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The Effect of the First Observation in Regression Models with First‐Order Autoregressive Disturbances

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  • Dale J. Poirier

Abstract

Based on well‐known updating formulae used in Kalman filtering and recursive residual estimation, this study presents simple formulae for determining the effect of including the first observation in regression models with first‐order autoregressive disturbances. These formulae describe the changes in coefficient estimates, variance estimates and covariance estimates in terms of similar quantities involving the first observation.

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  • Dale J. Poirier, 1978. "The Effect of the First Observation in Regression Models with First‐Order Autoregressive Disturbances," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(1), pages 67-68, March.
    • Handle: RePEc:bla:jorssc:v:27:y:1978:i:1:p:67-68
    DOI: 10.2307/2346228
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    Cited by:

    1. Avdis, Efstathios & Wachter, Jessica A., 2017. "Maximum likelihood estimation of the equity premium," Journal of Financial Economics, Elsevier, vol. 125(3), pages 589-609.
    2. Wachter, Jessica A. & Warusawitharana, Missaka, 2015. "What is the chance that the equity premium varies over time? Evidence from regressions on the dividend-price ratio," Journal of Econometrics, Elsevier, vol. 186(1), pages 74-93.
    3. Wachter, Jessica A. & Warusawitharana, Missaka, 2009. "Predictable returns and asset allocation: Should a skeptical investor time the market?," Journal of Econometrics, Elsevier, vol. 148(2), pages 162-178, February.
    4. Roland Jeske & Seuck Song, 2003. "Relative efficiency of OLSE and COTE for seasonal autoregressive disturbances," Statistical Papers, Springer, vol. 44(3), pages 421-432, July.
    5. Efstathios Avdis & Jessica A. Wachter, 2013. "Maximum likelihood estimation of the equity premium," NBER Working Papers 19684, National Bureau of Economic Research, Inc.

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