You can diagnose autocorrelation with an autocorrelation plot created with the ARIMA procedure.
ods graphics on; ods select ChiSqAuto SeriesACFPlot SeriesPACFPlot; proc arima data=Chemical plots(only)=series(acf pacf); identify var = xt; run; quit;
Refer to SAS/ETS User's Guide for details on the ARIMA procedure. The output, shown in Figure 17.191 and Figure 17.192, indicates that the data are highly autocorrelated with a lag 1 autocorrelation of 0.83.
Figure 17.191: Autocorrelation Check for Chemical Data
Individual Measurements Chart |
Autocorrelation Check for White Noise | |||||||||
---|---|---|---|---|---|---|---|---|---|
To Lag | Chi-Square | DF | Pr > ChiSq | Autocorrelations | |||||
6 | 228.15 | 6 | <.0001 | 0.830 | 0.718 | 0.619 | 0.512 | 0.426 | 0.381 |
12 | 315.34 | 12 | <.0001 | 0.360 | 0.364 | 0.380 | 0.347 | 0.348 | 0.354 |
18 | 406.76 | 18 | <.0001 | 0.349 | 0.371 | 0.348 | 0.353 | 0.368 | 0.341 |
24 | 442.15 | 24 | <.0001 | 0.303 | 0.261 | 0.230 | 0.184 | 0.141 | 0.098 |
Figure 17.192: Autocorrelation Plots for Chemical Data
The partial autocorrelation plot in Figure 17.192 suggests that the data can be modeled with a first-order autoregressive model, commonly referred to as an AR(1) model.
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You can fit this model with the ARIMA procedure. The results in Figure 17.193 show that the equation of the fitted model is .
ods select ParameterEstimates; proc arima data=Chemical; identify var=xt; estimate p=1 method=ml; run;
Figure 17.193: Fitted AR(1) Model
Individual Measurements Chart |
Maximum Likelihood Estimation | |||||
---|---|---|---|---|---|
Parameter | Estimate | Standard Error | t Value | Approx Pr > |t| |
Lag |
MU | 85.28375 | 2.32973 | 36.61 | <.0001 | 0 |
AR1,1 | 0.84694 | 0.05221 | 16.22 | <.0001 | 1 |