Modeling and Multivariate Methods - SAS

362 Performing Time Series Analysis Chapter 14
Modeling Reports
Sum of Squared Errors
is the sum of the squared residuals.
Variance Estimate the unconditional sum of squares (SSE) divided by the number of degrees of
freedom, SSE / (n – k). This is the sample estimate of the variance of the random shocks a t , described in
the section “ARIMA Model” on page 365.
Standard Deviation is the square root of the variance estimate. This is a sample estimate of the standard
deviation of a t , the random shocks.
Akaike’s Information Criterion [AIC], Schwarz’s Bayesian Criterion [SBC or BIC]
these criteria indicate better fit. They are computed:
AIC
= – 2loglikelihood + 2k
Smaller values of
SBC
=
– 2loglikelihood + kln( n)
RSquare
RSquare is computed
n
n
where SST = ( y i
– y i ) 2
and SSE = ( y i
– ŷ i ) 2
, ŷ i are the one-step-ahead forecasts, and y i is
i = 1
i = 1
the mean y i .
If the model fits the series badly, the model error sum of squares, SSE might be larger than the total sum
of squares, SST and R 2 will be negative.
RSquare Adj
MAPE
SSE
1 – ---------
SST
1 –
The adjusted R 2 is
---------------- ( n – 1)
(
( n–
k)
1 – R 2 )
is the Mean Absolute Percentage Error, and is computed
n
100
--------
n
i = 1
y i
– ŷ i
-------------
y i