Time Series Modeling - Water Quality Management: Assessment and Interpretation - page 54

Table 4.1 Stage of Box-Jenkins modeling (Lohani and Wang 1987 )
Step Description

1 Check the data for normality

No transformation
Square root transformation
Logarithmic transformation
Power transformation

2 Identification

Plot of the transformed series
Autocorrelation function (ACF)
Partial autocorrelation function (PACF)

3 Estimation

Maximum likelihood estimate (MLE) for the model parameters (Ansley algorithm)

4 Diagnostic checks

Over-fitting
Examination of residuals (modi ed Portmanteau test)

5 Model Structure Selection Criteria

(a) AIC criteria
(b) PP criteria
(c) BIC criteria

4.13 Exponential Smoothing Methods

Exponential smoothing is a forecasting technique that attempts to track changes in a
time series. This is done by using newly observed values to update the estimates of
parameters in the time series model. The well-known methods of exponential
smoothing are:

1. Simple exponential smoothing,
2. Winter

s Method appropriates for seasonal data, and
3. One- and two- parameter double exponential smoothing.

'

When using an exponential smoothing method, it is often useful to employ
adaptive control procedures to monitor the accuracy of the forecasting system
(Chow 1965 ).
Exponential smoothing techniques are essentially equivalent to some special
Box-Jenkins models (McKenzie 1984 ). For this reason, only a brief mention of their
main features is presented (Bowerman and O ' Connell 1987 ).