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Confidence Regions For Parameters In The Ar(1) Model

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  • David Hamilton
  • Ka Ho Wu

Abstract

. The construction of approximate joint and marginal confidence regions for parameters in the first‐order autoregressive time series model is discussed. These regions are based on the large sample distributions of the likelihood ratio (and approximations to it), of the maximum likelihood estimates and of the score statistics. All these approaches are illustrated using a well‐known example from Box and Jenkins (Time Series Analysis:Forecasting and Control, revised edn. San Francisco:Holden Day, 1976) and some simulated series. In addition, a simulation study is provided for comparing the coverage properties of the various procedures.

Suggested Citation

  • David Hamilton & Ka Ho Wu, 1995. "Confidence Regions For Parameters In The Ar(1) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 249-265, May.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:3:p:249-265
    DOI: 10.1111/j.1467-9892.1995.tb00233.x
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    References listed on IDEAS

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    1. Tanaka, Katsuto, 1983. "Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean," Econometrica, Econometric Society, vol. 51(4), pages 1221-1231, July.
    2. Dent, Warren & Min, An-Sik, 1978. "A Monte Carlo study of autoregressive integrated moving average processes," Journal of Econometrics, Elsevier, vol. 7(1), pages 23-55, February.
    3. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
    4. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
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