Markov Switching Process Research Articles

Fast Filtering in Switching Approximations of Nonlinear Markov Systems With Applications to Stochastic Volatility

We consider the problem of optimal statistical filtering in general non-linear non-Gaussian Markov dynamic systems. The novelty of the proposed approach consists in approximating the non-linear system by a recent Markov switching process, in which one can perform exact and optimal filtering with a linear time complexity. All we need to assume is that the system is stationary (or asymptotically stationary), and that one can sample its realizations. We evaluate our method using two stochastic volatility models and results show its efficiency.

Derivation and analysis of simplified filters

Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those arising in turbulence, in which effective low-dimensional representation of the desired probability distribution is challenging. Nonetheless recent advances have shown considerable success in filtering based on certain carefully chosen simplifications of the underlying system, which allow closed form filters. This leads to filtering algorithms with significant, but judiciously chosen, model error. The purpose of this article is to analyze the effectiveness of these simplified filters, and to suggest modifications of them which lead to improved filtering in certain time-scale regimes. We employ a Markov switching process for the true signal underlying the data, rather than working with a fully resolved DNS PDE model. Such Markov switching models haven been demonstrated to provide an excellent surrogate test-bed for the turbulent bursting phenomena which make filtering of complex physical models, such as those arising in atmospheric sciences, so challenging.

Leaders, followers, and equity risk premiums in booms and busts

Abstract We study an investment problem in which two asymmetric firms face competition and the regime characterizing the economic condition follows a Markov switching process. We derive the value functions and investment thresholds of the leader and follower. The option value of regime uncertainty is found to be quite important for the investment decision of firms. We also show the relationship between the equity risk premium and the economic cycle that has not been done in previous studies, which proxy economic conditions by the level of demand or other state variables.

Estimation and Solution of Models with Expectations and Structural Changes

SummaryIn this paper, we develop solutions for linearized models with forward‐looking expectations and structural changes under a variety of assumptions regarding agents' beliefs about those structural changes. For each solution, we show how its associated likelihood function can be constructed by using a ‘backward–forward’ algorithm. We illustrate the techniques with two examples. The first considers an inflationary program in which beliefs about the inflation target evolve differently from the inflation target itself, and the second applies the techniques to estimate a new Keynesian model through the Volcker disinflation. We compare our methodology with the alternative in which structural change is captured by switching between regimes via a Markov switching process. We show that our method can produce accurate results much faster than the Markov switching method as well as being easily adapted to handle beliefs departing from reality. Copyright © 2016 John Wiley & Sons, Ltd.

A novel seizure detection algorithm informed by hidden Markov model event states

Objective. Recently the FDA approved the first responsive, closed-loop intracranial device to treat epilepsy. Because these devices must respond within seconds of seizure onset and not miss events, they are tuned to have high sensitivity, leading to frequent false positive stimulations and decreased battery life. In this work, we propose a more robust seizure detection model. Approach. We use a Bayesian nonparametric Markov switching process to parse intracranial EEG (iEEG) data into distinct dynamic event states. Each event state is then modeled as a multidimensional Gaussian distribution to allow for predictive state assignment. By detecting event states highly specific for seizure onset zones, the method can identify precise regions of iEEG data associated with the transition to seizure activity, reducing false positive detections associated with interictal bursts. The seizure detection algorithm was translated to a real-time application and validated in a small pilot study using 391 days of continuous iEEG data from two dogs with naturally occurring, multifocal epilepsy. A feature-based seizure detector modeled after the NeuroPace RNS System was developed as a control. Main results. Our novel seizure detection method demonstrated an improvement in false negative rate (0/55 seizures missed versus 2/55 seizures missed) as well as a significantly reduced false positive rate (0.0012 h versus 0.058 h−1). All seizures were detected an average of 12.1 ± 6.9 s before the onset of unequivocal epileptic activity (unequivocal epileptic onset (UEO)). Significance. This algorithm represents a computationally inexpensive, individualized, real-time detection method suitable for implantable antiepileptic devices that may considerably reduce false positive rate relative to current industry standards.

Government spending multipliers and the zero lower bound

It is well-known that when the nominal interest rate hits the zero lower bound, the size of the fiscal multiplier can be large. The effectiveness of fiscal stimulus depends on the duration and the expected duration of the zero-lower-bound regime. Most studies fix this duration and therefore suffer from a bias. In this paper, we propose a way to estimate the government spending multiplier that allows this duration to be endogenously determined. Specifically, we incorporate into the Smets and Wouters (2007) model a monetary policy reaction function that follows a two-state Markov-switching process, and use data to pin down the transitional probability from one policy regime to the other. We then estimate the model and compute the fiscal multiplier using a data set that spans 1985:2–2015:3.

The determinants of regime switching in the natural gas and crude oil cointegrating relationship

The goal of this analysis is to find determinants of the endogenous regime-switching process underlying the cointegrating relationship between natural gas and crude oil. We do so by modeling the cointegrating equation as a two-state, Markov-switching process with time-varying transition probabilities. Many factors across energy markets and the macroeconomy were tried. Ultimately, we found that regime switching in the cointegrating relationship was driven by (a) natural gas supplies (though not crude oil supplies), (b) the deviation of the number of heating degree days from average (reflecting natural gas demand) and (c) the collapse of Enron. This result is consistent with previous research, which found crude oil to be exogenous in the cointegrating relationship. Last, we found that macroeconomic data has no effect on the transition probabilities.

Markov-Switching Time-Varying Copula Modeling of Dependence Structure between Oil and GCC Stock Markets

This paper proposes a Markov-switching copula model to examine the presence of regime change in the time-varying dependence structure between oil price changes and stock market returns in six GCC countries. The marginal distributions are assumed to follow a long-memory model while the copula parameters are supposed to evolve according to the Markov-switching process. Furthermore, we estimate the Value-at-Risk (VaR) based on the proposed approach. The empirical results provide evidence of three regime changes, representing precrisis, financial crisis and post-crisis, in the dependence structure between energy and GCC stock markets. In particular, in the pre- and post-crisis regimes, there is no dependence, while in the crisis regime, there is significant tail dependence. For OPEC countries, we find lower tail dependence whereas in non-OPEC countries, we see upper tail dependence. VaR experiments show that the Markov-switching time- varying copula model performs better than the time-varying copula model.

Skewness and kurtosis of multivariate Markov-switching processes

Exact formulae are provided for the calculation of multivariate skewness and kurtosis of Markov-switching Vector Auto-Regressive (MS VAR) processes as well as for the general class of MS state space (MS SS) models. The use of the higher-order moments in non-linear modeling is illustrated with two examples. A Matlab code that implements the results is available from the authors.

On the Markov-switching bilinear processes: stationarity, higher-order moments and β-mixing

This article investigates some probabilistic properties and statistical applications of general Markov-switching bilinear processes that offer remarkably rich dynamics and complex behaviour to model non-Gaussian data with structural changes. In these models, the parameters are allowed to depend on unobservable time-homogeneous and stationary Markov chain with finite state space. So, some basic issues concerning this class of models including necessary and sufficient conditions ensuring the existence of ergodic stationary (in some sense) solutions, existence of finite moments of any order and -mixing are studied. As a consequence, we observe that the local stationarity of the underlying process is neither sufficient nor necessary to obtain the global stationarity. Also, the covariance functions of the process and its power are evaluated and it is shown that the second (respectively, higher)-order structure is similar to some linear processes, and hence admit representation. We establish also sufficient conditions for the model to be mixing and geometrically ergodic. We then use these results to give sufficient conditions for mixing of a family of processes. A number of illustrative examples are given to clarify the theory and the variety of applications.

Evaluating forecasts of political conflict dynamics

There is considerable interest today in the forecasting of conflict dynamics. Commonly, the root mean square error and other point metrics are used to evaluate the forecasts from such models. However, conflict processes are non-linear, so these point metrics often do not produce adequate evaluations of the calibration and sharpness of the forecast models. Forecast density evaluation improves the model evaluation. We review tools for density evaluation, including continuous rank probability scores, verification rank histograms, and sharpness plots. The usefulness of these tools for evaluating conflict forecasting models is explained. We illustrate this, first, in a comparison of several time series models’ forecasts of simulated data from a Markov-switching process, and second, in a comparison of several models’ abilities to forecast conflict dynamics in the Cross Straits. These applications show the pitfalls of relying on point metrics alone for evaluating the quality of conflict forecasting models. As in other fields, it is more useful to employ a suite of tools. A non-linear vector autoregressive model emerges as the model which is best able to forecast conflict dynamics between China and Taiwan.

Modeling the complex dynamics and changing correlations of epileptic events

Patients with epilepsy can manifest short, sub-clinical epileptic “bursts” in addition to full-blown clinical seizures. We believe the relationship between these two classes of events—something not previously studied quantitatively—could yield important insights into the nature and intrinsic dynamics of seizures. A goal of our work is to parse these complex epileptic events into distinct dynamic regimes. A challenge posed by the intracranial EEG (iEEG) data we study is the fact that the number and placement of electrodes can vary between patients. We develop a Bayesian nonparametric Markov switching process that allows for (i) shared dynamic regimes between a variable number of channels, (ii) asynchronous regime-switching, and (iii) an unknown dictionary of dynamic regimes. We encode a sparse and changing set of dependencies between the channels using a Markov-switching Gaussian graphical model for the innovations process driving the channel dynamics and demonstrate the importance of this model in parsing and out-of-sample predictions of iEEG data. We show that our model produces intuitive state assignments that can help automate clinical analysis of seizures and enable the comparison of sub-clinical bursts and full clinical seizures.

Random Walk or Switching Regimes in Stock Prices? Evidence from Out-of-Sample Forecasts

We use monthly observations on general stock price indices, over January 2001–August 2013, in order to assesssimple stochastic time series models in terms of out-of-sample forecasts. Specifically, we examine the relativestrength of out-of-sample forecasts of a random walk, with and without drift, against that of a non-linearsegmented trends model where the switch between states is governed by a Markov chain. The forecastingperformance of these processes is assessed by the root mean squared error of short- and long-term out-of-sampleforecasts, varying from 1- to 12-month horizons. We obtain compelling evidence in favor of the Markovswitching process in forecasting stock prices over short and medium-term horizons and across all countriesconsidered. These results are most likely due to risk averse behavior of investors which has been amplified bythe recent financial crisis.

Double Markov Process blind estimation: Application to communication in a long memory channel

Also called a Markov switching process, a Double Markov Process (DMP) is an extension of the Hidden Markov Chain (HMC) where the observed process conditionally to the hidden one is modelled by a Markov process. This paper focuses on the estimation of a DMP model, the goal being twofold. First we provide the Cramer–Rao bound of the covariance matrix of any unbiased estimator in order to assess the accuracy limitations. Then we develop a DMP blind estimator for communication through a long memory channel. The results show the benefit of such a modelling in terms of both performance and complexity.

Using time-varying transition probabilities in Markov switching processes to adjust US fiscal policy for asset prices

This paper tests for nonlinear effects of asset prices on the US fiscal policy. By modeling government spending and taxes as time-varying transition probability Markovian processes (TVPMS), we find that taxes significantly adjust in a nonlinear fashion to asset prices. In particular, taxes respond to housing and (to a smaller extent) to stock price changes during normal times. However, at periods characterized by high financial volatility, government taxation only counteracts stock market developments (and not the dynamics of the housing sector). As for government spending, it is neutral vis-a-vis the asset market cycles. We conclude that, correcting the fiscal balance and, notably, the revenue side for time-varying effects of asset prices provides a more accurate assessment of the fiscal stance and its sustainability.

Stochastic volatility model with regime-switching skewness in heavy-tailed errors for exchange rate returns

A Bayesian analysis of the stochastic volatility model with regime-switching skewness in heavy-tailed errors is proposed using a generalized hyperbolic (GH) skew Student’s t -distribution. The skewness parameter is allowed to shift according to a first-order Markov switching process. We summarize Bayesian methods for model fitting and discuss analyses of exchange rate return time series. Empirical results show that interpretable regime-switching skewness can improve model fit and Value-at-Risk performance in a comparison against several other SV models with constant skewness or jump diffusions.

EARLY WARNING INDICATORS STUDY OF BANK RUNS IN INDONESIA : MARKOV-SWITCHING APPROACH

A run on a particular bank can lead to a banking crisis if it spreads to other banks (contagious effect). In the case of Indonesia, bank runs have also reoccurred time and again. In 1992, bank runs affected several national banks, subsequently precipitating the liquidation of one bank. Then in 1997/1998, bank runs developed into the worst banking crisis ever witnessed in the banking history of Indonesia. Considering the extent of losses attributable to bank runs and the banking crisis, extensive studies on the early warning indicators of bank runs are urgently required to prevent future bank runs and banking crises. This paper aims to comprehensively analyse the early warning indicators of bank runs for all banks in Indonesia, both during the sample period of 1990-2005 as well as during the banking crisis in 1997-1998. The study of early warning indicators of bank runs uses the Markov-Switching model. To calculate the transition probability from a tranquil state to a state of bank run uses the Markov-Switching process through an auto-regressive approach. The change in deposits held at each bank is used as a variable of bank runs. The results of Markov-Switching (MS) show that the MS model is robust as an early warning indicator of bank runs. This is reflected by testing, which was performed on the actual incident of 102 banks, showing that the MS model only produced false signals an estimated 0.69% - 2.08% of the time. Keywords: Bank Runs, Early Warning Indicators, Markov-SwitchingJEL Classification: C22, G21

KAJIAN INDIKATOR PERINGATAN DINI BANK RUNS DI INDONESIA: PENDEKATAN MARKOV-SWITCHING

A run on a particular bank can lead to a banking crisis if it spreads to other banks (contagious effect). In the case of Indonesia, bank runs have also reoccurred time and again. In 1992, bank runs affected several national banks, subsequently precipitating the liquidation of one bank. Then in 1997/1998, bank runs developed into the worst banking crisis ever witnessed in the banking history of Indonesia. Considering the extent of losses attributable to bank runs and the banking crisis, extensive studies on the early warning indicators of bank runs are urgently required to prevent future bank runs and bankingcrises. This paper aims to comprehensively analyse the early warning indicators of bank runs for all banks in Indonesia, both during the sample period of 1990-2005 as well as during the banking crisis in 1997-1998. The study of early warning indicators of bank runs uses the Markov-Switching model. To calculate the transition probability from a tranquil state to a state of bank run uses the Markov-Switching process through an auto-regressive approach. The change in deposits held at each bank is used as a variable of bank runs. The results of Markov-Switching (MS) show that the MS model is robust as an early warning indicator of bank runs. This is reflected by testing, which was performed on the actual incident of 102 banks, showing that the MS model only produced false signals an estimated 0.69% - 2.08% of the time.Keywords: Bank Runs, Early Warning Indicators, Markov-SwitchingJEL Classification: C22, G21

Time variation of CAPM betas across market volatility regimes

We investigate time variation in Captial Asset Pricing Model (CAPM) betas for Book-to-Market (B/M) and momentum portfolios across stock market volatility regimes. For our analysis, we jointly model market and portfolio returns using a two-state Markov-switching process, with beta and the market risk premium allowed to vary between ‘low’ and ‘high’ volatility regimes. Our empirical findings suggest strong evidence of time variation in betas across volatility regimes in almost all the cases for which the unconditional CAPM can be rejected. Although the regime-switching conditional CAPM can still be rejected in many cases, the time-varying betas help explain portfolio returns much better than the unconditional CAPM, especially when market volatility is high.

Markov-switching models and the unit root hypothesis in real US GDP

I find that real US GDP is better characterized as a trend stationary Markov-switching process than as having a (regime-dependent) unit root. I examine the effects of both assumptions on the analysis of business cycle features and their implications for the persistence of the dynamic response of output to a random disturbance.