Time Series Using Holt Winter Smoothing Method
HTime series using Holt-Winters Forecasting Procedure
Summary
The Holt-Winters forecasting procedure is a simple widely used projection method which can cope with trend and seasonal variation. We can apply this method to lots of fields such as banking data analysis, investment forecasting, inventory controlling and so on. This paper shows us a practical banking credit card example using Holt-Winter method in Java programming for data forecasting. The reason we use Holt-Winter is that this method is simple while generally works well in practice, and is particularly suitable for producing short-term forecasts for sales or demand time-series data.
Theorem
Xt(1)= Lt+ Tt+ It-p+1
Xt(h)= Lt+ hTt+ It-p+h Lt= Lt-1+ Tt-1+ αet
Tt= Tt-1+ αγet
It= It-p+ δ(1-α)et
Xth=Lt+ hTt* It-p+h for h=1,2,… ,p
Lt= αXtIt-p+(1-α)(Lt-1+ Tt-1)
Tt= γ(Lt-Lt-1)+ 1-γTt-1
It= δXtLt+(1-δ)It-p et= Xt-Xt-1(1)
There are two types of seasonal model: an additive version which assumes that the seasonal effects are of constant size and a multiplicative version which assumes that the seasonal effects are proportional in size to the local deseasonalized mean level. Both seasonal models assume that the local deseasonalized mean level may be modified by an additive trend term and also that there is an additive error term of constant variance.
Suppose we have an observed time series, denoted by X1, X2, …, Xn , and wish to forecast Xn+k.
The forecast made at time n for k steps ahead will be denoted by Xnk. For a univariate forecast this depends only on Xn, Xn-1,…… In simple exponential smoothing, the one-step-ahead predictor can be written in the recurrence form
Xt(1)= Lt+ Tt+ It-p+1
Where the smoothing parameter, α, is usually constrained so that 0 < α <1. The Holt-Winters method (sometimes called the Winters method or seasonal exponential smoothing) generalizes this approach to deal with trend and seasonality. Let α, γ, δ denote three smoothing parameters and let p
Summary
The Holt-Winters forecasting procedure is a simple widely used projection method which can cope with trend and seasonal variation. We can apply this method to lots of fields such as banking data analysis, investment forecasting, inventory controlling and so on. This paper shows us a practical banking credit card example using Holt-Winter method in Java programming for data forecasting. The reason we use Holt-Winter is that this method is simple while generally works well in practice, and is particularly suitable for producing short-term forecasts for sales or demand time-series data.
Theorem
Xt(1)= Lt+ Tt+ It-p+1
Xt(h)= Lt+ hTt+ It-p+h Lt= Lt-1+ Tt-1+ αet
Tt= Tt-1+ αγet
It= It-p+ δ(1-α)et
Xth=Lt+ hTt* It-p+h for h=1,2,… ,p
Lt= αXtIt-p+(1-α)(Lt-1+ Tt-1)
Tt= γ(Lt-Lt-1)+ 1-γTt-1
It= δXtLt+(1-δ)It-p et= Xt-Xt-1(1)
There are two types of seasonal model: an additive version which assumes that the seasonal effects are of constant size and a multiplicative version which assumes that the seasonal effects are proportional in size to the local deseasonalized mean level. Both seasonal models assume that the local deseasonalized mean level may be modified by an additive trend term and also that there is an additive error term of constant variance.
Suppose we have an observed time series, denoted by X1, X2, …, Xn , and wish to forecast Xn+k.
The forecast made at time n for k steps ahead will be denoted by Xnk. For a univariate forecast this depends only on Xn, Xn-1,…… In simple exponential smoothing, the one-step-ahead predictor can be written in the recurrence form
Xt(1)= Lt+ Tt+ It-p+1
Where the smoothing parameter, α, is usually constrained so that 0 < α <1. The Holt-Winters method (sometimes called the Winters method or seasonal exponential smoothing) generalizes this approach to deal with trend and seasonality. Let α, γ, δ denote three smoothing parameters and let p