 ## Seasonal Linear Regression ### Use

You can use seasonal linear regression (forecast strategy 35) alternatively to forecast with season models (forecast strategy 30) or forecast according to Winters (forecast strategy 31). Use seasonal linear regression especially if the historical time series contains many zeros or very small values. Forecast strategy 30 could calculate basic values that are too high in these cases.

### Features

Before the system applies seasonal linear regression, it carries out a seasonal test. The system uses this test to check if the historical data contains any seasonal patterns. For this, the system determines the autocorrelation coefficient for all periods (see Automatic Model Selection Procedure 1). If the value determined is at least 0.3, the system applies seasonal linear regression. If the value is less than 0.3, the system does not recognize a seasonal pattern and applies linear regression.

### Activities

The system calculates the seasonal linear regression line as follows:

...

1.      The seasonal indices are calculated:

Determination of the starting seasonal index for each historical period t

a.      The number nk of seasons available within the whole historical time series is calculated:

nk = ntotal / nseason

where nseason is the number of periods per season and ntotal is the total number of historical values.

b.      The average value Ak of each season k is calculated:

Ak = Σ V(t) / nseason

where V(t) is the historical value of period t and nseason is the number of periods per season.

c.      The starting seasonal index sstart (t) is calculated for each period t within each season.

Sstart (t) = V(t) / Ak

If a non-completed season exists (that is, if nk is not an integer number) the starting seasonal index sstart (t) of the oldest historical data is calculated with the average Akof the nkth season.

Determination of the average seasonal index

d.      If k complete seasons are available, the starting seasonal indices are averaged:

saverage(s) = (sstart (s) + sstart(nseason + s) + ....+sstart((k-1) nseason+s))/k,

s = 1, ... , nseason

Smoothing of the average seasonal indices

e.      If you have entered a smoothing factor in field PERSMO of the univariate forecast profile, the result of step d is smoothed. We recommend that you enter a smoothing factor of ‘1‘.

2.      The actual data is corrected on the basis of the seasonal indices calculated in step 1.

3.      Linear regression is performed on the non-seasonal actual values.

4.      The seasonal indices are applied to the results of the linear regression calculation, which produces the forecast results. 