MATLAB: Do I get different results when using the ‘ADFTEST’ and ‘PARCORR’ functions in the Statistics Toolbox 7.4 (R2010b)

Statistics and Machine Learning Toolbox

For my data, I am trying to use the ADFTEST test and PARCORR functions to identify the presence of a null root.
[h1_cpi,pVal1_cpi,stat,~,reg1_cpi]= adftest(data,'model','ard','lags',0)
figure;parcorr(data);
The output of the ADFTEST rejects the null hypothesis for the presence of a unit root, and the results show that the data has a structure of:
 r_t = 0.5646 r_t-1 +e_t.
The t-stat for this coefficient of the first lag term is 4.7373 while the p-value is 1.96e-5, indicating that this coefficient is significant.
However, when I run the PARCORR function on the same series to check for the presence of autocorrelations, the results tell me that there is no autocorrelation in the series.

Best Answer

The issue here is that PARCORR includes a constant in its OLS regression estimates of the partial autocorrelation coefficients, per references such as Box & Jenkins. So, we should compare the results of ADFTEST using the 'ARD' model instead of 'AR' as follows:
[h1_cpi,pVal1_cpi,stat,~,reg1_cpi]= adftest(data,'model','ard','lags',0);
When the constant (drift term) is included in ADFTEST, and the number of lags of differenced data is 0 (i.e., the simple DF test), then the results should match.
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