ACF 和 PACF plot 的置信度非常小。 如何解读？

Question

I'm rather new at programming at general so do forgive me if the question is rather basic.

I'm trying to determine my p , d , q values for an ARIMA model and I've already conducted an adfuller test that determined that my time series is stationary. However, when I plot out my ACF and PACF plots, I get the following:

ACF plot

PACF plot

From what I've read about the p values, I'm supposed to pick the value where the line first crosses the confidence interval except I'm not sure why my confidence intervals for both are that small? Does this mean that my MA value should be 2 according to the PACF plot? Any help in interpreting the graphs would be appreciated!

My code:

from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
fig = plt.figure(figsize=(20, 12))

fig = plot_acf(train_set.dropna(), lags=10)
fig = plot_pacf(train_set.dropna(), lags=10)

Answer 1

The d component is used to make the data stationary by differencing, if the adf test (and kpss test) shows that the data is stationary, you can probably set it to 0. However, keep in mind that you cannot trust these tests by 100 %.

The confidence interval indicates whether the correlation is statistically significant, meaning that the correlation is very likely not to be random. All bars that cross the confidence interval are “real” correlations that you can use for modeling.

There are thousands of thumb rules to interpret these plots. I recommend the following:

If the ACF trails off, use an MA model with the significant and strong correlations from the PACF.

If the PACF trails off, use an AR model with the significant and strong correlations from the ACF.

You can also have a look here:

https://towardsdatascience.com/identifying-ar-and-ma-terms-using-acf-and-pacf-plots-in-time-series-forecasting-ccb9fd073db8

I guess you created the plots with statsmodels, in that case you shoud keep in mind that lag 0 (the first in the plots) is the correlation of the time series with itself, therefore it will always be +1 and significiant, you can ignore this lag.In your case, the ACF is trailing off, and the PACF has only one statistically significant and strong correlation with the first lag, perhaps you can also use 2, 3 and 4 but they are very weak. Best is of course if you just try it out. Or you can use pmdarima's auto_arima() function:

https://alkaline-ml.com/pmdarima/tips_and_tricks.html

https://alkaline-ml.com/pmdarima/modules/generated/pmdarima.arima.auto_arima.html