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H1
A
time series
is a collection of observations
{}
t
x
made sequentially through time.
When the variation of some quantity over a region of
space
is studied,
t
is a
spatial
variable.
Examples
of time series:
1)
Lynx data:
a periodic oscillation with an approximate period of ten years.
2)
Company earnings data:
note the upward trend, seasonal variation and increase in variability.
3)
Global temperature record: note an apparent upward trend in the series that has been used
as an argument for the global warming hypothesis.
4)
Southern Oscillation Index (SOI) measures changes in air pressure, related to sea surface
temperature in the central Pacific.
Deterministic, stochastic, and chaotic time series
.
Almost all quantitative phenomena occurring in science should be treated as random processes.
Objectives of time series analysis
:
to
understand the underlying dynamics and to forecast future events.
Probability models for time series
.
For
each
t
,
t
x
is treated as a value of the random variable
t
X
, and an observed record is merely one
record out of a whole collection of possible records which we might have observed.
This collection is
called the
ensemble
, and each particular record is called a
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 Spring '09
 gUR

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