Xiao Liu PhD Thesis.pdf - Faculty of Information and Communication ...

esource management strategies that give preferences to a limited range of resources
[10]. Furthermore, if these segments reappear frequently during a duration series,
they can be deemed as potential patterns which represent unique behaviour of the
duration series under certain circumstances. Therefore, if we are able to define and
discover these typical patterns, the intervals of future durations can be estimated
with the statistical features of the closest patterns by matching the latest duration
sequences. Based on this motivation, here, we present the definition of our statistical
time-series patterns as follows.
Definition 4.1 (Statistical Time-Series Patterns):
For a specific time series T = { X1,
X 2...
X n}
which consists of n observations, its
pattern set is { P 1,
P 2...
P
m
Patterns = m}
where ∑ Length ( P i ) ≤ n . For pattern P i of
i=1
length k , it is a reoccurred segment which has unique statistical features of sample
mean µ and sample standard deviation σ , where µ = ∑ X k and
⎛ k ⎞
σ = ⎜ ∑ ( Xi − µ ) ⎟ ( k −1)
.
⎝i=
1 ⎠
2
Note that in this chapter, since we use statistical features to describe the
behaviour of each time-series segment in an overall sense, the order of patterns is
important for time-series forecasting while the order of sample points within each
pattern is not. Meanwhile, for the purpose of generality, sample mean and standard
deviation are employed as two basic statistical features to formulate each pattern.
However, other criteria such as the median value, the trend and the length of each
segment (the number of samples it consists of), can also be considered to make finegrained
definitions.
k
i=1
i
4.3.2 Strategy Overview
As depicted in the outlier of Figure 4.1, our statistical time-series pattern based
forecasting strategy consists of four major steps which are duration series building,
duration pattern recognition, duration pattern matching and duration interval
forecasting. The inner three circles stand for the three basic factors concerned with
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