# How to pick coefficients for Holt Winters?

I'm using Holt Winters to predict sales revenue from past performance. Seasonality and changing trends exist in the data.

One of the reasons chosen for Holt Winters is that it is fairly simple (implementable in excel) and explainable to non-statisticians. If other methodologies are more appropriate I’m happy to hear about them.

A key implementation detail is to choose coefficients $\alpha, \beta$, and $\gamma$. Are there “standard” values for these?

The other reason for this methodology is that it auto-updates. This will be useful as the series will change with market shifts. I was planning to adjust the “standard” value by eye, to try to mitigate likely changes. Is this a reasonable approach?

## 2 Answers

You should not "choose" coefficients, you should estimate them from the data. The values of $\alpha$, $\beta$ and $\gamma$ control how quickly the model components change over time. What values are appropriate depend on the data. You can estimate them by minimizing the MSE, for example. Even in Excel you can do that using Solver.

• Thanks excellent help, would you minimise the MSE on out of time data or over the entire series? Nov 3, 2011 at 10:00
• On the entire series Nov 3, 2011 at 22:57
• @RobHyndman Assume we are given a time series for training, where the ts spans 2 time periods. We usually use this training set to bootstrap the estimation of level, trend, and seasonality. How can we use this training set for estimation of α, β and γ instead? Because to calculate MSE, we still need to be able to estimate the L,T, and S first. I hope I am making sense. Aug 18, 2016 at 23:22
• Use a nonlinear optimizer. Aug 18, 2016 at 23:35

You asked "If other methodologies are more appropriate I’m happy to here about them." A generalized ARIMA can be easily expressed as a lagged auto-regression ADL or PDL . THis model easily adpats to changes in levels, trends , parameters , seasonal pulses , variability. You are assuming a structure rather than allowing the data to suggest the structure.