Title: Inference of Seasonal Long-memory Time Series with Measurement Error
Authors: Tsai, Henghsiu
Rachinger, Heiko
Lin, Edward M. H.
資訊管理與財務金融系 註:原資管所+財金所
Department of Information Management and Finance
Keywords: measurement error;model uncertainty;seasonal autoregressive fractionally integrated moving-average models;spectral maximum likelihood estimator
Issue Date: 1-Mar-2015
Abstract: We consider the Whittle likelihood estimation of seasonal autoregressive fractionally integrated moving-average models in the presence of an additional measurement error and show that the spectral maximum Whittle likelihood estimator is asymptotically normal. We illustrate by simulation that ignoring measurement errors may result in incorrect inference. Hence, it is pertinent to test for the presence of measurement errors, which we do by developing a likelihood ratio (LR) test within the framework of Whittle likelihood. We derive the non-standard asymptotic null distribution of this LR test and the limiting distribution of LR test under a sequence of local alternatives. Because in practice, we do not know the order of the seasonal autoregressive fractionally integrated moving-average model, we consider three modifications of the LR test that takes model uncertainty into account. We study the finite sample properties of the size and the power of the LR test and its modifications. The efficacy of the proposed approach is illustrated by a real-life example.
URI: http://dx.doi.org/10.1111/sjos.12099
ISSN: 0303-6898
DOI: 10.1111/sjos.12099
Volume: 42
Begin Page: 137
End Page: 154
Appears in Collections:Articles