Power Comparison of Autocorrelation Tests in Dynamic Models

Year 2019, Volume: 11 Issue: 2, 58 - 69, 25.09.2019

Tanweer Islam , Erum Toor

https://doi.org/10.33818/ier.447133

Cited By: 3

Abstract

The four most readily available tests of autocorrelation in dynamic
models namely Durbin’s M test,
Durbin’s H test, Breusch Godfrey test
(BGF) and Ljung & Box (Q)
test are compared in terms of their power for varying sample sizes, levels of
autocorrelation and significance using Monte Carlo simulations in STATA. Power
comparison reveals that the Durbin M
test is the best option for testing the hypothesis of no autocorrelation in
dynamic models for all sample sizes. Breusch Godfrey’s test has comparable and
at times minutely better performance than Durbin’s M test however in small sample sizes, Durbin’s M test outperforms the Breusch Godfrey test in terms of power. The
Durbin H and the Ljung & Box Q
tests consistently occupy the second last and last positions respectively in
terms of power performance with maximum power gap of 63 & 60% respectively
from the best test (M test).

Keywords

Durbin test, Breusch Godfrey test, Ljung & Box test

References

• Ahlburg, D. A. (1985). The Effect of Strikes on Suicide: Time Series Evidence from the United States. Sociological Focus, 29-36.
• Blattberg, R. (1973). Evaluation of the Power of the Durbin-Watson Statistic for Non-First Order Serial Correlation Alternatives. The Review of Economics and Statistics, 55(4), 508-515. doi:10.2307/1925676
• Box, G., & Pierce, D. (1970). Distribution of Residual in Autoregressive- Integrated Moving Average Time Series Models. Journal of American Statistical Association, 1509-1526.
• Breusch, T. S. (1978). Testing for autocorrelation in dynamic linear models. Australian Economic Papers, 17(31), 334-355.
• Chirinko, R. S. (1980). The Real Wage Rate Over the Business Cycle. The Review of Economics and Statistics, 459-461.
• Davidson, R., & MacKinnon, J. G. (1996). The size distortion of bootstrap tests. working paper, Department of economics.
• Davidson, R., & MacKinnon, J. G. (2003). Econometrics theory and methods. New York: Oxford university press.
• Dezhbakhsh, H. (1990). The inappropriate use of serial correlation tests in dynamic linear models. The review of economics and statistics, 126-132.
• Durbin, J. (1970). Testing for Serial Correlation on Least Square Regression when some of the Regressors are Lagged Dependant Variables. Econometrica, 38.
• Durbin, J., & Watson, G. (1951). Testing for Serial Correlation in Least Square Regression. Biometrika, 38.
• Gastwirth, J. L., & Selwyn, M. R. (1980). The Robustness Properties of Two Tests for Serial Correlation. Journal of the American Statistical Association, 138-141.
• Geary, R. C. (1970). Relative efficiency of count of sign changes for assessing residual autoregression in least squares regression. Biometrika, 123-127.
• Gerhausser, K. (1990). Inflation and Realtive Price Variability under a Gold Standard: Evidence from Germany. Journal of Economics and Statistics, 391-394.
• Godfrey, L. (1978). Testing against General Autoregressive and Moving Average Error Models when the Regressors inclue Lagged Dependant Variablesl. Econometrica, 1293-1301.
• Godfrey, L. G. (2007). Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models. Computational statistics & data analysis, 51(7), 3282-3295.
• Goetzmann, W. N., & Jorion, P. (1993). Testing the Predictive Power of Dividend Yields. The Journal of Finance, 663-679.
• Greene, W. H. (2000). Eonometric Analysis. New Jersey: Prentice Hall.
• Hannan, E. J. (1957). Testing for serial correlation after least quare regression. Biometrika, 57-66.
• Inder, B. A. (1984). Finite-sample power of tests for autocorrelation in models containing lagged dependent variables. Economics Letters, 14(2-3), 179-185.
• Inder, B. A. (1990). A new test for autocorrelation in the disturbances of the dynamic linear regression model. International Economic Review, 341-354.
• Jerkins, G. H. (1954). Test of hypotheses in linear autoregressive model. Biometrika, 405-419.
• Kenkel, J. (1974). Some small sample properties of Durbin's tests for serial correlation in regression models containing lagged dependant variables. Econometrica, 763-769.
• Koerts , J., & Abrahamse, P. J. (1954). On the power of BLUS procedure. Journal of the American statistical association, 1227-1236.
• Lee, J., & Lund, R. (2004). Revisiting simple linear regression with autocorrelated errors. Biometrika, 240-245.Li, K. (1999). Testing Symmetry and Proportionality in PPP: A Panel-Data Approach. Journal of Business & Economic Statistics, 409-418.
• Ljung, G., & Box, G. E. (1978). On a measure of lack of fit in time series models. Biometrika, 67-72.
• Lubos, s., & Vaclav, A. (2013). Exploration into power of homogeneity and serial correlation tests. Acta universitatis Agriculturae et Silviculturae Mendelianae Brunensis.
• Maddala, G. S., & Rao, A. S. (1973). Tests for serial correlation in regression models with lagged dependanrt variables and serially correlated errors. Econometrica, 761-774.
• McCunn, A., & Huffman, W. E. (2000). Convergence in U.S. Productivity Growth for Agriculture: Implications of Interstate Research Spillovers for Funding Agricultural Research. American Journal of Agricultural Economics, 370-388.
• McNown, R. F., & Hunter, K. R. (1980). A test for autocorrelation in models with lagged dependant variables. the review of economics and statistics, 313-317.
• Park, S.-B. (1975). On the Small-Sample Power of Durbin's h Test. Journal of the American Statistical Association, 60-63.
• Rayner, R. K. (1993). Testing for Serial Correlation in Regression Models with Lagged Dependant Variables. The Review of Economics and Statistics, 716-721.
• Rois, R., Basak, T., Rahman, M. M., & Majumder, A. K. (2012). Modified Breusch-Godfrey Test for Restricted Higher Order Autocorrelation in Dynamic Linear Model–A Distance Based Approach. International Journal of Business and Management, 7(17), 88.
• Savin, N. E., & White, K. J. (1978). Testing for Autocorrelation with Missing Observations. Econometrica, 59-67.
• Schmidt, P., & Guilkey, D. K. (1975). Some further evidence on the power of the Durbin watson and Geary tests. The review of economics and statistics, 379-381.
• Scott, J. T., & Heady, E. O. (1967). Regional Demand for Farm Buildings in the United States. Journal of Farm Economics, 184-198.
• Sivo, S. A., & Willson, V. L. (1998). Is Parsimony Always Desirable?Identifying the Correct Model for a Longitudinal Panel Data Set. The Journal of Experimental Education, 249-255.
• Smith, V. K. (1976). The estimated power of several tests for autocorrelation with non-first-order alternatives. Journal of the American Statistical Association, 71(356), 879-883.
• Solomou, S., & Weale, M. (1993). Balances Estimates of National Accounts when Measurement Errors are Autocorrelated. Journal of the Royal Statistical Society, 89-105.
• Spix, C., & Wichmann, H. E. (1979). Daily Mortality and Air Pollutants. Journal of Epidemiology and Community Health , 52-58.
• Strelec, L., & Adamec, V. (2013). Exploration into power of homogeniety and serial correlation tests. Acta Univ.Agric.Sivic. Mendelianae, 1129-1136.
• Wallis, K. F. (1972). Testing for Fourth Order Autocorrelation in Quarterly Regression Equations. Econometrica, 617-636.
• Womer, N. K., & Patterson, J. W. (1983). Estimation and Testing of Learning Curves. Journal of Business & Economic Statistics, 256-272.