Markov Regime Switching in Economic Time Series
Abstract: This dissertation studies statistical properties and applications of the Markov switching models for economic time series in five separate papers. The two main statistical themes are (i) the task of choosing the number of states to use in the model, and (ii) inference on time-varying transition probabilities. Our empirical applications span a wide array of topics in international finance and macroeconomics. Specifically, we study the dynamics of nominal exchange rates, interest rates, the business cycle and currency crises. In the first paper, ?Exchange Rates and Markov Switching Dynamics (joint work with Yin-Wong Cheung), we develop a simulation procedure to construct a two-sided test for testing hypotheses regarding the number of states in an empirical data-set. We use the test to resolve conflicting results regarding the existence of Markov switching dynamics in three dollar-denominated exchange rates. Our test shows that some of the earlier data-sets were not informative enough to draw a conclusion upon, with the result of previous tests sometimes contradicting each other. In data spanning 1973-1998 and on the monthly and higher frequency, we do, however, find conclusive evidence of Markov switching dynamics. The second paper, ?Regime Switches in Swedish Interest Rates?, uses a similar simulation approach to arrive at the conclusion of three states in a set of weekly data on Swedish interbank offered interest rates. A short-lived and highly volatile states pin-point the repeated speculative attacks on the Swedish krona in the early 90s. With the states in place, we are able to obtain conditional normality even in this extremely leptokurtic time-series. Furthermore, we show that the specification is quite apt at forecasting interest rate volatility, and the evidence in favor of the model versus a number of competing alternatives is strong for all the forecast horizons we have applied. Turning to the dynamics of Markov models with time-varying transitions probabilities, the third paper, ?Constructing Early-Warning Systems: A Modified Markov Switching Approach? sets out to investigate the relatively infrequent use of this intuitive extension to the original model. It is shown in a simple theoretical setting, and in several simulation exercises, that the maximum likelihood estimator overemphasizes the short-run effects of predictors of transition probabilities in modestly sized samples. This leads to extreme parameter estimates and projected transition probabilities with too abrupt behavior. We introduce a penalized estimator, which is able to reduce parameter estimates toward their true magnitudes, and also increases correlation between the projected and true transition probabilities, and offer some suggestions on how to choose the magnitude of the penalty. In an application to the U.S. business cycle, we show that the penalized estimator yields a more parsimonious model with better forecasting properties in the medium to long term compared to its non-penalized counterpart. In the fourth paper, ?Transition Variables in the Markov Switching Model: Some Small Sample Properties?, we offer a note of caution in terms of using time-varying transition probabilities. We argue that rather than the nominal sample size, as measured by the total number of observations in the time-series, the number of regime switches should be considered instead when making inference on variable significance in the transition equations. By simulation, it is shown that for many cases the likelihood ratio statistic is over-sized, leading to too many transition variables being deemed significant. The size-distortion is not only dependent upon the number of switches in the data, but also the degree of uncertainty inherent in it and the persistence in the regressed variable. We suggest a straightforward, but computationally intensive approach to obtaining statistics with proper size. Looking at a number of business cycle predictors, we show that their statistics must be adjusted by a considerable magnitude to reflect true confidence levels. For model specification, this consequently has marked effect. The last paper (which is joint work with Guillaume Arias), ?Regime Switching as an Alternative Early-Warning System of Currency Crises: An Application to South-East Asia? is devoted to inferring indicators predicting the on-set of the South-East Asian currency crises in 1997. We survey the current literature in the area, and based on this, derive a number of possible determinants of currency crises. In a framework based on the Markov switching model with time-varying transition probabilities, we evaluate these determinants and specify models for forecasting of oncoming crises in the medium to long term. We show that the model is quite efficient in describing the underlying data and that it possesses relatively good forecasting properties.
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