Outlier correction

• US 20050137835A1
• Filed: 12/23/2004
• Published: 06/23/2005
• Est. Priority Date: 12/23/2003
• Status: Active Grant

• Current Assignee: SAP SE
• Original Assignee: SAP AG (SAP SE)
• Inventors: Moessner, Ralph
• Granted Patent: US 7,239,984 B2
• Time in Patent Office: Days
• US Class Current: 702/193
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202

Abstract

The invention provides methods and apparatus, including computer program products, for correcting outlier values in a series of values over time, the values representing a predetermined numerical parameter, the method comprising the following steps: for a predetermined time interval of the time series, the time interval having a beginning point and an end point, calculating an ex-post forecast time series on the basis of the historical time series and a predetermined model function; defining a lower tolerance limit line and an upper tolerance limit line on the basis of the ex-post forecast time series and on a quality function over the time interval; beginning at the beginning point of the time interval, correcting the historical time series by replacing the first value of the historical time series outside of the tolerance lines by a predetermined value not outside the tolerance lines; recalculating the ex-post forecast time series on the basis of the corrected historical time series (s_h) and the predetermined model function; and redefining the tolerance lines on the basis of the recalculated ex-post forecast time series (s_ep) and the quality function, whereby the quality function (qf) takes only values into account until the time point where the last outlier value has been replaced; repeating the above steps until all outlier values of the historical time series have been replaced.

Claims

1. Method for correcting outlier values in a series of values over time, the values representing a predetermined numerical parameter, the method comprising:

for a predetermined time interval of the time series, the time interval having a beginning point (b) and an end point (e),

a) calculating an ex-post forecast time series (s_ep) on the basis of the historical time series (s_h) and a predetermined model function (f);

b) defining a lower tolerance limit line (t_min) and an upper tolerance limit line (t_max) on the basis of the ex-post forecast time series and on a quality function (qf) over the time interval;

c) beginning at the beginning point (b) of the time interval, correcting the historical time series by replacing the first value of the historical time series (s_h) outside of the tolerance lines by a predetermined value not outside the tolerance lines (t_min, t_max);

d) recalculating the ex-post forecast time series (s_ep) on the basis of the corrected historical time series (s_h) and the predetermined model function; and

redefining the tolerance lines on the basis of the recalculated ex-post forecast time series (s_ep) and the quality function, whereby the quality function (qf) takes only values into account until the time point where the last outlier value has been replaced;

e) repeating c) to e) until all outlier values of the historical time series (s_h) have been replaced.

2. The method of claim 1, wherein the quality function (qf) is the mean average deviation between corresponding values of the historical time series (s_h) and the ex-post forecast time series (s_ep).

3. The method according to claim 1, wherein the predetermined replacement value can be chosen to be the value on the tolerance line (t_min, t_max) closer to the outlier value or the value of the ex-post forecast time series (s_ep).

4. The method according to one of claim 1, wherein the first recalculation of the tolerance lines is only made after a predetermined number of time points after the beginning point (b) of the time interval.

5. The method according to one of claim 1, wherein a recalculation of the tolerance lines is only made if a predetermined number of time points have not been corrected.

6. The method according to one of claim 1, wherein the parameter is one of economical, statistical, physical entity.

7. A method of forecasting values of a numerical parameter in future by using a forecast model, the method comprising:

determining model parameters on the basis of a time series (s_h) of parameter values in the past, whereby the time series (s_h) of the past is corrected by the method according to one of claims 1;

forecasting the future values by applying the model with the parameters determined.

8. The method of claim 7 wherein the parameter is one of economical, statistical, physical entity.

9. A system comprising:

means for calculating an ex-post forecast time series (s_ep) on the basis of the historical time series (s_h) and a predetermined model function (f);

means for defining a lower tolerance limit line (t_min) and an upper tolerance limit line (t_max) on the basis of the ex-post forecast time series and on a quality function (qf) over the time interval;

means for beginning at the beginning point (b) of the time interval, correcting the historical time series by replacing the first value of the historical time series (s_h) outside of the tolerance lines by a predetermined value not outside the tolerance lines (t_min, t_max); and

means for recalculating the ex-post forecast time series (s_ep) on the basis of the corrected historical time series (s_h) and the predetermined model function; and

redefining the tolerance lines on the basis of the recalculated ex-post forecast time series (s_ep) and the quality function, whereby the quality function (qf) takes only values into account until the time point where the last outlier value has been replaced.

10. A machine-accessible medium containing instructions that, when executed, cause a machine to:

for a predetermined time interval of the time series, the time interval having a beginning point (b) and an end point (e),

a) calculate an ex-post forecast time series (s_ep) on the basis of the historical time series (s_h) and a predetermined model function (f);

b) define a lower tolerance limit line (t_min) and an upper tolerance limit line (t_max) on the basis of the ex-post forecast time series and on a quality function (qf) over the time interval;

c) beginning at the beginning point (b) of the time interval, correct the historical time series by replacing the first value of the historical time series (s_h) outside of the tolerance lines by a predetermined value not outside the tolerance lines (t_min, t_max);

d) recalculate the ex-post forecast time series (s_ep) on the basis of the corrected historical time series (s_h) and the predetermined model function; and

redefining the tolerance lines on the basis of the recalculated ex-post forecast time series (s_ep) and the quality function, whereby the quality function (qf) takes only values into account until the time point where the last outlier value has been replaced;

e) repeat c) to e) until all outlier values of the historical time series (s_h) have been replaced.