This thesis applies Atheoretical Regression Trees (ART) to the
problem of locating changes in mean in a time series where the
number and location of those changes are unknown. We undertook
an extensive simulation study into ART's performance on a range
of time series. We found ART to be a useful addition to currently
established structural break methodologies such as the CUSUM and
that due to Bai and Perron. ART was found to be useful in the
analysis of long time series which are not practical to analyze
with the optimal procedure of Bai and Perron.
ART was applied to a long standing problem in the analysis of
long memory time series.
We propose two new methods based on ART
for distinguishing between true long memory
and spurious long memory due to structural breaks. These methods
are fundamentally different from current tests and procedures
intended to discriminate between the two sets of competing
models.
The methods were
subjected to a simulation study and shown to be effective in
discrimination between simple regime switching models and
fractionally integrated processes.
We applied the new methods to 16 realized volatility series and
concluded they were not fractionally integrated series. All 16
series had mean shifts, some of which could be identified with
historical events.
We applied the new methods to a range of geophysical time series
and concluded they were not fractional Gaussian noises. All
of the series examined had mean shifts, some of which could
be identified with known climatic changes.
We conclude that our new methods are a significant advance in
model discrimination in long memory series.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/1715 |
| Date | January 2008 |
| Creators | Rea, William Stanley |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright William Stanley Rea, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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