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On The Unimodality Of The Exact Likelihood Function For Normal Ar(2) Series

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  • M. Minozzo
  • A. Azzalini

Abstract

. For stationary second‐order autoregressive normal processes, the conjecture of uniqueness of the solution of the exact likelihood equations is examined. A sufficient condition for uniqueness is given; this condition is satisfied with very high probability if the number of observations is not extremely small. Moreover, it is shown that not more than two maxima may exist. Examples of data which actually produce a likelihood function with two local maxima are given.

Suggested Citation

  • M. Minozzo & A. Azzalini, 1993. "On The Unimodality Of The Exact Likelihood Function For Normal Ar(2) Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 497-509, September.
    • Handle: RePEc:bla:jtsera:v:14:y:1993:i:5:p:497-509
    DOI: 10.1111/j.1467-9892.1993.tb00160.x
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    Cited by:

    1. James W. Miller, 1995. "Exact Maximum Likelihood Estimation In Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 607-615, November.

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