Finite Sample Distributions oftandFStatistics in an AR(1) Model with Anexogenous Variable

John C. Nankervis · N. E. Savin

52 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Advanced Statistical Methods and Models Diverse Scientific and Economic Studies

Abstract

The distributions of the test statistics are investigated in the context of an AR(1) model where the root is unity or near unity and where the exogenous process is a stable process, a random walk or a time trend. The finite sample distributions are estimated by Monte Carlo methods assuming normal disturbances. The sensitivity of the distributions to both the values of the parameters of the AR(1) model and the process generating the exogenous time series is examined. The Monte Carlo results motivate several theorems which describe the exact sampling behavior of the test statistics. The analytical and empirical results present a mixed picture with respect to the accuracy of the relevant asymptotic approximations.

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References

1988Testing for a Unit Root in Time Series Regression 1981Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root 1982Trends and random walks in macroeconmic time series 1978Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence 1984Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order 1987Time Series Regression with a Unit Root 1988Trends and random walks in macroeconomic time series 1981The Adjustment of Consumption to Changing Expectations About Future Income

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1994Semiparametric Tests for Double Unit Roots 1994The distribution of the Durbin-Watson statistic in integrated and near-integrated models 2001Unit root testing in integer-valued AR(1) models 2009Modelling monetary transmission in UK manufacturing industry

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