Forecasting Methods

RHO

A parameter that is used to reduce the long-term trend and slows down the long-term trend to zero. The rho value should be set close to 1.0. If this value is set equal to 1.0, there will be no reduction in the trend effect. Generally, rho should not have a value lower than 0.9..... ...

MAD and MSE

• Moving Averages
• Weekly sales and a two week moving av
• Wk Sales 2wk Mvg Av Error Sq
• 1 246 -
• 2 256 -
• 3 Av = 255 - 251 = 4 Sq =16
• 4 .....248...255.5.7.5...56.25
• 5......263...251.5.11.5.132.25
• 6 .....254...255.5..1.5...2.25
• 7 .....256...258.5..2.5...6.25
• 8 .....258...257....3.....9
• 9 .....249...257....8....64
• 10 ....257...253.5..3.5..12.25
• 11 ....259...253....6....36
• 12 ....243...258...15...225
• 13 ....255...251....4....16
• 14 ....251...249....2.....4
• 15 ....253...253....0
• 16 ....252.........68.5.579.25

Ft+1 = ∑(Dt+dt-1)/n F= Forecast, D Actual Data (ie Sales), t=time period, n= moving av

Forecast errors Et+1=Dt+1-Ft+1 Error is the difference between the actual value and the forecast. The error in week 3 is 4. To assess the accuracy of the forecast method over the entire period and there are two methods of calculation

Mean absolute deviation (MAD)
Mean squared error (MSE)

MAD= ∑|e|

_____ = 68.5/13 = 5.27
t 

MSE 579.25/13 44.5 MSE effectively penalizes larger errors

Default Alphas and Betas

Alpha: A smoothing constant for level. The weights are broken down in an exponential manner from the most recent to the most distant period. For example, if the smoothing parameter is set equal to 0.20, the most recent period is weighted 20%, the next period is weighted 16% [(100 – 20) * 0.2], and so on until the oldest (earliest) period is reached in the exponential calculation. Generally, the alpha should be set between 0.1 and 0.3, depending on the selected forecast model.

Beta:

A smoothing constant for trend. This parameter helps to eliminate the risk of lag that occurs behind the currrent demand when the forecast is based on a moving average or exponential smoothing. The beta parameter brings the forecast to an approximate level. New values should be significantly higher or lower than the previous ones. Generally, the beta should be set between 0.1 and 0.3.

Naive

The naïve model simply states that any future period will have the same demand as the last actual (like saying the weather will be the same as yesterday). 4The naïve model can be used as a reference against which other models can be compared. For extremely volatile demand patterns and where the forecast horizon is very short, the Naïve model is often the best.

Moving Average

The moving average model uses an average of a number of periods (user specified) of actual demands to predict any future period. 4The optimum number of periods usually is between 4 and 12. An advantage of this method is that anomalies are “washed out” as the horizon rolls forward. The forecast always lags behind a trend. A larger number of periods results in a greater lag, which makes it unsuitable for long-term forecasting.

Least Squares Regression

Least square regression 4least square regression fits a straight line through the entire history so that the sum of the squared residuals is minimized. The line is then extrapolated into the future. 4This method is useful for intermediate- to long-term forecasts because, compared to the ewma and moving average models, it puts less weight on short-term fluctuations. It can also be used for the initialization of trend components in the ewma models. Generally, the rho parameter should not be given a value lower than 0.9.

Single EWMA

The single ewma model resembles the moving average model, but it puts more weight on recent demands. 4The higher the alpha, the more weight is given to the last observation. An alpha value between 0.1 and 0.3 is recommended. Single ewma always lags behind a trend; the lower the alpha, the greater the lag. The trade-off is that higher alpha values are more sensitive to random spikes in the demand history.

There is also Adaptive single EWMA - more weight on recent observations and Double EWMA with trend dampening

Croston's Method

This method is used for forecasting intermittent demands. It uses periods with the demand and the interval between demands to build up the forecast. The forecast is an average of demands, with consideration given to non-demand periods. 4The alpha value should be set to around 0.2 when this model is used.

Multiple Regression

This model is used when you know or suspect that one or more variables can influence the consumption of a part. When you want incorporate this knowledge into the forecast model, then use the multiple-regression model. §Manual forecast 4This model enables you simply to enter a cumulative sum of the expected demand for a year. The system then distributes it among the periods. 4This model can be used for new parts without any history or predecessor and where any market survey has predicted the total demand. §All models except naïve and multiple regression can be combined with seasonal profiles

Best Fit

Best fit. An algorithm that automatically selects the model and parameters that will minimize Theil’s U-statistics within a user-defined period. 4A search is made that tests all models and parameter combinations in a tournament fashion. Models included in the tournament are: 4moving average 4manual forecast 4least square regression 4ewma level 4ewma level and trend 4aewma 4Brown’s level and trend

Running best fit every period is useful for short-term forecasting but can be unreliable if used for intermediate or long-term forecasts