I am trying to understand following algorithm, but am having some trouble understanding what's happening under the hood in step 3, i.e regression under yule-walker framework and obtaining significance levels through that. Would appreciate any insight into how this works.
The STEPAR Algorithm
The STEPAR method consists of the following computational steps:
1. Fit the trend model as specified by the TREND= option by using
ordinary least-squares regression. This step detrends the data. The
default trend model for the STEPAR method is TREND=2, a linear trend
model.
2. Take the residuals from step 1 and compute the autocovariances to
the number of lags specified by the NLAGS= option.
3. Regress the current values against the lags, using the
autocovariances from step 2 in a Yule-Walker framework. Do not bring
in any autoregressive parameter that is not significant at the level
specified by the SLENTRY= option. (The default is SLENTRY=0.20.) Do
not bring in any autoregressive parameter that results in a
nonpositive-definite Toeplitz matrix.
4. Find the autoregressive parameter that is least significant. If the
significance level is greater than the SLSTAY= value, remove the
parameter from the model. (The default is SLSTAY=0.05.) Continue
this process until only significant autoregressive parameters
remain. If the OUTEST= option is specified, write the estimates to
the OUTEST= data set.
5. Generate the forecasts by using the estimated model and output to
the OUT= data set. Form the confidence limits by combining the trend
variances with the autoregressive variances.
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