Checks of model adequacy for univariate time series models and their application to econometric relationships

Tests derived from time series analysis play an important role in many empirical studies. These tests are frequently applied to the residuals obtained by fitting an econometric model using some standard estimator. We focus attention here on tests developed for univariate time series models. Various approaches to testing the adequacy of such models are discussed and compared. The validity and sefulness of applying these tests to econometric residuals are then examined and some Monte Carlo evidence is reported.

[1]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[2]  Adrian Pagan,et al.  Econometric Issues in the Analysis of Regressions with Generated Regressors. , 1984 .

[3]  R. J. Bhansali,et al.  Autoregressive and window estimates of the inverse correlation function , 1980 .

[4]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[5]  N. Savin,et al.  Testing for Unit Roots: 1 , 1981 .

[6]  L. Godfrey.  TESTING AGAINST GENERAL AUTOREGRESSIVE AND MOVING AVERAGE ERROR MODELS WHEN THE REGRESSORS INCLUDE LAGGED DEPENDENT VARIABLES , 1978 .

[7]  N. Savin,et al.  Testing for Unit Roots: 2 , 1984 .

[8]  David R. Cox,et al.  Further Results on Tests of Separate Families of Hypotheses , 1962 .

[9]  James Durbin,et al.  Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables , 1970 .

[10]  Anil K. Bera,et al.  Alternative forms and properties of the score test , 1986 .

[11]  S. D. Silvey,et al.  The Lagrangian Multiplier Test , 1959 .

[12]  Leslie Godfrey,et al.  Testing the adequacy of a time series model , 1979 .

[13]  Ruey S. Tsay,et al.  Model Identification in Dynamic Regression (Distributed Lag) Models , 1985 .

[14]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[15]  Richard T. Baillie,et al.  Testing rational expectations and efficiency in the foreign exchange market , 1983 .

[16]  Adrian Pagan,et al.  Diagnostic tests as residual analysis , 1983 .

[17]  M. Bartlett.  On the Theoretical Specification and Sampling Properties of Autocorrelated Time‐Series , 1946 .

[18]  The Properties of Autoregressive Instrumental Variables Estimators in Dynamic Systems , 1977 .

[19]  Kenneth F. Wallis,et al.  Testing for Fourth Order Autocorrelation in Qtrly Regression Equations , 1972 .

[20]  P. Phillips,et al.  Does Gnp Have a Unit Root? a Reevaluation , 1986 .

[21]  G. C. Tiao,et al.  Modeling Multiple Time Series with Applications , 1981 .

[22]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[23]  Lon-Mu Liu,et al.  Identification of multiple-input transfer function models , 1982 .

[24]  P. Trivedi.  Retail inventory investment behaviour , 1973 .

[25]  Leslie Godfrey,et al.  Testing AR(1) Against MA(1) Disturbances in the Linear Regression Model: An Alternative Procedure , 1990 .

[26]  M. King,et al.  Further Results on Testing AR (1) Against MA (1) Disturbances in the Linear Regression Model , 1987 .

[27]  L. Godfrey.  A Note on the Use of Durbin's h Test When the Equation is Estimated by Instrumental Variables , 1978 .

[28]  N. Davies,et al.  Significance levels of the Box-Pierce portmanteau statistic in finite samples , 1977 .

[29]  Paul Newbold.  The equivalence of two tests of time series model adequacy , 1980 .

[30]  E. J. Hannan,et al.  Multiple time series , 1970 .

[31]  William S. Cleveland,et al.  The Inverse Autocorrelations of a Time Series and Their Applications , 1972 .

[32]  E. Fama,et al.  Short-Term Interest Rates as Predictors of Inflation , 1975 .

[33]  D. Cox.  Tests of Separate Families of Hypotheses , 1961 .

[34]  Adrian Pagan,et al.  The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics , 1980 .

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

[36]  David F. Hendry,et al.  The Econometric-analysis of Economic Time-series , 1983 .

[37]  J. Durbin,et al.  Testing for serial correlation in least squares regression. II. , 1950, Biometrika.

[38]  Kenneth F. Wallis,et al.  Modelling Macroeconomic Time Series , 1976 .

[39]  Hrishikesh D. Vinod,et al.  “Generalization of the durbin-watson statistic for higher order autoregressive processes , 1973 .

[40]  D. A. Pierce.  Distribution of Residual Autocorrelations in the Regression Model with Autoregressive-Moving Average Errors , 1971 .

[41]  Ratnam V. Chitturi.  Distribution of Residual Autocorrelations in Multiple Autoregressive Schemes , 1974 .

[42]  D. Poskitt,et al.  Testing Misspecification in Vector Time Series Models with Exogenous Variables , 1984 .

[43]  L. Godfrey.  Discriminating between Autocorrelation and Misspecification in , 1987 .

[44]  Clive W. J. Granger,et al.  TIME SERIES AND SPECTRAL METHODS IN ECONOMETRICS , 1984 .

[45]  Phoebus J. Dhrymes,et al.  Distributed Lags: Problems of Estimation and Formulation , 1972 .

[46]  David A. Pierce,et al.  Residual Correlations and Diagnostic Checking in Dynamic-Disturbance Time Series Models , 1972 .

[47]  Michael R. Gibbons,et al.  Inflation, real returns and capital investment , 1982 .

[48]  David F. Hendry,et al.  On the Formulation of Empirical-models in Dynamic Econometrics , 1982 .

[49]  G. Ljung,et al.  Diagnostic testing of univariate time series models , 1986 .

[50]  David A. Pierce,et al.  Least squares estimation in the regression model with autoregressive-moving average errors , 1971 .

[51]  A. M. Walker.  Some tests of separate families of hypotheses in time series analysis. , 1967, Biometrika.

[52]  Money, Inflation and Casuality (Another Look at the Empirical Evidence for the USA, 1953–84) , 1987 .

[53]  Calyampudi R. Rao.  Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[54]  Leslie Godfrey,et al.  Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence , 1983 .

[55]  Donald Poskitt,et al.  Testing the specification of a fitted autoregressive-moving average model , 1980 .

[56]  L. Godfrey.  ON THE INVARIANCE OF THE LAGRANGE MULTIPLIER TEST WITH RESPECT TO CERTAIN CHANGES IN THE ALTERNATIVE HYPOTHESIS , 1981 .

[57]  Paul Newbold,et al.  Some power studies of a portmanteau test of time series model specification , 1979 .

[58]  J. R. M. Hosking,et al.  Lagrange‐Multiplier Tests of Multivariate Time‐Series Models , 1981 .

[59]  A. I. McLeod,et al.  On the Distribution of Residual Autocorrelations in Box–Jenkins Models , 1978 .

[60]  TESTING SEPARATE TIME SERIES MODELS , 1988 .

[61]  Donald Poskitt,et al.  An Approach to Testing Linear Times Series Models , 1981 .

[62]  G. Maddala,et al.  TESTS FOR SERIAL CORRELATION IN REGRESSION MODELS WITH LAGGED DEPENDENT VARIABLES AND SERIALLY CORRELATED ERRORS , 1973 .

[63]  T. Breusch.  TESTING FOR AUTOCORRELATION IN DYNAMIC LINEAR MODELS , 1978 .

[64]  D. Poskitt,et al.  Diagnostic Tests for Multiple Time Series Models , 1982 .

[65]  A TIME SERIES APPLICATION OF THE USE OF MONTE CARLO METHODS TO COMPARE STATISTICAL TESTS , 1981 .

[66]  W. M. Cox.  The behavior of treasury securities monthly, 1942–1984 , 1985 .

[67]  D. A. Pierce.  Least squares estimation in dynamic-disturbance time series models , 1972 .

[68]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[69]  John Geweke,et al.  Inference and causality in economic time series models , 1984 .

[70]  L. Godfrey,et al.  REGRESSION EQUATIONS WHEN THE REGRESSORS INCLUDE LAGGED DEPENDENT VARIABLES , 1978 .

[71]  E. Hannan.  The Estimation of the Order of an ARMA Process , 1980 .

[72]  T. Mills,et al.  The behaviour of expected short-term real interest rates in the UK , 1987 .