Forecasting Methods - Revision history

Paulreed: /* MAD and MSE */

2012-05-14T20:14:39Z

MAD and MSE

← Older revision		Revision as of 14:14, 14 May 2012
Line 12:		Line 12:
	*5......263...251.5.11.5.132.25		*5......263...251.5.11.5.132.25
	*6 .....254...255.5..1.5...2.25		*6 .....254...255.5..1.5...2.25
	*7 256 258.5 2.5 6.25		*7 .....256...258.5..2.5...6.25
	*8 258 257 3 9		*8 .....258...257....3.....9
	*9 249 257 8 64		*9 .....249...257....8....64
	*10 257 253.5 3.5 12.25		*10 ....257...253.5..3.5..12.25
	*11 259 253 6 36		*11 ....259...253....6....36
	*12 243 258 15 225		*12 ....243...258...15...225
	*13 255 251 4 16		*13 ....255...251....4....16
	*14 251 249 2 4		*14 ....251...249....2.....4
	*15 253 253 0		*15 ....253...253....0
	*16 252 68.5 579.25		*16 ....252.........68.5.579.25

	Ft+1 = ∑(Dt+dt-1)/n		Ft+1 = ∑(Dt+dt-1)/n

Paulreed at 20:10, 14 May 2012

2012-05-14T20:10:01Z

← Older revision		Revision as of 14:10, 14 May 2012
Line 9:		Line 9:
	*2 256 -		*2 256 -
	*3 Av = 255 - 251 = 4 Sq =16		*3 Av = 255 - 251 = 4 Sq =16
	*4 248 255.5 7.5 56.25		*4 .....248...255.5.7.5...56.25
	*5 263 251.5 11.5 132.25		*5......263...251.5.11.5.132.25
	*6 254 255.5 1.5 2.25		*6 .....254...255.5..1.5...2.25
	*7 256 258.5 2.5 6.25		*7 256 258.5 2.5 6.25
	*8 258 257 3 9		*8 258 257 3 9

Paulreed at 20:07, 14 May 2012

2012-05-14T20:07:54Z

← Older revision		Revision as of 14:07, 14 May 2012
Line 8:		Line 8:
	*1 246 -		*1 246 -
	*2 256 -		*2 256 -
	*3 255 251 4 16		*3 Av = 255 - 251 = 4 Sq =16
	*4 248 255.5 7.5 56.25		*4 248 255.5 7.5 56.25
	*5 263 251.5 11.5 132.25		*5 263 251.5 11.5 132.25
	*6 254 255.5 1.5 2.25		*6 254 255.5 1.5 2.25
	*7 256 258.5 2.5 6.25		*7 256 258.5 2.5 6.25
	*8 258 257 3 9		*8 258 257 3 9

Paulreed at 20:04, 14 May 2012

2012-05-14T20:04:06Z

← Older revision		Revision as of 14:04, 14 May 2012
Line 1:		Line 1:
	!!RHO		==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.....		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		==MAD and MSE==
	Moving Averages		*Moving Averages
	Weekly sales and a two week moving av		*Weekly sales and a two week moving av
	Wk Sales 2wk Mvg Av Error Sq		*Wk Sales 2wk Mvg Av Error Sq
	1 246 -		*1 246 -
	2 256 -		*2 256 -
	3 255 251 4 16		*3 255 251 4 16
	4 248 255.5 7.5 56.25		*4 248 255.5 7.5 56.25
	5 263 251.5 11.5 132.25		*5 263 251.5 11.5 132.25
	6 254 255.5 1.5 2.25		*6 254 255.5 1.5 2.25
	7 256 258.5 2.5 6.25		*7 256 258.5 2.5 6.25
	8 258 257 3 9		*8 258 257 3 9
	9 249 257 8 64		*9 249 257 8 64
	10 257 253.5 3.5 12.25		*10 257 253.5 3.5 12.25
	11 259 253 6 36		*11 259 253 6 36
	12 243 258 15 225		*12 243 258 15 225
	13 255 251 4 16		*13 255 251 4 16
	14 251 249 2 4		*14 251 249 2 4
	15 253 253 0		*15 253 253 0
	16 252 68.5 579.25		*16 252 68.5 579.25

	Ft+1 = ∑(Dt+dt-1)/n		Ft+1 = ∑(Dt+dt-1)/n
Line 31:		Line 31:
	To assess the accuracy of the forecast method over the entire period and there are two methods of calculation		To assess the accuracy of the forecast method over the entire period and there are two methods of calculation
	Mean absolute deviation (MAD)		Mean absolute deviation (MAD)
	Mean squared error		Mean squared error (MSE)

	MAD= ∑\|e\|		MAD= ∑\|e\|
Line 40:		Line 40:
	MSE effectively penalizes larger errors		MSE effectively penalizes larger errors

	!!Default Alphas and Betas		==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.		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.		===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		===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.		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		===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.		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 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.		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		===Single EWMA===
	~~Version 2002-04-19 © 2002 IFS AB. All rights reserved. Page 8 Forecasting ModelsForecast Models§Single ewma 4The~~ 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.		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		There is also Adaptive single EWMA - more weight on recent observations and Double EWMA with trend dampening

	!!Croston's Method		===Croston's Method===
	~~Croston’s method 4This~~ 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.		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		===Multiple Regression===
	~~Multiple regression 4This~~ 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		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===
	Best fit ~~4An~~ 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		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		Running best fit every period is useful for short-term forecasting but can be unreliable if used for intermediate or long-term forecasts

	[[Category:Finance]]		[[Category:Finance]]

Paulreed: Created page with "!!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..."

2010-12-28T19:57:36Z

Created page with "!!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..."

New page

!!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 -
3 255 251 4 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

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
Version 2002-04-19 © 2002 IFS AB. All rights reserved. Page 8 Forecasting ModelsForecast Models§Single ewma 4The 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
Croston’s method 4This 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
Multiple regression 4This 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 4An 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

[[Category:Finance]]