Estimation of a non-invertible moving average process: The case of overdifferencing

Abstract The effect of differencing all of the variables in a properly specified regression equation is examined. Excessive use of the difference transformation induces a non-invertible moving average (MA) process in the disturbances of the transformed regression. Monte Carlo techniques are used to examine the effects of overdifferencing on the efficiency of regression parameter estimates, inferences based on these estimates, and tests for overdifferenccing based on the estimator of the MA parameter for the disturbances of the differences regression. Overall, the problem of overdifferencing is not serious if careful attention is paid to the properties of the disturbances of regression equations.

[1]  D. Aigner.  A Compendium on Estimation of the Autoregressive-Moving Average Model from Time Series Data , 1971 .

[2]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[3]  The variate difference method. , 1940 .

[4]  A. Zellner.  An Introduction to Bayesian Inference in Econometrics , 1971 .

[5]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[6]  H. Vinod.  Effects of ARMA Errors on the Significance Tests for Regression Coefficients , 1976 .

[7]  P. Whittle,et al.  Prediction and Regulation. , 1965 .

[8]  H. A. David,et al.  THE DISTRIBUTION OF THE RATIO, IN A SINGLE NORMAL SAMPLE, OF RANGE TO STANDARD DEVIATION , 1954 .

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

[10]  D. F. Nicholls,et al.  Specification of the Disturbance for Efficient Estimation-An Extended Analysis , 1977 .

[11]  P. Newbold.  Bayesian Estimation of Box–Jenkins Transfer Function‐Noise Models , 1973 .

[12]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[13]  M. Pesaran.  Exact Maximum Likelihood Estimation of a Regression Equation with a First-Order Moving-Average Error , 1973 .

[14]  R. Jacobs.  Data Errors and Data Differences , 1976 .

[15]  Charles R. Nelson,et al.  The first-order moving average process: Identification, estimation and prediction , 1974 .

[16]  T. W. Anderson,et al.  Statistical analysis of time series , 1972 .

[17]  D. F. Nicholls,et al.  The Estimation and Use of Models with Moving Average Disturbance Terms: A Survey , 1975 .

[18]  G. Yule.  Why do we Sometimes get Nonsense-Correlations between Time-Series?--A Study in Sampling and the Nature of Time-Series , 1926 .

[19]  J. Chambers.  Fitting nonlinear models: numerical techniques , 1973 .

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

[21]  H. Chernoff.  On the Distribution of the Likelihood Ratio , 1954 .

[22]  D. Hendry,et al.  Maximum Likelihood Estimation of Difference Equations with Moving Average Errors: A Simulation Study , 1972 .

[23]  D. A. Pierce.  On trend and autocorrelation , 1975 .

[24]  Christopher A. Sims,et al.  The Role of Approximate Prior Restrictions in Distributed Lag Estimation , 1972 .

[25]  T. W. Anderson.  On Asymptotic Distributions of Estimates of Parameters of Stochastic Difference Equations , 1959 .

[26]  M. Kendall,et al.  A Study in the Analysis of Stationary Time-Series. , 1955 .

[27]  Dean W. Wichern,et al.  The behaviour of the sample autocorrelation function for an integrated moving average process , 1973 .

[28]  Maurice Henry Quenouille,et al.  The analysis of multiple time-series , 1957 .

[29]  R. Galbraith,et al.  ON THE INVERSES OF SOME PATTERNED MATRICES ARISING IN THE THEORY OF STATIONARY TIME SERIES , 1974 .

[30]  A. J. Kinderman,et al.  Computer Generation of Normal Random Variables , 1976 .

[31]  P. Shaman.  ON THE INVERSE OF THE COVARIANCE MATRIX OF A FIRST-ORDER MOVING AVERAGE. , 1969 .

[32]  C. Nelson,et al.  On testing the hypothesis that the real rate of interest is constant , 1977 .

[33]  C. Granger,et al.  Spurious regressions in econometrics , 1974 .

[34]  P. Trivedi.  Inventory Behaviour in U.K. Manufacturing 1956–67 , 1970 .