts of U.S. and Japanese uncertainty shocks on the transition mechanisms of the Japan stock market dynamics by utilizing the Markov-switching GARCH-jump model with a time-varying transition probability matrix and analyzes the economic policy uncertainty shock of Japan, the economic policy uncertainty shock of the U.S., and the uncertainty shock about the U.S. equity market volatility. The empirical results demonstrate that the Japan stock market responds to most shocks with the exception of the U.S. economic policy uncertainty shock. The equity market volatility shock of the U.S. plays a more crucial role than the economic policy uncertainty shock of Japan. Furthermore, an increase in the U.S. equity market volatility shock reveals totally different signals in different volatile states. It signals an adverse belief about the Japan stock market in a high-volatile state, but signals an optimism viewpoint about the Japan stock market in a low-volatile state. Finally, the impact of the uncertainty shock about the U.S. stock market volatility is stronger in a high-volatile market than in a low-volatile market.

Optimal investment with time-varying transition probabilities for regime switching

Abstract This study aims to generalize the following result of McDonald and Siegel (1986) on optimal investment: it is optimal for an investor to invest when project cash flows exceed a certain threshold. This study presents other results that refine or extend this one by integrating timing flexibility and changes in cash flows with time-varying transition probabilities for regime switching. This study emphasizes that optimal thresholds are either overvalued or undervalued in the absence of time-varying transition probabilities. Accordingly, the stochastic nature of transition probabilities has important implications to the search for optimal timing of investment.

Markov-Switching Models with State-Dependent Time-Varying Transition Probabilities

Markov-switching models with covariate-dependent transition functions that are subject to exogenous discrete stochastic changes are considered. These changes are associated with simultaneous stochastic changes in the covariance structure of the observable variables. Simulation experiments are carried out to assess the quality of large-sample approximations to the distributions of the maximum-likelihood estimator and of related statistics in such a model, and to examine the implications of misspecification due to unaccounted breaks in the transition mechanism. The practical use of the model is illustrated by analyzing the relationship between Argentinian sovereign bond spreads and output growth.