Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence

This paper investigates the possibility, raised by Perron (1989, 1990a), that aggregate economic time series can be characterized as being stationary around broken trend lines. Unlike Perron, we treat the break date as unknown a priori. Asymptotic distributions are developed for recursive, rolling, and sequential tests for unit roots and/or changing coefficients in time series regressions. The recursive and rolling tests are based on a time series of recursively estimated coefficients, computed using increasing subsamples of the data. The sequential statistics are computed using the full data set and a sequence of regressors indexed by a "break" date. When applied to data on real postwar output from seven DECO countries, these techniques fail to reject the unit root hypothesis for five countries (including the U.S.), but suggest stationarity around a shifted trend for Japan.

[1]  J. Stock,et al.  Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence , 1992 .

[2]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[3]  Pierre Perron,et al.  A Test for Changes in a Polynomial Trend Functions for a Dynamioc Time Series , 1991 .

[4]  International Evidence on the Size of the Random Walk in Output , 1990, Journal of Political Economy.

[5]  A Multicountry Characterization of the Nonstationarity of Aggregate Output , 1990 .

[6]  J. Stock,et al.  INFERENCE IN LINEAR TIME SERIES MODELS WITH SOME UNIT ROOTS , 1990 .

[7]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[8]  George W. Evans,et al.  Output and unemployment dynamics in the United States: 1950–1985 , 1989 .

[9]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[10]  W. Krämer,et al.  A new test for structural stability in the linear regression model , 1989 .

[11]  Lucrezia Reichlin,et al.  Segmented trends and non-stationary time series , 1989 .

[12]  P. Clark.  Trend reversion in real output and unemployment , 1989 .

[13]  N. Mankiw,et al.  International Evidence on the Persistence of Economic Fluctuations , 1989 .

[14]  W. Krämer,et al.  Testing for structural change in dynamic models , 1988 .

[15]  John H. Cochrane,et al.  How Big Is the Random Walk in GNP? , 1988, Journal of Political Economy.

[16]  Lawrence J. Christiano,et al.  Searching for a Break in Gnp , 1988 .

[17]  C. Z. Wei,et al.  Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes , 1988 .

[18]  J. Bradford DeLong,et al.  How Does Macroeconomic Policy Affect Output , 1988 .

[19]  James H. Stock,et al.  Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors , 1987 .

[20]  P. Phillips.  Time series regression with a unit root , 1987 .

[21]  D. Siegmund,et al.  Tests for a change-point , 1987 .

[22]  Alok Bhargava,et al.  On the Theory of Testing for Unit Roots in Observed Time Series , 1986 .

[23]  Mark W. Watson,et al.  Univariate detrending methods with stochastic trends , 1986 .

[24]  Andrew Harvey,et al.  Trends and Cycles in Macroeconomic Time Series , 1985 .

[25]  D. Picard,et al.  Off-line statistical analysis of change-point models using non parametric and likelihood methods , 1985 .

[26]  L. Cain.  Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest Rates, 1867–1975. By Milton Friedman and Anna J. Schwartz. (Chicago: University of Chicago Press, 1982. xxxi + 664 pp. $48.00.) , 1984, Business History Review.

[27]  M. Watson,et al.  Are Business Cycles All Alike? , 1984 .

[28]  N. Herrndorf.  A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables , 1984 .

[29]  Alok Bhargava,et al.  Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk , 1983 .

[30]  Jean-Marie Dufour,et al.  Recursive stability analysis of linear regression relationships: An exploratory methodology , 1982 .

[31]  C. Nelson,et al.  Trends and random walks in macroeconmic time series: Some evidence and implications , 1982 .

[32]  Michael J. Harrison,et al.  Testing the Constancy of Regression Relationships Over Time using Least Squares Residuals , 1980 .

[33]  Pranab Kumar Sen.  Asymptotic theory of some tests for a possible change in the regression slope occurring at an unknown time point , 1980 .

[34]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[35]  J. Durbin,et al.  Techniques for Testing the Constancy of Regression Relationships Over Time , 1975 .

[36]  R. Quandt.  Tests of the Hypothesis That a Linear Regression System Obeys Two Separate Regimes , 1960 .

[37]  D. Darling,et al.  A Test of Goodness of Fit , 1954 .