Arima modelling with nonstationarity series

Question

I am very confused with an article about arima-garch modelling:

http://article.sapub.org/10.5923.j.ajms.20130306.04.html

I am interested in modelling of safaricom closing price. I also just interested in the arima part of the modelling(not with garch part).

Part 4.2 of the article as below:

" The upper left graphs show ACF of Log Safaricom closing price, showing the ACF slowly decreases. It is probably that the model needs differencing. The lower left is PACF of Log Safaricom closing price, in dicating significant value at lag 1 and then PACF cuts off. Therefore, the model for Log Safaricom closing price might be ARIMA (1, 0, 0). The upper right shows ACF of differences of log Safaricom with no significant lags. The lower right is PACF of differences of log Safaricom, reflecting no significant lags. The model for differenced log Safaricom series is thus a white noise, and the original model resembles random walk model ARIMA (0, 1, 0)"

I am very confused with this part:

• If the acf(of safaricom log closing price) shows slow decay which indicates non-stationarity, is it proper to examine the pacf of the series and then determining the arima model as arima(1,0,0)?

I am very confused with this part of the article. In my opinion, if the series is determined to be nonstationary, it first must be first differenced and then must be examined of acf and pacf of the differenced series.

Am I missing something? I will be very glad for any help. Thanks a lot.

Answer 1

• The $ACF$ shows non-stationarity

You are right the $ACF$ does show non stationarity however, a visualization isn't a sure test and since both are exploratory graphs, there's no harm in continuing to look at the $PACF$.

A unit root test or other more formal method would nonetheless have been better to confirm this. The authors seem to have done this and the $p-value$ for safaricom price $ADF$ test rejects presence of a unit root so modelling with an $ARMA(p,d,q)$ might not be so wrong. However, these tests have their weaknesses.

• Differencing in presence of non stationarity

Be cautious here, differencing is not the automatic solution for non-stationarity. It needs to be determined whether the data is trend stationary or difference stationary first. Each has its own solution.