Testing for homogeneity of variance in time series: Long memory, wavelets, and the Nile River

By Brandon Whitcher, Simon D. Byers, Peter Guttorp, Donald B. Percival. 2002

122 citations recorded by the source corpus.

We consider the problem of testing for homogeneity of variance in a time series with long memory structure. We demonstrate that a test whose null hypothesis is designed to be white noise can, in fact, be applied, on a scale by scale basis, to the discrete wavelet transform of long memory processes. In particular, we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process. The point at which the test statistic, using a nondecimated version of the discrete wavelet transform, achieves its maximum value can be used to estimate the time of the unknown variance change. We apply our proposed test statistic on five time series derived from the historical record of Nile River yearly minimum water levels covering 622–1922 A.D., each series exhibiting various degrees of serial correlation including long memory. In the longest subseries, spanning 622–1284 A.D., the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 A.D., which coincides closely with the construction of a new device around 715 A.D. for measuring the Nile River. The test also detects a change in variance for a record of only 36 years.

Subfields: Economics and Econometrics, Finance, Signal Processing

View Paper: https://www.semanticscholar.org/paper/d7cd3913ad90161f36ad3054cd2923825fb219bd

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In Economics and Econometrics

1. Michael A. Osborne
2. Stephen J. Roberts
3. Steven Reece
4. H. Bakhshi

In Finance

1. Michael A. Osborne
2. Stephen J. Roberts
3. Roman Garnett

In Signal Processing

1. Michael A. Osborne
2. Stephen J. Roberts
3. Roman Garnett
4. Suzanne Aigrain

Citations in the corpus

• Bayesian Gaussian processes for sequential prediction, optimisation and quadrature (2010, background): “2 Nile data We next consider a canonical changepoint dataset, the minimum water levels of the Nile river during the period AD 622–1284 [Whitcher et al., 2002].”
• Gaussian processes for time-series modelling (2013, background): “We first consider a canonical changepoint dataset, the minimum water levels of the Nile river during the period AD 622–1284 [20].”
• Sequential Bayesian Prediction in the Presence of Changepoints and Faults (2010, background): “We first consider a canonical changepoint data set, the minimum water levels of the Nile river during the period AD 622–1284 [23].”