Forecasting Methods under Triple Exponential Smoothing

Introduction

In time series forecasting, there are two popular methods for triple exponential smoothing: TEMA (Triple Exponential Moving Average) and Holt-Winters method. Both methods are used to smooth out general trends along with seasonality factor in the data and improve prediction accuracy. However, there are some key differences between the two methods. TEMA uses three stage weighted averages of average to smooth the data whereas Holt-Winters uses a method that takes into account both trend and seasonality.

Holt-winters Triple Exponential Smoothing

Holt Winters method extends the concept of double exponential smoothing to account for both a Trend, Level and seasonality of the data. It employs three smoothing factors, one for the level (α – alpha) , one for the trend (β – beta) and one for seasonality (Ɣ -gamma)

Holt-Winters Triple exponential smoothing Formula:

• Level (Lt)

          L_t = α * (Y_t – S_t-m) + (1 – α) * (L_t-1 + T_t-1)

• Trend (Tt):

           T_t = β * (L_t – L_t-1) + (1 – β) * T_t-1

• Seasonality (St):

          S_t = Ɣ * (Y_t – L_t) + (1 – Ɣ) * S_t-m

• Forecasting:

          Forecast for time t + h (Ft+h) = (L_t +  T_t )* S_t-m

• Notes

 h : number of time steps into the future to forecast.

 α , β , Ɣ : smoothing parameters

 Y_t : actual data point at time t

 S_t-m : seasonal index at time t-m

 T_t-1  :  trend at time t-1