Inference of Seasonal Long-memory Time Series with Measurement Error

Author(s)
Henghsiu Tsai, Heiko Rachinger, Edward M. H. Lin
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.

Organisation(s)
Department of Economics
External organisation(s)
Academia Sinica - Taiwan, Universität Wien, National Chiao Tung University
Journal
Scandinavian journal of statistics
Volume
42
Pages
137-154
No. of pages
18
ISSN
0303-6898
DOI
https://doi.org/10.1111/sjos.12099
Publication date
03-2015
Peer reviewed
Yes
Austrian Fields of Science 2012
Statistics, Econometrics
Keywords
Portal url
https://ucris.univie.ac.at/portal/en/publications/inference-of-seasonal-longmemory-time-series-with-measurement-error(70d48383-2a36-44c4-b9b3-74e989da9ed3).html