Partial Autocorrelation parcorr bug?

When running parcorr on a sample of normally distributed noise, I get some strange results like one illustrated below. Others are shown in the attached pdf and .mlx. When I try longer (>1000) samples, the code seems to hang. The code is

N=400;

for itest=1:3

figure

y=randn(1,N);

stem(y,'o', 'MarkerFaceColor', 'r')

figure

parcorr(y,'NumLags',N-1)

end

Answer 1

[Shantanu Dixit]

Hi Duncan,

The issue you're observing might be due to the choice of 'NumLags = N-1'. The 'PACF' values at larger lags have very little data left that can be used to estimate them. Using too many lags can lead to unstable estimates due to increasing standard errors. You can also refer to a related query on the forum: https://www.mathworks.com/matlabcentral/answers/122337-wrong-function-partial-autocorrelation-pacf-parcorr-greater-than-1-1.

I am able to run 'parcorr' on >1000 samples as well, although due to more samples, the execution takes some time.

Using n = 25 as number of lags in the above script

N=400;
lags = 25

lags = 25

for itest=1:3
    figure
    y=randn(1,N);
    stem(y,'o', 'MarkerFaceColor', 'r')
    figure
    parcorr(y,'NumLags',lags)
end

'parcorr': https://www.mathworks.com/help/econ/parcorr.html

Hope this helps!

[Duncan Carlsmith]

Thank you, Shantanu!