How the instability of ranks under long memory affects large-sample inference
| Autor: | Murad S. Taqqu, Shuyang Bai |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
General Mathematics Hermite rank Inference Mathematics - Statistics Theory Statistics Theory (math.ST) non-Gaussian limit 01 natural sciences 010104 statistics & probability Long-range dependence 0502 economics and business FOS: Mathematics Applied mathematics Sample variance Limit (mathematics) 0101 mathematics large-sample inference Statistic 050205 econometrics Mathematics Long memory Hermite polynomials 05 social sciences Rank (computer programming) Estimator 62M10 60F05 instability power rank Statistics Probability and Uncertainty Random variable |
| Zdroj: | Statist. Sci. 33, no. 1 (2018), 96-116 |
| Popis: | Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue that a rank other than one is unstable, whereas, a rank equal to one is stable. We provide empirical evidence supporting this argument. This has important consequences. Assuming a higher-order rank when it is not really there usually results in underestimating the order of the fluctuations of the statistic of interest. We illustrate this through various examples involving the sample variance, the empirical processes and the Whittle estimator. 31 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|