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.

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.

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
n_{k
}of seasons_{ }available within the whole historical time series
is calculated:

n_{k}_{ = }n_{total}_{ / }n_{season}

where_{ }n_{season}_{ }is the number of periods per season and
n_{total}_{ }is the total number of_{ }historical values.

b.
The average value
A_{k} of each season k is calculated:

A_{k} = Σ V(t) / n_{season}

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

c.
The starting
seasonal index s_{start} (t) is calculated for each period t within each
season.

S_{start} (t) = V(t) / A_{k}

If a
non-completed season exists (that is, if n_{k }is not an integer number) the starting seasonal
index s_{start} (t) of the oldest historical data is calculated
with the average A_{k}of the n_{k}th season.

**Determination of the average seasonal
index**

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

s_{average}(s) = (s_{start} (s) + s_{start}(n_{season} + s) + ....+s_{start}((k-1) n_{season}+s))/k,

s = 1, ... ,
n_{season}

**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.