Least Squares Fit accounting for autocorrelation can be used when the error terms are thought to be corellated with prior
Usage
Performing a least squares fit with autocorrelation is done similarly to the simple Least Squares Fit. Before performing the fit, however, some options must be specified.
In the "Options" menu for the regression window, choose "Account for
Autocorrelation." Next, some options are necessary. Select
"Set autoregressive level..." to set the degree of autocorrelation.
Note that increasing the autoregressive level decreases the
degrees of freedom in the regression analysis by the same amount.
Finally, the technique and threshold can be set.
Currently the software only supports using the Cochrane-Orcutt Method
for accounting for autocorrelation, which is explained below.
Finally, select "Set number of iterations/threshold..." to fix
the maximum number of iterations to perform and the threshhold
requirement for convergence. The software will stop iterations
when either condition is met.
Options
The same options available to the Least Squares Fit still apply when autocorrelation is enabled.
Output
The output will appear the same as the Least Squares Fit output, but an
additional Autocorrelation Coefficient estimate will be generated, as
shown in the example below:
Results of the Multiple Regression Model Autocorrelation present Regression Variable: Y --------------------------------------------------------------- Sum Squared of the Residuals: 24.81906 Standard Error of the Fit : 1.24547 R-Squared Value : 0.88295 Adjusted R-Squared Value : 0.86831 --------------------------------------------------------------- Constant:
-0.15691 Std Err:
0.24893 t-Score: -0.63035 Coef 0 (C):
1.67013 Std Err:
0.20311 t-Score: 8.22297 Coef 1 (I):
0.58799 Std Err:
0.39741 t-Score: 1.47955 Autocorrelation Coeficient (1 Order): 0.91471
Method
The software currently implements the Cochrane-Orcutt iterative
method. The autocorrelated least squares fit (of order 1)
estimate takes the form:
Rho represents the autoregressive parameter.
Cochrane-Orcutt
The Cochrane-Orcutt method estimates the autoregressive parameter from
the residuals of each previous iteration. The value of rho for
autoregressive order a is estimated as:
In the first iteration, the program initially estimates the equation
using a least squares fit. The resulting residuals are used as
the first-pass estimate of the autoregressive parameter. New
variables are then computed based on the estimate of rho, and a least
squares fit is performed again. Rho is updated accordingly, and
the iterations continue until either the maximum number of iterations are performed or the change in the estimate of the autoregressive parameter is less than the absolute tolerance specified.