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 Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt Road, 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
- 502025 Econometrics, 101018 Statistics
- Keywords
- ASJC Scopus subject areas
- Statistics and Probability, Statistics, Probability and Uncertainty
- 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