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A Wavelet Characterization of Continuous‐Time Periodically Correlated Processes with Application to Simulation
Author(s) -
Ghanbarzadeh Mitra,
Aminghafari Mina
Publication year - 2016
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12185
Subject(s) - autocovariance , mathematics , wavelet , estimator , algorithm , characterization (materials science) , simple (philosophy) , process (computing) , mathematical analysis , computer science , statistics , artificial intelligence , fourier transform , philosophy , materials science , epistemology , nanotechnology , operating system
We introduce a wavelet characterization of continuous‐time periodically correlated processes based on a linear combination of infinite‐dimensional stationary processes. The finite version of this linear combination converges to the main process. The first‐order and second‐order estimators based on the wavelets are presented. Under a simple and easy algorithm, the periodically correlated process is simulated for a given autocovariance function. The proposed algorithm has two main advantages: first, it is fast, and second, it is distribution free. We indicate through four examples that the simulated data are periodically correlated with the desired period.