Issue with Incorrect Seasonality Updates in Holt-Winters Model

I'm having an issue with the seasonality updates in my Holt-Winters model. Sometimes the values seem wrong. Could it be an indexing problem? How can I fix this?

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Answer 1

[Adit]

Hello Caden,

Issues with seasonality updates in the Holt-Winters model are often due to errors in indexing. Here’s a step-by-step guide to help you diagnose and fix this issue:

With Holt-Winters, you usually keep your seasonal factors in an array (let’s call it S). The length of this array matches your seasonal cycle—so if you’re working with monthly data, it’ll have 12 slots. As you process each new data point, you update the relevant spot in S, looping back to the start once you reach the end of the cycle.

For the additive version in MATLAB, the update for the seasonal component often looks something like this:

S(mod(t-1, period) + 1) = gamma * (y(t) - L(t)) + (1 - gamma) * S(mod(t-period-1, period) + 1);

A few things to keep in mind here:

• t is just your time index.
• period is your season length (like 12 for monthly).
• L(t) is your level estimate at time t.
• gamma controls the smoothing for seasonality.
• y(t) is your observed value.

And don’t forget: MATLAB uses 1-based indexing, not 0, so always add +1 after the mod operation.

Please note that off-by-one mistakes are easy to make since MATLAB’s arrays are 1-based. Also, keep an eye out for negative indices—if you’re not careful, (t-period-1) can go below zero. A good rule of thumb is to start your loop at t = period + 1.

Example code:

% Initialization
period = 12;
S = zeros(1, period);
% ... Initialize S with initial seasonal values ...

for t = period+1:length(y)
    % Update level, trend, etc.
    idx_current = mod(t-1, period) + 1;
    idx_prev = mod(t-period-1, period) + 1;
    S(idx_current) = gamma * (y(t) - L(t)) + (1 - gamma) * S(idx_prev);
end

Quick tips for debugging:

• Print out your indices and seasonal values to make sure they’re updating as expected.
• Check your loop bounds to avoid stepping outside your array.
• If you’re stuck, try comparing your results to MATLAB’s built-in forecasting tools, they’re a good sanity check.

I hope this helps, thanks!