Changjin kim korea university james morley washington university in st. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markovswitching rational expectations models, and we develop an algorithm to check these conditions in practice. Advances in markovswitching models applications in. We consider markov switching autoregressions of order 1 or msar1 with only two different regimes. Threshold and markov switching models of regime change this section describes the threshold and markov switching approaches to modeling regime switching using a specific example.
The key difference between tar and markov switching models is that, under the former, the state variable is assumed known and observable, while it is latent in msms for instance in the case of. A markovswitching model of business cycle dynamics with a postrecession bounceback effect. This book is a collection of stateoftheart papers on the properties of business cycles and financial analysis. The aim of this book is to impart the finite mixture and markov switching approach to statistical modelling to a wideranging community. Hamiltons paper initiated a large number of applications of markovswitching models, and these models are now a. We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forwardlooking markov switching rational expectations models, and we develop an algorithm to check these conditions in practice. This includes not only statisticians, but also biologists, economists, engineers, financial agents, market researcher, medical researchers or any other frequent user of statistical models. Jun 08, 2016 markov switching autoregression models. It provides a way to model the dependencies of current information e. Markov switching autoregressive models for interpreting. One possibility is to obtain forecasts as the weighted average of the forecasts based on the parameter estimates of each regime. A test of using markovswitching garch models in oil and. Exhaustiveness requires to refer to the recent developments of sims and zha 2006. This book proposes new methods to value equity and model the markowitz efficient frontier using markov switching models and provide new evidence and solutions to capture the persistence observed in stock returns across developed.
The introduction surveys the existing methods and new results of the last decade. Introduction to markovswitching regression models using the. The weights are the smoothed probabilities of each regime, as obtained for example via the kims smoothing algorithm. Understanding markovswitching rational expectations models.
Application markov switching regression ar 24 to evaluate the sensitivity of maximum likelihood estimation based on gaussian model misspecification for endogenous switching models, we had a battery of monte carlo experiments in which the process of generating the correct data is endogenous switching models are nongaussian. Markov switching autoregression models chad fulton. These models can quickly adapt to variations in the unconditional volatility level, which improves risk predictions see ardia, 2008. Modeling business cycle fluctuations through markov switching. Following hamilton 1989, 1994, we shall focus on the markov switching ar model. A markov model is a stochastic model which models temporal or sequential data, i.
Markovswitching garch models have become popular methods to account for regime changes in the conditional variance dynamics of time series. Statespace models with regime switching department of. Researchers familiar with the subject also will profit from reading this book. Later studied the structural break in the variance of growth rate of gdp for the. Markov switching regressions were introduced in econometrics by. A markovswitching model of business cycle dynamics with a. We extend the markovswitching dynamic factor model to account for some of the specificities of the daytoday monitoring of economic developments from. Time varying transition probabilities for markov regime. It applies the hamilton 1989 filter the kim 1994 smoother. We perform a largescale empirical study in order to compare the forecasting performances of singleregime and markovswitching garch msgarch models from a risk management perspective.
Markovswitching models are not limited to two regimes, although tworegime models are common. Lecture outline contd 6 ms model of conditional variance switching arch models switching garch models 7 ms model of conditional mean and variance 8 application. Guidolin 15 simulating from ms models a mixture of normal densities is a weighted sum of normal densities, in which the weights are themselves random variables and may change over time o in the case of ms, weights are random state probabilities over time. Modeling regime shifts markov switching models hidden markov model applications thesis pdf available june 2016 with 421 reads how we measure reads.
Markov switching models msms are probabilistic models that em ploy multiple sets of. In this paper, we test the use of markovswitching ms garch msgarch models for trading either oil or natural gas futures. Markov switching models are not limited to two regimes, although tworegime models are common. In particular, suppose we are interested in modeling the sample path of a time series, t y t t 1, where y t is a scalar, stationary, random variable. Markov regimeswitching and some state space models in. So, the models were also estimated on monthly data.
In financial econometrics, the markov switching multifractal msm is a model of asset returns developed by laurent e. An application to roadway safety a draft, august, 2008 a dissertation submitted to the faculty of purdue university by nataliya v. Most of the literature mentioned above allows for multivariate versions of the markov switching autoregressive model. Markovswitching with constant transition probabilities dependent on the prior or lagged regime. Markov switching garch models msgarch in r rstatsgsoc. Poisson model, twostate markov switching negative binomial model, and standard zeroin. It is composed of states, transition scheme between states, and emission of outputs discrete or continuous. Applications in business cycle research and finance james d. Can the markov switching model forecast exchange rates. The individual contributions cover new advances in markovswitching models with applications to business cycle research and finance. Outline 1 when we use markovswitching regression models 2 introductory concepts 3 markovswitching dynamic regression predictions state probabilities predictions level predictions state expected durations transition probabilities 4 markovswitching ar models statacorp markovswitching regression in stata october 22 3 1. Latent class analysis for intensive longitudinal data, hidden.
One approach, in the classical framework, approximates the likelihood function. Pt price of stock dt dividend coefficient of relative risk aversion pt dt k 1 ke tdt k 1. This notebook provides an example of the use of markov switching models in statsmodels to replicate a number of results presented in kim and nelson 1999. The literature on hidden markov models and markov switching time series models is now quite extensive. The dynamics of the observed process is driven by the dynamics of the latent one, so that the regimes of the hidden process can be reconstructed by the series of observations. Threshold and markovswitching models of regime change this section describes the threshold and markovswitching approaches to modeling regimeswitching using a specific example. Markov switching models, business cycles, msvar, iran. This discussion paper series represents research workinprogress and is. In currency and equity series, msm compares favorably with. In this section, we rst illustrate the features of markovian switching using a simple model and then discuss more general.
The formulation of the problem described here, in which all. Msre models are more complicated than linear rational expectations models since the agents of the model must be allowed to take account of the possibility of future regime changes when formingexpectations. We use three examples, based on the new keynesian model of monetary policy, to illustrate our technique. Hmm hidden markov models, msar markov switching autoregressive, mskf markov switching kalman filter twolevel hmm, msar, mskf tihomir asparouhov, bengt muth. This book should help newcomers to the field to understand how finite mixture and markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated. Droumaguet, matthieu 2012, markovswitching vector autoregressive. Markov switching models in classical performance and risk analysis.
Markovswitching regressions were introduced in econometrics by. Markovswitching rational expectations models 2 2006, 2007, and farmer, waggoner, and zha 2008a. Hidden markov models in time series, with applications in. Markovswitching regressions were introduced in econometrics by goldfeld and quandt 1973, the likelihood function for which was. The individual contributions cover new advances in markov switching models with applications to business cycle research and finance. Taiwans short term interest rates 9 concluding remarks c. The subset dt can be chosen in advance with a simpler. Nstate endogenous markov switching models shihtang hwuy changjin kimz jeremy pigerx december 2015 abstract. Stationarity and ergodicity conditions are given, and an easytocheck general sufficient stationarity condition based on a tailormade norm is introduced. The model in this thesis is based on a mixture of normal distributions, extended to include a markov switching behaviour. Abstract we develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of.
Markov state switching models are a type of specification which allows for the transition of states as an intrinsic property of the econometric model. To set the stage for the rest of the course, we will describe in the next two sections a number of representative examples of hidden markov models in applications taken from a variety of. Understanding markov switching rational expectations models roger e. Closedform solution of dsges and assetpricing implications lucas tree model with crra utility. Then the finite markov mixture distribution is outlined, with emphasis on extensions of markov switching models. Forecasting risk with markovswitching garch models. We find that msgarch models yield more accurate valueatrisk, expected shortfall, and lefttail distribution forecasts than their singleregime counterparts for daily, weekly, and tenday equity logreturns. An important advantage of markov switching models over zeroin. An r package for hidden markov models ingmar visser university of amsterdam maarten speekenbrink university college london abstract this introduction to the r package depmixs4 is a slightly modi ed version ofvisser and speekenbrink2010, published in the journal of statistical software. Such type of statistical representations are well known and utilized in different problems in the field of economics and finance. Msm captures the outliers, logmemorylike volatility persistence and power variation of financial returns.
This book proposes new methods to value equity and model the markowitz efficient frontier using markov switching models and provide new evidence and solutions to capture the persistence observed in stock returns across developed and emerging markets. Finite mixture and markov switching models sylvia fruhwirth. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. Pdf modeling regime shifts markov switching models. Francq and zakoian 2001 have investigated markov switching arma models and. Statespace models with regime switching the mit press. Pdf modeling regime shifts markov switching models hidden. The markov regime switching model is a popular approach, much in behalf of the way it takes the shifts in the time series behaviour into account. A markov switching model is constructed by combining two or more dynamic models via a markovian switching mechanism.
A way to cope with this problem is provided by markovswitching garch models msgarch whose parameters vary over time according to some regimes. We develop an nregime markov switching regression model in which the latent state variable driving the regime switching is endogenous. Request pdf advances in markovswitching models this paper serves as a partial introduction to and survey of the literature on markovswitching models. In particular, distinct attention is devoted to the ability of markov switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypothesesformulated in the light of financial theories, and to their. Latent class analysis for intensive longitudinal data. Markov switching models are a popular family of models that introduces. Here, we only give an introduction to the main ideas by having a detailed look at a simple, but nontrivial example in the following.
In financial econometrics, the markovswitching multifractal msm is a model of asset returns developed by laurent e. Using weekly data from 7 january 1994 to 31 may 2019, we tested the next trading rule. Regimeswitching models uc san diego department of economics. Advances in markovswitching models applications in business. Fisher that incorporates stochastic volatility components of heterogeneous durations. Valuing equity when discounted cash flows are markov. We perform a largescale empirical study in order to compare the forecasting performances of singleregime and markov switching garch msgarch models from a risk management perspective. In the example above, we described the switching as being abrupt.
The package msgarch allows the user to perform simulations as well as maximum likelihood and mcmcbayesian estimations of a very large class of markovswitching garchtype models. Time varying transition probabilities for markov regime switching models marco bazzi a, francisco blasques b siem jan koopman b. Such regimeswitching vector autoregressions and their applications in economics are discussed in particular in the monograph by krolzig 1997. The individual contributions cover new advances in markovswitching models. Markovswitching with timevarying transition probabilities the regime is a function of other variables2. Introduction to markovswitching regression models using the mswitch command gustavo sanchez statacorp october 22, 2015 madrid, spain statacorp markovswitching regression in stata october 22 1 1.