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.
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