Problem of extremly increasing Partial Autocorrelations in time series data

[Doro Drees]

Hey dear statalists,

I'm currently trying to make a forecast of the use of prepaid payment instruments using ARIMA modelling in Stata. I have a time series data set, containing monthly oberservations from April 2011 to October 2016 (67 observations).

In order to make the data stationary, I took first differences of the data. Plotting the data it looks quite stationary, but the variance is increasing over time.

Nevertheless, the Augmented-Dickey Fuller test did reject the null hypothesis of a unit root, so I concluded that the differenciated data is roughly stationary.

In order to find the appropriate ARIMA specification I follow the general procedure plotting the autocorrelation function (ACF) and the partial autocorrelation function (PACF) of the differenciated data. Unfortunately, my PACF shows a very uncommon pattern: The partial autocorrelation are increasing extremly from lag 17 onwards.

I was wondering if the increasing partial autocorrelations are maybe due to the heteroskedasticity of my data. Taking the logarithm, the Problem of heteroskedasticity seems to be avoided (despite two outliers in the beginning).

Nontheless, the PACF has its Peak with the last lag.

So my question is if anyone can explain to me what is the reason for the PACF to behave like this? And how can I counteract the increasing partial autocorrelations?


I appreciate any hint you can give me. I did a lot of Research but have never seen a PACF like mine anywhere.

Thanks in advance.

Best wishes,
Doro

[Nick Cox]

Cross-posted in different form at https://stats.stackexchange.com/ques...me-series-data

I didn't know that partial autocorrelations could be outside [-1, 1].

[Doro Drees]

You are right Nick Cox , I posted this also to stackexchange as I have not been sure which platform is most suitable for my question. I hope this does not violate any forum rule I have not been aware of..

I think partial autocorrelations greater than |1| can occur due to calculation problems of Stata with small data sets beeing not stationary due to outliers or changing variance. I was wondering if someone may can give a more concrete explication of what is the reason for these extremly increasing partial autocorrelations.

[Nick Cox]

Our policy on cross-posting is explicit at https://www.statalist.org/forums/help#crossposting and is just that you are asked to tell us about it. You are reminded to read this document every time you post.

I can't help on your substantive problem. I have a prejudice that ARIMA models are vastly oversold, and that structural time series models make much more sense, but that is where i stop.