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Integrated processes and the discrete cosine transform

Part of: Inference from stochastic processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Robert B. Davies
Robert B. Davies*
Affiliation:
Statistics Research Associates Ltd
*
1Postal address: Statistics Research Associates Limited, PO Box 12–649, Thorndon, Wellington, New Zealand. Email: robert@statsresearch.co.nz
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Abstract

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.

Keywords

Beta-optimal testBrownian motionDCT-IIdiscrete cosine transformintegrated processrandom walkspectrumtime-seriesunit root

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 62M15: Spectral analysis 91B84: Economic time series analysis
Type
Time series analysis
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 105 - 121
Copyright
Copyright © Applied Probability Trust 2001 

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