G05PMF returns , a realisation of a time series from an exponential smoothing model defined by one of five smoothing functions:
Single Exponential Smoothing
Brown Double Exponential Smoothing
Linear Holt Exponential Smoothing
Additive Holt–Winters Smoothing
Multiplicative Holt–Winters Smoothing
where is the mean, is the trend and is the seasonal component at time with being the seasonal order. The errors, are either drawn from a normal distribution with mean zero and variance or randomly sampled, with replacement, from a user-supplied vector.
Chatfield C (1980) The Analysis of Time Series Chapman and Hall
1: MODE – INTEGERInput
On entry: indicates if G05PMF is continuing from a previous call or, if not, how the initial values are computed.
On entry: IFAIL must be set to , . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value is recommended. If the output of error messages is undesirable, then the value is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is . When the value is used it is essential to test the value of IFAIL on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6 Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
On entry, , or .
On entry, , , , or .
or and .
On entry, at least one of , or or .
On entry, and .
On entry, .
or and the array R has not been initialized correctly.
On entry, the array STATE has not been initialized correctly.
and model is unsuitable for multiplicative Holt–Winter.
8 Further Comments
This example reads observations from a time series relating to the rate of the earth's rotation about its polar axis and fits an exponential smoothing model using G13AMF.
G05PMF is then called multiple times to obtain simulated forecast confidence intervals.