TY - JOUR

T1 - Large deviation results for statistics of short-and long-memory Gaussian processes

AU - Sato, Toshiyuki

AU - Kakizawa, Yoshihide

AU - Taniguchi, Masanobu

PY - 1998/3

Y1 - 1998/3

N2 - This paper discusses the large deviation principle of several important statistics for short- and long-memory Gaussian processes. First, large deviation theorems for the log-likelihood ratio and quadratic forms for a short-memory Gaussian process with mean function are proved. Their asymptotics are described by the large deviation rate functions. Since they are complicated, they are numerically evaluated and illustrated using the Maple V system (Char et al., 1991a,b). Second, the large deviation theorem of the log-likelihood ratio statistic for a long-memory Gaussian process with constant mean is proved. The asymptotics of the long-memory case differ greatly from those of the short-memory case. The maximum likelihood estimator of a spectral parameter for a short-memory Gaussian stationary process is asymptotically efficient in the sense of Bahadur.

AB - This paper discusses the large deviation principle of several important statistics for short- and long-memory Gaussian processes. First, large deviation theorems for the log-likelihood ratio and quadratic forms for a short-memory Gaussian process with mean function are proved. Their asymptotics are described by the large deviation rate functions. Since they are complicated, they are numerically evaluated and illustrated using the Maple V system (Char et al., 1991a,b). Second, the large deviation theorem of the log-likelihood ratio statistic for a long-memory Gaussian process with constant mean is proved. The asymptotics of the long-memory case differ greatly from those of the short-memory case. The maximum likelihood estimator of a spectral parameter for a short-memory Gaussian stationary process is asymptotically efficient in the sense of Bahadur.

KW - Bahadur efficiency

KW - Gaussian process

KW - Large deviation principle

KW - Long-memory process

KW - Maximum likelihood estimator

KW - Short-memory process

KW - Spectral density

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U2 - 10.1111/1467-842X.00003

DO - 10.1111/1467-842X.00003

M3 - Article

AN - SCOPUS:0010083185

VL - 40

SP - 17

EP - 29

JO - Australian and New Zealand Journal of Statistics

JF - Australian and New Zealand Journal of Statistics

SN - 1369-1473

IS - 1

ER -