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187
Moments of Markov Switching Models
, 1999
"... This paper derives the moments for a range of Markov switching models. We characterize in detail the patterns of volatility, skewness and kurtosis that these models can produce as a function of the transition probabilities and parameters of the underlying state densities entering the switching proce ..."
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Cited by 62 (9 self)
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This paper derives the moments for a range of Markov switching models. We characterize in detail the patterns of volatility, skewness and kurtosis that these models can produce as a function of the transition probabilities and parameters of the underlying state densities entering the switching process. The autocovariance of the level and squares of time series generated by Markov switching processes is also derived and we use these results to shed light on the relationship between volatility clustering, regime switches and structural breaks in time series models. JEL Code: C1. Key Words: Markov Switching, Higher Order Moments, Mixtures of Normals, Volatility Clustering. # Two anonymous referees and an associate editor provided many useful suggestions for improvements of the paper. Discussions with Jim Hamilton and Martin Sola also were very helpful. + Financial Markets Group, Houghton Street, London WC2A 2AE, England. 1 1. Introduction Markov switching models have become increasing...
Dealing with Structural Breaks
 IN PALGRAVE HANDBOOK OF ECONOMETRICS
, 2006
"... This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. A central theme of the review is the interplay between structural change and unit root and on methods to distinguish between the two. The top ..."
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Cited by 44 (8 self)
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This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. A central theme of the review is the interplay between structural change and unit root and on methods to distinguish between the two. The topics covered are: methods related to estimation and inference about break dates for single equations with or without restrictions, with extensions to multiequations systems where allowance is also made for changes in the variability of the shocks; tests for structural changes including tests for a single or multiple changes and tests valid with unit root or trending regressors, and tests for changes in the trend function of a series that can be integrated or trendstationary; testing for a unit root versus trendstationarity in the presence of structural changes in the trend function; testing for cointegration in the presence of structural changes; and issues related to long memory and level shifts. Our focus is on the conceptual issues about the frameworks adopted and the assumptions imposed as they relate to potential applicability. We also highlight the potential problems that can occur with methods that are commonly used and recent work that has been done to overcome them.
Nonparametric Nonlinear Cotrending Analysis, with an Application to Interest and Inflation in the United States
 Journal of Business and Economic Statistics, July
"... Given the assumption that the components of a vector time series are stationary about nonlinear deterministic time trends, nonlinear cotrending is the phenomenon that one or more linear combinations of the time series are stationary about a linear trend or a constant, hence the series have common n ..."
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Cited by 33 (0 self)
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Given the assumption that the components of a vector time series are stationary about nonlinear deterministic time trends, nonlinear cotrending is the phenomenon that one or more linear combinations of the time series are stationary about a linear trend or a constant, hence the series have common nonlinear deterministic time trends. In this paper we develop nonparametric tests for nonlinear cotrending. These tests are based on generalized eigenvalues, where the two matrices involved are constructed nonparametrically on the basis of partial sums. We apply this approach to the federal funds rate and the CPI inflation rate in the U.S., using monthly data. It appears that these series are nonlinear cotrended, where the nonlinear trend in the inflation rate is positively related to the nonlinear trend in the interest rate. Moreover, the price puzzle seems to a large extent due to this common nonlinear trend. Furthermore, the common nonlinear trend seems to be related to the oil price shocks induced by the OPEC cartel in the early and late seventies.
Long Memory and Level Shifts: ReAnalyzing Inflation Rates
 Empirical Economics
, 1998
"... A key application of long memory time series models concerns inflation. Long memory implies that shocks have a longlasting effect. It may however be that empirical evidence for long memory is caused by neglecting one or more level shifts. Since such level shifts are not unlikely for inflation, wher ..."
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Cited by 31 (7 self)
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A key application of long memory time series models concerns inflation. Long memory implies that shocks have a longlasting effect. It may however be that empirical evidence for long memory is caused by neglecting one or more level shifts. Since such level shifts are not unlikely for inflation, where the shifts may be caused by sudden oil price shocks, we examine whether evidence for long memory (indicated by the relevance of an ARFIMA model) in G7 inflation rates is spurious or exaggerated. Our main findings are that apparent long memory is quite resistant to level shifts, although for a few inflation rates we find that evidence for long memory disappears. Keywords: Long memory, fractional integration, structural change, inflation Correspondence to Charles S. Bos, Tinbergen Institute, Erasmus University Rotterdam, P.O. Box 1738, NL3000 DR Rotterdam, The Netherlands. Email: cbos@few.eur.nl 1 Introduction A key application of long memory time series models concerns inflation. For ...
Minimum LM Unit Root Test with Two Structural Breaks
"... The twobreak unit root test of Lumsdaine and Papell (1997) is examined and found to suffer from bias and spurious rejections in the presence of structural breaks under the null. A twobreak minimum LM unit root test is proposed as a remedy. The twobreak LM test does not suffer from bias and spurio ..."
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Cited by 29 (2 self)
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The twobreak unit root test of Lumsdaine and Papell (1997) is examined and found to suffer from bias and spurious rejections in the presence of structural breaks under the null. A twobreak minimum LM unit root test is proposed as a remedy. The twobreak LM test does not suffer from bias and spurious rejections and is mostly invariant to the size, location, and misspecification of the breaks. We test the Nelson and Plosser (1982) data and find fewer rejections of the unit root than Lumsdaine and Papell. JEL classification: C12, C15, and C22 Key words: Lagrange Multiplier, Unit Root Test, Structural Break, and Endogenous Break Corresponding author: Junsoo Lee, Associate Professor, Department of Economics, University of Central Florida, Orlando, FL, 328161400, USA. Telephone: 4078232070. Fax: 4078233269. Email: Junsoo.Lee@bus.ucf.edu. We thank John List for helpful comments. 1 1.
Detecting periodically collapsing bubbles: a Markovswitching unit root test
 Journal of Applied Econometrics
, 1999
"... This paper addresses the problem of testing for the presence of a stochastic bubble in a time series in the case that the bubble is periodically collapsing so that the asset price keeps returning to the level implied by the market fundamentals. As this is essentially a problem of identifying the col ..."
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Cited by 22 (0 self)
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This paper addresses the problem of testing for the presence of a stochastic bubble in a time series in the case that the bubble is periodically collapsing so that the asset price keeps returning to the level implied by the market fundamentals. As this is essentially a problem of identifying the collapsing periods from the expanding ones, we propose using a generalization of the Dickey–Fuller test procedure which makes use of the class of Markov regimeswitching models. The potential of the new methodology is illustrated via simulation, and an empirical example is given. Copyright # 1999 John Wiley & Sons, Ltd. 1.
A Bayesian Approach to Testing for Markov Switching in Univariate and Dynamic Factor Models
, 2000
"... Though Hamilton's (1989) Markov switching model has been widely estimated in various contexts, formal testing for Markov switching is not straightforward. Univariate tests in the classical framework by Hansen (1992) and Garcia (1998) do not reject the linear model for GDP. We present Bayesian t ..."
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Cited by 20 (6 self)
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Though Hamilton's (1989) Markov switching model has been widely estimated in various contexts, formal testing for Markov switching is not straightforward. Univariate tests in the classical framework by Hansen (1992) and Garcia (1998) do not reject the linear model for GDP. We present Bayesian tests for Markov switching in both univariate and multivariate settings based on sensitivity of the posterior probability to the prior. We #nd that evidence for Markov switching, and thus the business cycle asymmetry, is stronger in a switching version of the dynamic factor model of Stock and Watson (1991) than it is for GDP by itself. Key Words: Bayesian Model Selection, Business Cycle Asymmetry, Dynamic Factor Model, Pseudo Prior, Model Indicator Parameter, Test of Markov Switching. JEL Classi#cations: C11, C12, E32. \The Bayesian moral is simple: Never make anything more than relative probability statements about the models explicitly entertained. Be suspicious of those who promise more!" [Po...
Testing for unit roots in time series with level shifts
 Discussion Paper No. 27, SFB 373, HumboldtUniversität zu
, 1999
"... Unit root tests for time series with level shifts of general form are considered when the timing of the shift is unknown. It is proposed to estimate the nuisance parameters of the data generation process including the shift date in a rst step and apply standard unit root tests to the residuals. The ..."
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Cited by 19 (2 self)
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Unit root tests for time series with level shifts of general form are considered when the timing of the shift is unknown. It is proposed to estimate the nuisance parameters of the data generation process including the shift date in a rst step and apply standard unit root tests to the residuals. The estimation of the nuisance parameters is done in such a way that the unit root tests on the residuals have limiting distributions for which critical values are tabulated elsewhere in the literature. Empirical examples are discussed to illustrate the procedure. JEL classification: C22, C12
2006): “Unit Root Tests Allowing for a Break in the Trend Function at a Unknown Time Under Both the Null and Alternative Hypothesis,” Unpublished manuscript
"... Perron (1989) introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is al ..."
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Cited by 18 (1 self)
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Perron (1989) introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is allowed under both the null and alternative hypotheses. This analysis was carried under the assumption of a known break date. The subsequent literature aimed to devise testing procedures valid in the case of an unknown break date. However, in doing so, most of the literature and, in particular the commonly used test of Zivot and Andrews (1992), assumed that if a break occurs, it does so only under the alternative hypothesis of stationarity. This is undesirable since a) it imposes an asymmetric treatment when allowing for a break, so that the test may reject when the noise is integrated but the trend is changing; b) if a break is present, this information is not exploited to improve the power of the test. In this paper, we propose a testing procedure that addresses both issues. It allows a break under both the null and alternative hypotheses and, when a break is present, the limit distribution of the test is the same as in the case of a known break date, thereby allowing increased power while maintaining the correct size. Simulation experiments confirm that our procedure offers an improvement over commonly used methods in small samples. JEL Classification Number: C22.