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Seminar on Probability and Statistics Wednesday June 27 2007 Tokyo 122 4:20-5:30 pm
Empirical likelihood method for time series analysis
小方 浩明 / OGATA, Hiroaki 早稲田大学, 国際教養学部 / School of International Liberal Studies, Waseda University Abstract For a class of vector-valued non-Gaussian stationary processes
with unkown parameters, we develop the empirical likelihood
approach which was proposed in the i.i.d. setting. In the time
series analysis it is known that Whittle likelihood is one of
fundamental tools to get a good estimator of unknown parameters
and that the score functions are asymptotically normal. Motivated
by the Whittle likelihood, we take its score as an estimating
function and obtain the asymptotic distribution of our test statistic.
Since the fitted spectral model may be different from true spectral
structure, the results enable us to construct confidence rigions
for various important time series parameters without knowing true
spectral structure.
We also consider the approach to a minimum contrast estimation
and Cressie-Read power-divergence statistic. Numerical studies are
introduced and illuminate some interesting features of the empirical
approach.
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