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.
URL 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.

Bai, J. and Perron, P. (2003b), “Critical Values for Multiple Structural Change Tests,” Econometrics Journal, 6, 72–78.

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

Baillie, R. (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 R. J. Gordon, ed., The American Business Cycle, 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. Edition, 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 at 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 O. Blanchard and S. Fisher, eds., NBER Macroeconomics Annual, 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 Edition, Baltimore: Johns Hopkins University Press.

Greene, W. H. (1993), Econometric Analysis, 2nd Edition, 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 Edition, 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,” University of British Columbia, Discussion Paper No. 78-10.

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 Edition, 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 Edition, New York: John Wiley & Sons.

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

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 R. F. Engle and C. W. J. Granger, eds., Long-Run Economic Relationships, 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.

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 R. F. Engle and D. L. McFadden, eds., Handbook of Econometrics, 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 Edition, 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,” Communication 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.