Time Series Seasonality Strength Calculator

Work out time series seasonality strength instantly with clear inputs, formula shown and shareable results.

About Time Series Seasonality Strength Calculator

After STL decomposition into trend, seasonal and remainder components, strength is measured as 1 minus the remainder variance over the variance of the component plus remainder. Values near 1 mean the component explains almost all the variation that is not noise, and near 0 mean it explains almost none. This is a principled way to decide whether a seasonal model is warranted at all.

Formula

Component strength

Fs = 1 - Var(remainder) / Var(seasonal + remainder); Ft = 1 - Var(remainder) / Var(trend + remainder)

Worked example

With the default values below, Time Series Seasonality Strength Calculator returns Seasonal strength Fs of 0.7692. Change any input above and every figure here is recalculated in your browser.

Inputs used

Variance of the seasonal componentminimum 0: 40
Variance of the remainderminimum 0: 12
Variance of the trend componentminimum 0: 90

Results

Seasonal strength Fs: 0.7692
Trend strength Ft: 0.8824
Share of variance left unexplained: 8.45%
Modelling guidance: Strongly seasonal - use a seasonal model

Step by step

1Values used
2Component strength
3Seasonal strength Fs= 0.7692
4Trend strength Ft= 0.8824
5Share of variance left unexplained= 8.45
6Modelling guidance= Strongly seasonal - use a seasonal model

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Can a series have both strong trend and strong seasonality?

Yes, they are measured independently. Retail sales typically show high values for both, which is why models such as Holt-Winters carry separate trend and seasonal states.

What if seasonal strength is near zero?

Drop the seasonal terms. Fitting seasonality that is not there costs parameters and adds variance to the forecast without reducing bias.