Locally stationary wavelet process models for autoregressive conditional duration data

Summary

Duration data are a type of time series where we are interested both in the observed value of some variable and also how long it takes for the next event in a related sequence to happen. (For example, how frequently a given asset is traded and at what price, how often a group of animals visit a location and how many animals there are, or patient monitoring data recorded once per heartbeat).

They can be analysed in two different ways. One is to take the time intervals (durations) as the observations of interest, and then they become a regular time series which can be analysed using standard methods, or methods which have been proposed specifically for duration data. The classic reference here is Engle and Russell (1998). Such data could be analysed using wavelet methods such as wavelet variance (Percival and Walden, 2006) and the locally stationary wavelet process model (Nason, von Sachs and Kroisandt, 2000) to accommodate non-stationarity.

Another way is to use the values that are observed at the irregular time points and analyse these. There are fewer methods available for analysing irregular time series, and it would be interesting to develop wavelet tools for this. It would be even more interesting to bring the two ideas together and develop methods (wavelet or otherwise) to jointly analyse both the durations and the values observed at the irregular intervals.

References

Engle, RF & Russell, JR (1998). Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica 66, 1127-1162.

Percival, DB & Walden, AT (2006). Wavelet methods for time series analysis.
Cambridge: Cambridge University Press.

Nason, GP, Von Sachs, R, & Kroisandt, G (2000). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(2), 271-292.

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