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Residual Autocovariances And Unit Root Tests Based On Instrumental Variable Estimators From Time Series Regression Models

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  • Alastair Hall

Abstract

. Hall (Testing for a unit root in the presence of moving average errors. Biometrika 76 (1989), 49–56; Joint hypothesis tests for a random walk based on instrumental variable estimators. J. Time Ser. Anal. 13 (1992), 29–45), Pantula and Hall (Testing for unit roots in autoregressive moving average models:an instrumental variable approach. J. Econometrics 48 (1991), 325–53) and Lee and Schmidt (Unit root tests based on instrumental variable estimation. Int. Econ. Rev. 39 (1994), 449–62) proposed instrumental variable (IV) based tests for a unit root in an ARMA(p+ 1, q) time series. To perform the tests it is essentially necessary to know (p, q) but in many cases this information is unknown. In practice a natural solution to this problem is to estimate (p, q) from the data using a strategy based on the residual autocovariances from the IV regression. In this paper we examine the properties of these residual autocovariances under various assumptions about the true nature of the time series. This analysis allows us to propose a model selection procedure which has desirable asymptotic and finite sample properties whether the time series is stationary or possesses a unit root. A sideproduct of our analysis is that we extend Box and Pierce's (Distribution of residual autocorrelations in autoregressive integrated moving average time series models. J. Am. Statist. Assoc. 65 (1970), 1509–26) analysis of the least squares residual autocorrelations to the residual autocovariances from IV regressions.

Suggested Citation

  • Alastair Hall, 1995. "Residual Autocovariances And Unit Root Tests Based On Instrumental Variable Estimators From Time Series Regression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 555-569, November.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:6:p:555-569
    DOI: 10.1111/j.1467-9892.1995.tb00255.x
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    2. Lee, Junsoo & Schmidt, Peter, 1994. "Unit Root Tests Based on Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 449-462, May.
    3. Hall, Alastair, 1992. "Testing for a unit root in time series using instrumental variable estimators with pretest data based model selection," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 223-250.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Alastair Hall, 1992. "Joint Hypothesis Tests For A Random Walk Based On Instrumental Variable Estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(1), pages 29-45, January.
    6. Pantula, Sastry G. & Hall, Alastair, 1991. "Testing for unit roots in autoregressive moving average models : An instrumental variable approach," Journal of Econometrics, Elsevier, vol. 48(3), pages 325-353, June.
    7. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-470, October.
    8. C. Agiakloglou & P. Newbold, 1992. "Empirical Evidence On Dickey‐Fuller‐Type Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(6), pages 471-483, November.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Pantula, Sastry G, 1991. "Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 63-71, January.
    11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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