@TREND

Calculates future values based on curve-fitting to historical values. The @TREND procedure considers a number of observations; constructs a mathematical model of the process based on these observations (that is, fits a curve); and predicts values for a future observation. You can use weights to assign credibility coefficients to particular observations, report errors of the curve fitting, choose the forecasting method to be used (for example, linear regression), and specify certain data filters.

Syntax

@TREND (Ylist, [Xlist], [weightList], [errorList], [XforecastList], YforecastList, method[, method parameters] [, Xfilter1 [, parameters]] [, XfilterN [, parameters]]  [, Yfilter1 [, parameters]] [, YfilterN [, parameters]])
ParameterDescription

Ylist

An expression list that contains known observations; for example, sales figures over a period of time.

Xlist

Optional. An expression list that contains underlying variable values. For example, for each sales figure in Ylist, Xlist may contain a value for associated time periods. If you do not specify Xlist, the default variable values are 1,2,3, and so on, up to the number of values in Ylist.

weightList

Optional. An expression list that contains weights for the data points in Ylist, for the linear regression method only. If values in weightList are #MISSING, the default is 1. Weights for methods other than linear regression are ignored. Negative weights are replaced with their absolute values.

errorList

Optional. Member list that represents the differences between the data points in Ylist and the data points on the line or curve (as specified for method).

XforecastList

Optional. Expression list that contains the underlying variable values for which the forecasting is sought. If you do not specify XforecastList, the values are assumed to be as follows: {(last value in Xlist + 1), (last value in Xlist + 2), ...}up to (last value in Xlist + the number of values in YforecastList)

If you forecast consecutively from where Ylist stops, you do not need to specify XforecastList. If you want to move the forecasting period forward, specify the new period with XforecastList.

YforecastList

A member list into which the forecast values are placed.

method

A choice among LR (linear regression), SES (single exponential smoothing), DES (double exponential smoothing), and TES (triple exponential smoothing). Method parameters must be numeric values, not member names. Method parameters may be any of the following:

  • LR[,t]: standard linear regression with possible weights assigned to each data point and an optional seasonal adjustment period [t], where [t] is the length of the period. In general, the weights are equal to 1 by default. You might want to increase the weight if the corresponding observation is important, or decrease the weight if the corresponding observation is an outlier or is unreliable.

  • SES[,c]: single exponential smoothing with parameter c (default c=0.2). This method uses its own weight system, using the single parameter c. Increasing this parameter gives more weight to early observations than to later ones.

  • DES[[,c1],c2]: double exponential smoothing (Holt's method) with optional parameters c1, c2 (default c1=0.2, c2=0.3). This is a two-parameter weight system and a linear subsequent approximation scheme. The first parameter controls weight distribution for the intercept; the second parameter controls weight distribution for the slope of the line fit.

  • TES[[[[,T],c1],c2],c3]: triple exponential smoothing (Holt-Winters method) with optional parameters c1, c2, c3, T (default c1=0.2, c2=0.05, c3=0.1, T=1). This is a three-parameter weight system and a linear model with a multiplicative seasonal component.

Xfilter1 ... XfilterN

Optional. Use one or more of the following filter methods to scale Xlist:

  • XLOG[,c]: logarithmic change with shift c (x' = log(x+c)) (default c=1

  • XEXP[,c]: exponential change with shift c (x' = exp(x+c)) (default c=0).

  • XPOW[,c]: power change with power c (x' = x^c) (default c=2).

Yfilter1 ... YfilterN

Optional. Use one or more of the following filter methods to scale Ylist:

  • YLOG[,c]: logarithmic change with shift c (y' = log(y+c)) (default c=1)

  • YEXP[,c]: exponential change with shift c (y' = exp(y+c)) (default c=0).

  • YPOW[,c]: power change with power c (y' = y^c) (default c=2).

Notes

Algorithm for Linear Regression

Linear regression algorithm, part one.
Linear regression algorithm, part two.

Algorithm for Linear Regression with Seasonal Adjustment

Linear regression with seasonal adjustment algorithm, part one.
Linear regression with seasonal adjustment algorithm, part two.
Linear regression with seasonal adjustment algorithm, part three.
Linear regression with seasonal adjustment algorithm, part four.
Linear regression with seasonal adjustment algorithm, part five.
Linear regression with seasonal adjustment algorithm, part six.

Algorithm for Single Exponential Smoothing (SES)

SES algorithm, part one.
SES algorithm, part two.

Algorithm for Double Exponential Smoothing (DES)

DES algorithm, part one.
DES algorithm, part two.

Algorithm for Triple Exponential Smoothing (TES)

TES algorithm, part one.
TES algorithm, part two.
TES algorithm, part three.
TES algorithm, part four.

Example

The following example is based on the Sample Basic database. It forecasts sales data for May through December, based on the trend of the same sales data from January through April. The method used is linear regression with no seasonal adjustment.

Sales(@TREND(Jan:Apr,,,,,May:Dec,LR););

This example produces the following report:

           Actual    Sales    West
                     Colas
                     =====
Jan                   2339                      
Feb                   2298                      
Mar                   2313                      
Apr                   2332                      
May                   2319                      
Jun                   2318.4                    
Jul                   2317.8                    
Aug                   2317.2                    
Sep                   2316.6                    
Oct                   2316                      
Nov                   2315.4                    
Dec                   2314.8                    
  Year               27817.2            

See Also

  • @LIST