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I just want to check that I am interpreting the ACF and PACF plots correctly:

enter image description here

enter image description here

The data corresponds to the errors generated between the actual data points and the estimates generated using an AR(1) model.

I've looked at the answer here:

https://stats.stackexchange.com/questions/106038/estimate-arma-coefficients-through-acf-and-pacf-inspection/

After reading that it seems that the errors are not autocorrelated but I just want to be sure, my concerns are:

1.) The first error is right on the boundary (when this is the case should I accept or reject that there is significant auto-correlation at lag 1)?

2.) The lines represent the 95% confidence interval and given that there are 116 lags I would expect no more than (0.95*116=5.8 which I round up to 6) 6 lags to be exceed the boundary. For the ACF this is the case but for the PACF there are about 10 exceptions. If you include those on the border it's more like 14? Does this still indicate no auto-correlation?

3.) Should I read anything into the fact that all the breaches of the 95% confidence interval occur to the downside?

Thanks

Baz

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    $\begingroup$ I don't see anything interesting in these. Looks stationary. $\endgroup$ – John Sep 30 '14 at 19:27
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I can offer my opinion in response to your first two questions:

1.) Unfortunately, this is one of the problems with numbers; the answer is that if the observation is outside of the confidence interval by even a millionth of a percent, it is significant. If it is below by even the smallest amount, it is not significant. Changing your significance level or increasing your sample size might help.

2.) Remember first that, unless you specified otherwise, the confidence interval refers to a standard normal Gaussian distribution (no skew and normal kurtosis and so on); this may or may not be a valid approach if the distribution is perceptibly different from normal in some respect (your information suggests a slightly negative skew...?). Secondly, you only have 116 observations - one moderately-sized sample out of an indefinite set of samples in the observable population: this means that, even if the population is standard normal, there is a definite possibility that any given sample can deviate perceptibly from the population's distribution (such as having 14 points outside of your confidence interval when there should only be 6).

I hope that helps at least a little!

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