Integrated processes and the discrete cosine transform

2001 ◽  
Vol 38 (A) ◽  
pp. 105-121 ◽  
Author(s):  
Robert B. Davies
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Brownian Motion ◽  
White Noise ◽  
Discrete Cosine Transform ◽  
Unit Root ◽  
Stationary Time Series ◽  
Cosine Transform ◽  
Stationary Time ◽  
Integrated Processes

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

Integrated processes and the discrete cosine transform

2001 ◽  
Vol 38 (A) ◽  
pp. 105-121
Author(s):  
Robert B. Davies
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Brownian Motion ◽  
White Noise ◽  
Discrete Cosine Transform ◽  
Unit Root ◽  
Stationary Time Series ◽  
Cosine Transform ◽  
Stationary Time ◽  
Integrated Processes

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

scholarly journals Quantile spectral analysis for locally stationary time series

2017 ◽  
Vol 79 (5) ◽  
pp. 1619-1643 ◽  
Author(s):  
Stefan Birr ◽  
Stanislav Volgushev ◽  
Tobias Kley ◽  
Holger Dette ◽  
Marc Hallin
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Locally Stationary Time Series

scholarly journals Testing the equality of several independent stationary and non-stationary time series models with fractional Brownian motion errors

2021 ◽  
Vol 60 (1) ◽  
pp. 1767-1775
Author(s):  
Mohammad Reza Mahmoudi ◽  
Dumitru Baleanu ◽  
Sultan Noman Qasem ◽  
Amirhosein Mosavi ◽  
Shahab S. Band
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Stationary Time

Quantile spectral analysis and long-memory time series

1986 ◽  
Vol 23 (A) ◽  
pp. 41-54 ◽  
Author(s):  
Emanuel Parzen
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Long Memory ◽  
Model Identification ◽  
Time Series Model ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Memory Time ◽  
Short Memory ◽  
Simultaneous Use

An approach to time series model identification is described which involves the simultaneous use of frequency, time and quantile domain algorithms; the approach is called quantile spectral analysis. It proposes a framework to integrate the analysis of long-memory (non-stationary) time series with the analysis of short-memory (stationary) time series.

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