Empirical Likelihood for a Long Range Dependent Process Subordinated to a Gaussian Process
| Autor: | Ujjwal Das, Daniel J. Nordman, Soumendra N. Lahiri |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
education.field_of_study Series (mathematics) Applied Mathematics Population Estimating equations symbols.namesake Empirical likelihood symbols Applied mathematics Time domain Statistics Probability and Uncertainty Constant (mathematics) education Gaussian process Scaling Mathematics |
| Zdroj: | Journal of Time Series Analysis. 40:447-466 |
| ISSN: | 1467-9892 0143-9782 |
| DOI: | 10.1111/jtsa.12465 |
| Popis: | This article develops empirical likelihood methodology for a class of long range dependent processes driven by a stationary Gaussian process. We consider population parameters that are defined by estimating equations in the time domain. It is shown that the standard block empirical likelihood (BEL) method, with a suitable scaling, has a non‐standard limit distribution based on a multiple Wiener–Ito integral. Unlike the short memory time series case, the scaling constant involves unknown population quantities that may be difficult to estimate. Alternative versions of the empirical likelihood method, involving the expansive BEL (EBEL) methods are considered. It is shown that the EBEL renditions do not require an explicit scaling and, therefore, remove this undesirable feature of the standard BEL. However, the limit law involves the long memory parameter, which may be estimated from the data. Results from a moderately large simulation study on finite sample properties of tests and confidence intervals based on different empirical likelihood methods are also reported. |
| Databáze: | OpenAIRE |
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