Detection of hidden components (seasonal and cyclical) for long memory time series by spectral analysis of kernal estimators.

long memory time series by spectral analysis

Abstract

Abstract

The concept of long memory or long dependency (LRD) implies that the process is made up of many temporal correlations, and that the sum of the autocorrelations is slowly decreasing. Due to the length of the time series, hidden seasonal and periodic components arise in this type of series that cannot be detected through the temporal method of analysis, but through the iterative method of analysis. so non-parametric estimators have been proposed Lomax Kernel estimator, Reciprocal inverse Gaussian Kernel estimator) And compare it with by RMAD statistic. To determine the best method, simulation was used, and the results showed that the Lomax Kernel estimator was the best for its ability to detect hidden components, and it also had the lowest value for the RMAD statistic.  It was applied to real data for a time series related to respiratory diseases. Kernel estimators are considered to have good advantages in the spectral analysis of time series. We also show that these infections are greatly affected by seasonality, which recurs approximately every 8 months, and its duration is not short, as it lasts for approximately 3 months.

Keywords: long memory, spectrum analysis, nonparametric estimators, hidden components, Fourier transform.