Solved – what does it mean if the partial auto correlation function of a time series have a value >+1 or <- 1

autocorrelationpartial-correlationtime series

I have a time series data and I applied the first difference operator to make it stationary. When I plot the partial autocorrelation function of this differenced time series, I find peaks with value >1 and less than <-1 at certain lags.
1)Should I consider these lags for my analysis?
2)I am using MATLAB to plot the PACF, would there be any bugs? Because how can the correlation be >+1 or <-1.

I have attached the image of PACF plot. Kindly help me. Any help is appreciated.enter image description here

Edit:
Actual Time series data.
enter image description here
Time series data after first difference.
enter image description here

Best Answer

Should I consider these lags for my analysis?

Would the scope of your question of research be changed? If yes, I would say that dropping out these lags is a bad idea.

I am using MATLAB to plot the PACF, would there be any bugs?

It is almost sure that not.

How can the correlation be >+1 or <-1.

Because these values are very likely to come from a regression of your series over its ~550 (simultaneously considered) lagged versions. To me the reason why you get greater-than $1$ (absolute) values is either because:

  1. your data are not time series, e.g. spatial series with overlapping autocorrelation structures
  2. your data are temporal but with redundant values. (which is another manner to say that you have overlapping autocorrelation structure).

Did you check your data ? Are you sure that you have no duplicate entries ?

Another possibility is that your series is over/under-differenced. You may want to take a look at Identifying the order of differencing

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