The AUTOREG Procedure

Anderson, T. W., and Mentz, R. P. (1980). “On the Structure of the Likelihood Function of Autoregressive and Moving Average Models.” Journal of Time Series 1:83–94.

Andrews, D. W. K. (1991). “Heteroscedasticity and Autocorrelation Consistent Covariance Matrix Estimation.” Econometrica 59:817–858.

Ansley, C. F., Kohn, R., and Shively, T. S. (1992). “Computing p-Values for the Generalized Durbin-Watson and Other Invariant Test Statistics.” Journal of Econometrics 54:277–300.

Bai, J. (1997). “Estimation of a Change Point in Multiple Regression Models.” Review of Economics and Statistics 79:551–563.

Bai, J., and Perron, P. (1998). “Estimating and Testing Linear Models with Multiple Structural Changes.” Econometrica 66:47–78. http://www.jstor.org/stable/2998540.

Bai, J., and Perron, P. (2003a). “Computation and Analysis of Multiple Structural Change Models.” Journal of Applied Econometrics 18:1–22. 10.1002/jae.659.

Bai, J., and Perron, P. (2003b). “Critical Values for Multiple Structural Change Tests.” Econometrics Journal 6:72–78. 10.1111/1368-423X.00102.

Bai, J., and Perron, P. (2006). “Multiple Structural Change Models: A Simulation Analysis.” In Econometric Theory and Practice: Frontiers of Analysis and Applied Research, edited by D. Corbae, S. N. Durlauf, and B. E. Hansen, 212–237. Cambridge: Cambridge University Press.

Baillie, R. T. (1979). “The Asymptotic Mean Squared Error of Multistep Prediction from the Regression Model with Autoregressive Errors.” Journal of the American Statistical Association 74:175–184.

Baillie, R. T., and Bollerslev, T. (1992). “Prediction in Dynamic Models with Time-Dependent Conditional Variances.” Journal of Econometrics 52:91–113.

Balke, N. S., and Gordon, R. J. (1986). “Historical Data.” In The American Business Cycle, edited by R. J. Gordon, 781–850. Chicago: University of Chicago Press.

Bartels, R. (1982). “The Rank Version of von Neumann’s Ratio Test for Randomness.” Journal of the American Statistical Association 77:40–46.

Beach, C. M., and MacKinnon, J. G. (1978). “A Maximum Likelihood Procedure for Regression with Autocorrelated Errors.” Econometrica 46:51–58.

Bhargava, A. (1986). “On the Theory of Testing for Unit Roots in Observed Time Series.” Review of Economic Studies 53:369–384.

Bollerslev, T. (1986). “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31:307–327.

Bollerslev, T. (1987). “A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return.” Review of Economics and Statistics 69:542–547.

Box, G. E. P., and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. Rev. ed. San Francisco: Holden-Day.

Breitung, J. (1995). “Modified Stationarity Tests with Improved Power in Small Samples.” Statistical Papers 36:77–95.

Breusch, T. S., and Pagan, A. R. (1979). “A Simple Test for Heteroscedasticity and Random Coefficient Variation.” Econometrica 47:1287–1294.

Brock, W. A., Dechert, W. D., and Scheinkman, J. A. (1987). “A Test for Independence Based on the Correlation Dimension.” Departments of Economics, University of Wisconsin–Madison, University of Houston, and University of Chicago.

Brock, W. A., Scheinkman, J. A., Dechert, W. D., and LeBaron, B. (1996). “A Test for Independence Based on the Correlation Dimension.” Econometric Reviews 15:197–235.

Campbell, J. Y., and Perron, P. (1991). “Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots.” In NBER Macroeconomics Annual, edited by O. Blanchard, and S. Fisher, 141–201. Cambridge, MA: MIT Press.

Caner, M., and Kilian, L. (2001). “Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate.” Journal of International Money and Finance 20:639–657.

Chipman, J. S. (1979). “Efficiency of Least Squares Estimation of Linear Trend When Residuals Are Autocorrelated.” Econometrica 47:115–128.

Chow, G. (1960). “Tests of Equality between Sets of Coefficients in Two Linear Regressions.” Econometrica 28:531–534.

Cochrane, D., and Orcutt, G. H. (1949). “Application of Least Squares Regression to Relationships Containing Autocorrelated Error Terms.” Journal of the American Statistical Association 44:32–61.

Cribari-Neto, F. (2004). “Asymptotic Inference under Heteroskedasticity of Unknown Form.” Computational Statistics and Data Analysis 45:215–233.

Cromwell, J. B., Labys, W. C., and Terraza, M. (1994). Univariate Tests for Time Series Models. Thousand Oaks, CA: Sage Publications.

Davidson, R., and MacKinnon, J. G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press.

Davies, R. B. (1973). “Numerical Inversion of a Characteristic Function.” Biometrika 60:415–417.

DeJong, D. N., Nankervis, J. C., Savin, N. E., and Whiteman, C. H. (1992). “The Power Problems of Unit Root Rest in Time Series with Autoregressive Errors.” Journal of Econometrics 53:323–343.

Dickey, D. A., and Fuller, W. A. (1979). “Distribution of the Estimators for Autoregressive Time Series with a Unit Root.” Journal of the American Statistical Association 74:427–431.

Ding, Z., Granger, C. W. J., and Engle, R. F. (1993). “A Long Memory Property of Stock Market Returns and a New Model.” Journal of Empirical Finance 1:83–106.

Duffie, D. (1989). Futures Markets. Englewood Cliffs, NJ: Prentice-Hall.

Durbin, J. (1969). “Tests for Serial Correlation in Regression Analysis Based on the Periodogram of Least-Squares Residuals.” Biometrika 56:1–15.

Durbin, J. (1970). “Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors Are Lagged Dependent Variables.” Econometrica 38:410–421.

Edgerton, D., and Wells, C. (1994). “Critical Values for the CUSUMSQ Statistic in Medium and Large Sized Samples.” Oxford Bulletin of Economics and Statistics 56:355–365.

Elliott, G., Rothenberg, T. J., and Stock, J. H. (1996). “Efficient Tests for an Autoregressive Unit Root.” Econometrica 64:813–836.

Engle, R. F. (1982). “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica 50:987–1007.

Engle, R. F., and Bollerslev, T. (1986). “Modelling the Persistence of Conditional Variances.” Econometric Reviews 5:1–50.

Engle, R. F., and Granger, C. W. J. (1987). “Co-integration and Error Correction: Representation, Estimation, and Testing.” Econometrica 55:251–276.

Engle, R. F., Lilien, D. M., and Robins, R. P. (1987). “Estimating Time Varying Risk in the Term Structure: The ARCH-M Model.” Econometrica 55:391–407.

Engle, R. F., and Ng, V. K. (1993). “Measuring and Testing the Impact of News on Volatility.” Journal of Finance 48:1749–1778.

Engle, R. F., and Yoo, B. S. (1987). “Forecasting and Testing in Co-integrated Systems.” Journal of Econometrics 35:143–159.

Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: John Wiley & Sons.

Gallant, A. R., and Goebel, J. J. (1976). “Nonlinear Regression with Autoregressive Errors.” Journal of the American Statistical Association 71:961–967.

Glosten, L., Jaganathan, R., and Runkle, D. (1993). “Relationship between the Expected Value and Volatility of the Nominal Excess Returns on Stocks.” Journal of Finance 48:1779–1802.

Godfrey, L. G. (1978a). “Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables.” Econometrica 46:1293–1301.

Godfrey, L. G. (1978b). “Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables.” Econometrica 46:1303–1310.

Godfrey, L. G. (1988). Misspecification Tests in Econometrics. Cambridge: Cambridge University Press.

Golub, G. H., and Van Loan, C. F. (1989). Matrix Computations. 2nd ed. Baltimore: Johns Hopkins University Press.

Greene, W. H. (1993). Econometric Analysis. 2nd ed. New York: Macmillan.

Hamilton, J. D. (1994). Time Series Analysis. Princeton, NJ: Princeton University Press.

Hannan, E. J., and Quinn, B. G. (1979). “The Determination of the Order of an Autoregression.” Journal of the Royal Statistical Society, Series B 41:190–195.

Harvey, A. C. (1981). The Econometric Analysis of Time Series. New York: John Wiley & Sons.

Harvey, A. C. (1990). The Econometric Analysis of Time Series. 2nd ed. Cambridge, MA: MIT Press.

Harvey, A. C., and McAvinchey, I. D. (1978). “The Small Sample Efficiency of Two-Step Estimators in Regression Models with Autoregressive Disturbances.” Discussion Paper No. 78-10, University of British Columbia.

Harvey, A. C., and Phillips, G. D. A. (1979). “Maximum Likelihood Estimation of Regression Models with Autoregressive–Moving Average Disturbances.” Biometrika 66:49–58.

Hayashi, F. (2000). Econometrics. Princeton, NJ: Princeton University Press.

Hildreth, C., and Lu, J. Y. (1960). Demand Relations with Autocorrelated Disturbances. Technical Report 276, Michigan State University Agricultural Experiment Station.

Hobijn, B., Franses, P. H., and Ooms, M. (2004). “Generalization of the KPSS-Test for Stationarity.” Statistica Neerlandica 58:483–502.

Hurvich, C. M., and Tsai, C.-L. (1989). “Regression and Time Series Model Selection in Small Samples.” Biometrika 76:297–307.

Inder, B. A. (1984). “Finite-Sample Power of Tests for Autocorrelation in Models Containing Lagged Dependent Variables.” Economics Letters 14:179–185.

Inder, B. A. (1986). “An Approximation to the Null Distribution of the Durbin-Watson Statistic in Models Containing Lagged Dependent Variables.” Econometric Theory 2:413–428.

Jarque, C. M., and Bera, A. K. (1980). “Efficient Tests for Normality, Homoskedasticity, and Serial Independence of Regression Residuals.” Economics Letters 6:255–259.

Johansen, S. (1988). “Statistical Analysis of Cointegration Vectors.” Journal of Economic Dynamics and Control 12:231–254.

Johansen, S. (1991). “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models.” Econometrica 59:1551–1580.

Johnston, J. (1972). Econometric Methods. 2nd ed. New York: McGraw-Hill.

Jones, R. H. (1980). “Maximum Likelihood Fitting of ARMA Models to Time Series with Missing Observations.” Technometrics 22:389–396.

Judge, G. G., Griffiths, W. E., Hill, R. C., Lütkepohl, H., and Lee, T.-C. (1985). The Theory and Practice of Econometrics. 2nd ed. New York: John Wiley & Sons.

Kanzler, L. (1999). “Very Fast and Correctly Sized Estimation of the BDS Statistic.” Working paper, Department of Economics, Christ Church, University of Oxford.

King, M. L., and Wu, P. X. (1991). “Small-Disturbance Asymptotics and the Durbin-Watson and Related Tests in the Dynamic Regression Model.” Journal of Econometrics 47:145–152.

Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y. (1992). “Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root.” Journal of Econometrics 54:159–178.

Lee, J. H., and King, M. L. (1993). “A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances.” Journal of Business and Economic Statistics 11:17–27.

L’Esperance, W. L., Chall, D., and Taylor, D. (1976). “An Algorithm for Determining the Distribution Function of the Durbin-Watson Test Statistic.” Econometrica 44:1325–1326.

MacKinnon, J. G. (1991). “Critical Values for Cointegration Tests.” In Long-Run Economic Relationships: Readings in Cointegration, edited by R. F. Engle, and C. W. J. Granger, 267–276. Oxford: Oxford University Press.

Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.

Maeshiro, A. (1976). “Autoregressive Transformation, Trended Independent Variables and Autocorrelated Disturbance Terms.” Review of Economics and Statistics 58:497–500.

McLeod, A. I., and Li, W. K. (1983). “Diagnostic Checking ARMA Time Series Models Using Squared-Residual Autocorrelations.” Journal of Time Series Analysis 4:269–273.

Nelson, C. R., and Plosser, C. I. (1982). “Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications.” Journal of Monetary Economics 10:139–162.

Nelson, D. B. (1990). “Stationarity and Persistence in the GARCH(1,1) Model.” Econometric Theory 6:318–334.

Nelson, D. B. (1991). “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica 59:347–370.

Nelson, D. B., and Cao, C. Q. (1992). “Inequality Constraints in the Univariate GARCH Model.” Journal of Business and Economic Statistics 10:229–235.

Newey, W. K., and West, D. W. (1987). “A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica 55:703–708.

Newey, W. K., and West, D. W. (1994). “Automatic Lag Selection in Covariance Matrix Estimation.” Review of Economic Studies 61:631–653.

Ng, S., and Perron, P. (2001). “Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power.” Econometrica 69:1519–1554.

Park, R. E., and Mitchell, B. M. (1980). “Estimating the Autocorrelated Error Model with Trended Data.” Journal of Econometrics 13:185–201.

Phillips, P. C. B. (1987). “Time Series Regression with a Unit Root.” Econometrica 55:277–301.

Phillips, P. C. B., and Ouliaris, S. (1990). “Asymptotic Properties of Residual Based Tests for Cointegration.” Econometrica 58:165–193.

Phillips, P. C. B., and Perron, P. (1988). “Testing for a Unit Root in Time Series Regression.” Biometrika 75:335–346.

Prais, S. J., and Winsten, C. B. (1954). “Trend Estimators and Serial Correlation.” Cowles Commission Discussion Paper No. 383.

Ramsey, J. B. (1969). “Tests for Specification Errors in Classical Linear Least Squares Regression Analysis.” Journal of the Royal Statistical Society, Series B 31:350–371.

Said, S. E., and Dickey, D. A. (1984). “Testing for Unit Roots in ARMA Models of Unknown Order.” Biometrika 71:599–607.

Savin, N. E., and White, K. J. (1978). “Testing for Autocorrelation with Missing Observations.” Econometrica 46:59–67.

Schwarz, G. (1978). “Estimating the Dimension of a Model.” Annals of Statistics 6:461–464.

Schwert, G. (1989). “Tests for Unit Roots: A Monte Carlo Investigation.” Journal of Business and Economic Statistics 7:147–159.

Shin, Y. (1994). “A Residual-Based Test of the Null of Cointegration against the Alternative of No Cointegration.” Econometric Theory 10:91–115. 10.1017/S0266466600008240.

Shively, T. S. (1990). “Fast Evaluation of the Distribution of the Durbin-Watson and Other Invariant Test Statistics in Time Series Regression.” Journal of the American Statistical Association 85:676–685.

Spitzer, J. J. (1979). “Small-Sample Properties of Nonlinear Least Squares and Maximum Likelihood Estimators in the Context of Autocorrelated Errors.” Journal of the American Statistical Association 74:41–47.

Stock, J. H. (1994). “Unit Roots, Structural Breaks, and Trends.” In Handbook of Econometrics, edited by R. F. Engle, and D. L. McFadden, 2739–2841. Amsterdam: North-Holland.

Stock, J. H., and Watson, M. W. (1988). “Testing for Common Trends.” Journal of the American Statistical Association 83:1097–1107.

Stock, J. H., and Watson, M. W. (2002). Introduction to Econometrics. 3rd ed. Reading, MA: Addison-Wesley.

Theil, H. (1971). Principles of Econometrics. New York: John Wiley & Sons.

Vinod, H. D. (1973). “Generalization of the Durbin-Watson Statistic for Higher Order Autoregressive Process.” Communications in Statistics 2:115–144.

Wallis, K. F. (1972). “Testing for Fourth Order Autocorrelation in Quarterly Regression Equations.” Econometrica 40:617–636.

White, H. (1980). “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica 48:817–838.

White, H. (1982). “Maximum Likelihood Estimation of Misspecified Models.” Econometrica 50:1–25.

White, K. J. (1992). “The Durbin-Watson Test for Autocorrelation in Nonlinear Models.” Review of Economics and Statistics 74:370–373.

Wong, H., and Li, W. K. (1995). “Portmanteau Test for Conditional Heteroscedasticity, Using Ranks of Squared Residuals.” Journal of Applied Statistics 22:121–134.

Zakoian, J. M. (1994). “Threshold Heteroscedastic Models.” Journal of Economic Dynamics and Control 18:931–955.