Are Seasonal Patterns Constant Over Time? A Test for Seasonal Stability

Fabio Canova · Bruce E. Hansen

191 citations0/0 files storedJournal of Business and Economic Statistics

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Monetary Policy and Economic Impact Time Series Analysis and Forecasting Diverse Scientific and Economic Studies

Abstract

This article introduces Lagrange multiplier tests of the null hypothesis of no unit roots at seasonal frequencies against the alternative of a unit root at either a single seasonal frequency or a set of seasonal frequencies. The tests complement those of Dickey, Hasza, and Fuller and Hylleberg, Engle, Granger, and Yoo that examine the null of seasonal unit roots. We derive an asymptotic distribution theory for the tests, and investigate their size and power with a Monte Carlo exercise. Application of the tests to three sets of seasonal variables shows that in most cases seasonality is nonstationary.

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References

1992Testing the null hypothesis of stationarity against the alternative of a unit root 1977Time Series Analysis: Forecasting and Control 1990Forecasting, Structural Time Series Models and the Kalman Filter 1991Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation 1990Seasonal integration and cointegration 1989Testing for the Constancy of Parameters Over Time 1992Testing for parameter instability in linear models 1986Forecasting Economic Time Series

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2009Structural Changes, Common Stochastic Trends, and Unit Roots in Panel Data 2015Performance of state space and ARIMA models for consumer retail sales forecasting 2006Tests of seasonal integration and cointegration in multivariate unobserved component models 2006Chapter 7 Forecasting with Unobserved Components Time Series Models 2004The forecasting performance of various models for seasonality and nonlinearity for quarterly industrial production 2001

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