2011/12/13 by Junbum Lee, Lee, Junbum, Suhasini Subba Rao +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Fault Detection and Control Systems #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1112.2759
openalex publication_date 2011/12/13 · arxiv created 2012/03/10 · arxiv updated 2012/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density, which can be considered as a quantile version of the usual spectral density function. The quantile spectral density 'measures' sequential dependence structure of a time series, and is well defined under relatively weak mixing conditions. We propose an estimator for the quantile spectral density and derive its asympototic sampling properties. We use the quantile spectral density to construct a goodness of fit test for time series and explain how this test can also be used for comparing the sequential dependence structure of two time series. The method is illustrated with simulations and some real data examples.