Information Technology Reference
In-Depth Information
2.4 Time Series Analysis
Time series analysis deals with the problems of identification of basic
characteristic features of time series, as well as with discovering - from the
observation data on which the time series is built - the internal time series
structure.
2.4.1 Objectives of Analysis
The main objectives of time series analysis are
x
building of input-output models
that represent the equivalent transfer
functions of processes behind the time series
x
forecasting the future time series values
from the past values using the
models developed
x
control systems design
, based on the result of analysis.
Depending on the origin of the observation data, forecasting of future values of
time series can also provide support in efficient process and production monitoring
and failure diagnosis, in product quality inspection,
etc
., using the time-domain or
frequency-domain approach.
Once the time series model has been developed and tested it can be used for
forecasting the future time series values at various time distances
d
. Of course, the
forecasting does not deliver the exact future values of data that the given time
series will really have, but rather their estimates. For example, using the auto-
regressive model
x
I
x
I
x
H
t
11
t
2 2
t
t
based on a one-step movement along the time series
x
,
I
x
I
x
H
t
1
1
t
2
t
1
t
1
we can formally write the predicted value to be
ˆ
t
x
.
I
x
I
x
1
1
t
2
t
1
For the
two-steps ahead prediction
, based on a two-steps movement along the
time series, we can also formally write
x
I
x
IH
x
2
,
t
2
1
t
1
2
t
t
or
x
I II H
(
x
x
)
IH
x
,
t
2
1
1
t
2
t
1
t
1
2
t
t
2
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