Least Squares Fit (Autocorrelation)


Description Usage Options Output Method See Also

Description

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.

Autocorellation in Options Menu
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.

Autocorrelation technique menu
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:

Autocorrelation LS Fit

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:

Autoregressive Parameter

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.

See Also

Least Squares Fit
Iteration Controls
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