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Long memory and changepoint models: a spectral classification procedure. (English) Zbl 1384.62293

Summary: Time series within fields such as finance and economics are often modelled using long memory processes. Alternative studies on the same data can suggest that series may actually contain a ‘changepoint’ (a point within the time series where the data generating process has changed). These models have been shown to have elements of similarity, such as within their spectrum. Without prior knowledge this leads to an ambiguity between these two models, meaning it is difficult to assess which model is most appropriate. We demonstrate that considering this problem in a time-varying environment using the time-varying spectrum removes this ambiguity. Using the wavelet spectrum, we then use a classification approach to determine the most appropriate model (long memory or changepoint). Simulation results are presented across a number of models followed by an application to stock cross-correlations and US inflation. The results indicate that the proposed classification outperforms an existing hypothesis testing approach on a number of models and performs comparatively across others.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M15 Inference from stochastic processes and spectral analysis
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