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.

Edit:

Actual Time series data.

Time series data after first difference.

**Contents**hide

#### 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:

- your data are not time series, e.g. spatial series with overlapping autocorrelation structures
- 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