# Triple Exponential Smoothing

Triple Exponential Smoothing

The triple Exponential Smoothing is more of the Double Exponential Smoothing only this time, it is modified to take into account Seasonal fluctuations and Trends in the Time Series. It was first brought up by Peter Winters, in 1960, a student of Charles C. Holt and has been seen through experiments to be more infective in explaining seasonal trends than the Double And Single Exponential Smoothing techniques. The technique is widely called the Holt-Winters Triple Exponential Smoothing.

The brings in the seasonal parameter (γ), combining it with the Trend parameter (β) and Smoothing Factor (α). Supposed you have a Time Series Y(t) which starts at (t=0) and has a seasonal period (p)

Let
S(t) represent the smoothened value
b(t) the best estimate for seasonal trend
C(t)  the Seasonal correction factor

C(t) is the expected proportion of the predicted trend at any time(t) at the period (p) in the cycle that the observations. For it to be correctly computed there must be at least two or three seasons present in the historical data to correctly predict the seasonal trend.

The Forecasting values will be represented by F(t+m), which is an estimate of Y(t)  at time (t+m) and M>0 for all t.

S(0)=Y(0)
S(t) = α(Y(t)/C(t-p)) + (1- α)(S(t-1)-b(t-1))
b(t) = β(S(t)-S(t-1)) +(1- β)b(t-1)
C(t) = γ(Y(t)/S(t)) + (1- γ)C(t-p)
F(t+m) = S(t) + mb(t) + C(t-L+1(m-1))

Where

y - is the time series Value
S - Smoothened Value
b - Trend estimate
C - Seasonal Estimate
F - Forecast value
T- time

While α, β, γ are constants.

Click Other Related Topics

⏩  Introduction To Exponential Smoothing
⏩  Single Exponential Smoothing
⏩   Double Exponential Smoothing

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