TY - JOUR
T1 - Testing composite hypotheses for locally stationary processes
AU - Sakiyama, Kenji
AU - Taniguchi, Masanobu
PY - 2003/7
Y1 - 2003/7
N2 - For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to χ2 distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.
AB - For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to χ2 distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.
KW - Gaussian likelihood ratio test
KW - Lagrange multiplier test
KW - Local asymptotic normality
KW - Local power
KW - Locally asymptotically optimal test
KW - Locally stationary processes
KW - Tests for stationarity
KW - Time-varying spectral density
KW - Transfer function
KW - Wald test
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U2 - 10.1111/1467-9892.00317
DO - 10.1111/1467-9892.00317
M3 - Article
AN - SCOPUS:0141976688
VL - 24
SP - 483
EP - 504
JO - Journal of Time Series Analysis
JF - Journal of Time Series Analysis
SN - 0143-9782
IS - 4
ER -