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A Time Series Model with Periodic Stochastic Regime Switching

Discussion Paper 84 | Published May 1, 1993

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Eric Ghysels

A Time Series Model with Periodic Stochastic Regime Switching


A general class of Markov switching regime time series models is presented that allows one to estimate the nontrivial interdependencies between different types of cycles which make the economy grow at an unsteady rate. The paper further explores results obtained in Ghysels (1991b) suggesting that the economy transits from recessions to expansions with an uneven propensity throughout the year. It is also built on the work of Hamilton (1989) who proposed a stochastic switching-regime model for GNP and has important connections with hidden periodic structures discussed by Tiao and Grupe (1980) or Hansen and Sargent (1990), for instance. The time series models we present may have periodic transition probabilities and the drifts may be seasonal. In the latter case, the model exhibits seasonal dummy variation that may change with the stage of the business cycle. While the model is intrinsically nonlinear and stochastic, it produces a linear representation with seasonal effects that appear to be deterministic. The paper provides an elaborate discussion of the regularity conditions for a well-defined covariance structure including explicit formula for characterizing first and second moments. Finally, we present empirical evidence using U.S. GNP data series which tends to support a periodic structure for switching probabilities. The most significant result is the following: it is found that the seasonal in GNP growth significantly affects switching probabilities for regime switches in the nonseasonal growth of GNP. We also analyze the out-of-sample forecast performance of the different models and find that the models exploiting seasonality in transition probabilities perform best.