Thick-pen
transformation for time series
Piotr Fryzlewicz (LSE)
26/01/10
Traditional
visualisation of time series data often consists of plotting the time
series values against time and “connecting the dots”. We propose an
alternative, multiscale visualisation technique, motivated by the
scale-space approach in computer vision. In brief, our method also
“connects the dots”, but uses a range of pens of varying thicknesses
for this purpose. The resulting multiscale map, termed the Thick-Pen
Transform
(TPT) corresponds to viewing the time series from a range of distances.
We formally prove that the TPT is a discriminatory statistic for two
Gaussian time series with distinct correlation structures. Further, we
show interesting possible applications of the TPT to measuring
cross-dependence in multivariate time series, and to testing for
stationarity.
In particular, we derive the asymptotic distribution of our test
statistic, and argue that the test is applicable to both linear and
nonlinear processes under low moment assumptions. Various other aspects
of the methodology, including other possible applications, are also
discussed. This is joint work with Hee-Seok Oh, Seoul National
University, Korea.
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[Last modified: Jan. 18th 2010 by Kostas
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