Predictor Selection for Positive Autoregressive Processes

REFERENCES

• Barndorff-Nielsen, O.E., and Shephard, N. (2001), “Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics” (with discussion), Journal of the Royal Statistical Society, Series B, 63, 167–241.
   Google Scholar
• Bell, C.B., and Smith, E.P. (1986), “Inference for Nonnegative Autoregressive Schemes,” Communications in Statistics: Theory and Methods, 15, 2267–2293.
   Web of Science ®Google Scholar
• Burr, I.W. (1976), Statistical Quality Control Methods, New York: Marcel Dekker.
   Google Scholar
• Chan, N.H. (1989), “Asymptotic Inference for Unstable Autoregressive Time Series With Drifts,” Journal of Statistical Planning and Inference, 23, 301–312.
   Web of Science ®Google Scholar
• Chow, Y.S. (1965), “Local Convergence of Martingales and the Law of Large Numbers,” The Annals of Mathematical Statistics, 36, 552–558.
   Google Scholar
• Clark, T.E., and West, K.D. (2006), “Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference Hypothesis,” Journal of Econometrics, 135, 155–186.
   Web of Science ®Google Scholar
• Datta, D., and McCormick, W.P. (1995), “Bootstrap Inference for a First-Order Autoregression With Positive Innovations,” Journal of the American Statistical Association, 90, 1289–1300.
   Web of Science ®Google Scholar
• Davis, R.A., and McCormick, W.P. (1989), “Estimation for First-Order Autoregressive Processes With Positive or Bounded Innovations,” Stochastic Processes and Their Applications, 31, 237–250.
   Web of Science ®Google Scholar
• Dickey, D.A., and Fuller, W.A. (1981), “Likelihood Ratio Statistics for Autoregressive Time Series With a Unit Root,” Econometrica, 49, 1057–1072.
   Web of Science ®Google Scholar
• Gaver, D.P., and Lewis, P. A.W. (1980), “First-Order Autoregressive Gamma Sequences and Point Processes,” Advances in Applied Probability, 12, 727–745.
   Web of Science ®Google Scholar
• Hamilton, J.D. (1994), Time Series Analysis, Princeton, NJ: Princeton University Press.
   Google Scholar
• Hemerly, E.M., and Davis, M. H.A. (1989), “Strong Consistency of the pls Criterion for Order Determination of Autoregressive Processes,” The Annals of Statistics, 17, 941–946.
   Web of Science ®Google Scholar
• Hutton, J.L. (1990), “Nonnegative Time Series Models for Dry River Flow,” Journal of Applied Probability, 27, 171–182.
   Web of Science ®Google Scholar
• Ing, C.-K. (2001), “A Note on Mean-Squared Prediction Errors of the Least Squares Predictors in Random Walk Models,” Journal of Time Series Analysis, 22, 711–724.
   Web of Science ®Google Scholar
• Ing, C.-K. (2004), “Selecting Optimal Multistep Predictors for Autoregressive Processes of Unknown Order,” The Annals of Statistics, 32, 693–722.
   Web of Science ®Google Scholar
• Ing, C.-K. (2007), “Accumulated Prediction Errors, Information Criteria and Optimal Forecasting for Autoregressive Time Series,” The Annals of Statistics, 35, 1238–1277.
   Web of Science ®Google Scholar
• Lawrance, A.J., and Lewis, P. A.W. (1985), “Modelling and Residual Analysis of Nonlinear Autoregressive Time Series in Exponential Variables” (with discussion), Journal of the Royal Statistical Society, Series B, 47, 165–202.
   Google Scholar
• Lewis, P. A.W., McKenzie, E., and Hugus, D.K. (1989), “Gamma Processes,” Communications in Statistics: Stochastic Models, 5, 1–30.
   Google Scholar
• Nicholson, A.J. (1950), “Population Oscillations Caused by Competition for Food,” Nature, 165, 476–477.
   Web of Science ®Google Scholar
• Nielsen, B. (2006), “Correlograms for Non-Stationary Autoregressions,” Journal of the Royal Statistical Society, Series B, 68, 707–720.
   Google Scholar
• Nielsen, B., and Shephard, N. (2003), “Likelihood Analysis of a First-Order Autoregressive Model With Exponential Innovations,” Journal of Time Series Analysis, 24, 337–344.
   Web of Science ®Google Scholar
• Sarlak, N. (2008), “Annual Streamflow Modelling With Asymmetric Distribution Function,” Hydrological Processes, 22, 3403–3409.
   Web of Science ®Google Scholar
• Sim, C.H. (1987), “A Mixed Gamma ARMA(1,1) Model for River Flow Time Series,” Water Resources Research, 23, 32–36.
   Web of Science ®Google Scholar
• Speed, T.P., and Yu, B. (1993), “Model Selection and Prediction: Normal Regression,” Annals of the Institute of Statistical Mathematics, 45, 35–54.
   Web of Science ®Google Scholar
• Wei, C.-Z. (1987), “Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models With Application to Time Series,” The Annals of Statistics, 15, 1667–1682.
   Web of Science ®Google Scholar
• Wei, C.-Z. (1992), “On Predictive Least Squares Principles,” The Annals of Statistics, 20, 1–42.
   Web of Science ®Google Scholar
• Wei, W. W.S. (2006), Time Series Analysis: Univariate and Multivariate Methods (2nd ed.), Boston, MA: Pearson.
   Google Scholar
• Yu, S.-H., Lin, C.-C., and Cheng, H.-W. (2012), “A Note on Mean Squared Prediction Error Under the Unit Root Model With Deterministic Trend,” Journal of Time Series Analysis, 33, 276–286.
   Web of Science ®Google Scholar