Forecasting Process Details 
Time Trend Curves
When you specify a time trend curve as a predictor in a forecasting model,
the system computes a predictor series that is a deterministic
function of time.
This variable is then included in the model as a regressor,
and the trend curve is fit to the dependent series by linear regression
, in addition to other predictor series.
Some kinds of nonlinear trend curves are fit by transforming the
dependent series. For example, the exponential trend curve is
actually a linear time trend fit to the logarithm of the series.
For these trend curve specifications, the series transformation
option is set automatically,
and you cannot independently control both the time trend curve
and transformation option.
The computed time trend variable is included in the output data set
in a variable named in accordance with the trend curve type.
Let t represent the observation count from the start of
the period of fit for the model,
and let X_{t} represent the value of the time trend variable
at observation t within the period of fit.
The names and definitions of these variables are as follows.
(NOTE: These deterministic variables are reserved variable names.)
 Linear Trend

Variable name _LINEAR_, with X_{t}=tc.
 Quadratic Trend

Variable name _QUAD_,
with X_{t}=(tc)^{2}.
Note that a quadratic trend implies a linear trend
as a special case and results in two regressors
_QUAD_ and _LINEAR_.
 Cubic Trend

Variable name _CUBE_,
with X_{t}=(tc)^{3}.
Note that a cubic trend implies a quadratic trend
as a special case and results in three regressors
_CUBE_, _QUAD_, and _LINEAR_.
 Logistic Trend

Variable name _LOGIT_,
with X_{t} = t.
The model is a linear time trend applied to the logistic
transform of the dependent series.
Thus, specifying a logistic trend is equivalent to specifying
the Logistic series transformation and a linear time trend.
A logistic trend predictor can be used only in conjunction
with the logistic transformation,
which is set automatically when you specify logistic trend.
 Logarithmic Trend

Variable name _LOG_,
with X_{t}=ln(t).
 Exponential Trend

Variable name _EXP_,
with X_{t}=t.
The model is a linear time trend applied to the logarithms
of the dependent series.
Thus, specifying an exponential trend is equivalent to specifying
the log series transformation and a linear time trend.
An exponential trend predictor can be used only in conjunction
with the log transformation,
which is set automatically when you specify exponential trend.
 Hyperbolic Trend

Variable name _HYP_,
with X_{t}=1/t.
 Power Curve Trend

Variable name _POW_,
with X_{t}=ln(t).
The model is a logarithmic time trend applied to the logarithms
of the dependent series.
Thus, specifying a power curve is equivalent to specifying
the log series transformation and a logarithmic time trend.
A power curve predictor can be used only in conjunction
with the log transformation,
which is set automatically when you specify a power curve trend.
 EXP(A+B/TIME) Trend
 Variable name _ERT_,
with X_{t}=1/t.
The model is a hyperbolic time trend applied to the logarithms
of the dependent series.
Thus, specifying this trend curve is equivalent to specifying
the log series transformation and a hyperbolic time trend.
This trend curve can be used only in conjunction
with the log transformation, which is set automatically
when you specify this trend.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.