TY - JOUR

T1 - Cressie-read power-divergence statistics for non-gaussian vector stationary processes

AU - Ogata, Hiroaki

AU - Taniguchi, Masanobu

PY - 2009/3/1

Y1 - 2009/3/1

N2 - For a class of vector-valued non-Gaussian stationary processes, we develop the Cressie-Read power-divergence (CR) statistic approach which has been proposed for the i.i.d. case. The CR statistic includes empirical likelihood as a special case. Therefore, by adopting this CR statistic approach, the theory of estimation and testing based on empirical likelihood is greatly extended. We use an extended Whittle likelihood as score function and derive the asymptotic distribution of the CR statistic. We apply this result to estimation of autocorrelation and the AR coefficient, and get narrower confidence intervals than those obtained by existing methods. We also consider the power properties of the test based on asymptotic theory. Under a sequence of contiguous local alternatives, we derive the asymptotic distribution of the CR statistic. The problem of testing autocorrelation is discussed and we introduce some interesting properties of the local power.

AB - For a class of vector-valued non-Gaussian stationary processes, we develop the Cressie-Read power-divergence (CR) statistic approach which has been proposed for the i.i.d. case. The CR statistic includes empirical likelihood as a special case. Therefore, by adopting this CR statistic approach, the theory of estimation and testing based on empirical likelihood is greatly extended. We use an extended Whittle likelihood as score function and derive the asymptotic distribution of the CR statistic. We apply this result to estimation of autocorrelation and the AR coefficient, and get narrower confidence intervals than those obtained by existing methods. We also consider the power properties of the test based on asymptotic theory. Under a sequence of contiguous local alternatives, we derive the asymptotic distribution of the CR statistic. The problem of testing autocorrelation is discussed and we introduce some interesting properties of the local power.

KW - Empirical likelihood

KW - Estimating function

KW - Local asymptotic normality

KW - Spectral density matrix

KW - Whittle likelihood

UR - http://www.scopus.com/inward/record.url?scp=60249088305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60249088305&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9469.2008.00618.x

DO - 10.1111/j.1467-9469.2008.00618.x

M3 - Article

AN - SCOPUS:60249088305

VL - 36

SP - 141

EP - 156

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 1

ER -