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ON THE UNIMODALITY OF THE EXACT LIKELIHOOD FUNCTION FOR NORMAL AR(2) SERIES
Author(s) -
Minozzo M.,
Azzalini A.
Publication year - 1993
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1993.tb00160.x
Subject(s) - unimodality , mathematics , maxima , uniqueness , autoregressive model , likelihood function , conjecture , series (stratigraphy) , function (biology) , likelihood principle , maximum likelihood , statistics , mathematical analysis , combinatorics , quasi maximum likelihood , art , paleontology , evolutionary biology , performance art , biology , art history
. 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.
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