Holt-Winters level
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The triple exponential smoothing level calculator (Holt-Winters level) is a statistical tool used to forecast values in time series. It adjusts historical data to remove seasonal fluctuations and identify a trend pattern.
The triple exponential smoothing formula is L_t = α·(y_t − S_{t−s}) + (1−α)·(L_{t−1}+T_{t−1}), where L_t is the smoothed value at time t, α is the smoothing parameter, y_t is the observed value at time t, S_{t−s} is the seasonal value at time t-s, L_{t−1} is the previous smoothed value and T_{t−1} is the previous trend.
This calculator is useful for cases where there is a long-term trend and seasonal fluctuations. It's essential to be careful when choosing the value of the smoothing parameter (α) and the seasonal frequency (s), as both affect the accuracy of the model.
Frequently asked questions
What is the smoothing parameter (α) and how to choose its value?
The smoothing parameter (α) controls the amount of smoothing applied to the data. If α is too high, the data will be smoothed too much, while if α is too low, it will not be smoothed enough. The optimal value of α depends on the specific dataset and may be found through experimentation or more advanced optimization methods.
What is the seasonal frequency (s) and how to choose it?
The seasonal frequency (s) is the period in which seasonal fluctuations occur. For example, if seasonal fluctuations occur annually, the seasonal frequency (s) would be 12. The choice of seasonal frequency depends on the type of data and may be found through time series analysis.
What is the trend (T) and how is it used?
The trend (T) is the long-term component of the time series, representing the continuous change in the value of the series over time. The trend is used to forecast future values and is calculated through the formula L_t = α·(y_t − S_{t−s}) + (1−α)·(L_{t−1}+T_{t−1}).
How can I use this calculator to forecast future values?
To forecast future values, simply enter the historical data and the smoothing and seasonal parameters into the form. The calculator will then calculate the smoothed and trend values to forecast future values.