I have some multivariate time series data for each location. My objective is to build predictive model for each multivariate time series.

The ACF and PACF plots(50 lags) of both the original and differenced(d = 1) of the response variable for one location is given below:

Leve/Original Series

Question 1: Is the response time series data(level) stationary? Augmented Dickey–Fuller (ADF) and KPSS tests suggest the time series is stationary. However, splitting the time series in two halves and calculating means and variances, give non-constant means and variances at two different time points. For example, see code below for calculating mean and variance values at two different time points:

X = df.values
split = int(len(X) / 2)
X1, X2 = X[0:split], X[split:]
mean1, mean2 = X1.mean(), X2.mean()
var1, var2 = X1.var(), X2.var()
print('mean1=%f, mean2=%f' % (mean1, mean2))
print('variance1=%f, variance2=%f' % (var1, var2))

Results: mean1=236.297719, mean2=161.075122 variance1=1127026.727438, variance2=352837.058991

Thus, I took a first-order difference of the series as shown below:

Differenced Series

Question 2: Is the differenced series over-differenced(d = 1)? Question 3: How many significant lags are recommended for modeling assuming the series isn't over-differenced?

I will appreciate your response to the foregoing questions.

  • $\begingroup$ Your title includes "neural networks" but I don't see any mention of them in the body of your question. If you're asking about neural networks, can you clarify what you want to know about them in your question? Or if you're not asking about neural networks, can you edit your title to focus on what you are asking about? $\endgroup$
    – Sycorax
    Oct 12, 2020 at 23:41
  • $\begingroup$ Thanks, Sycorax. I have edited the title as suggested. I wanted to know what the interpretation of my ACF and PACF plots for both original and differenced series look like. Though some statistical tests suggest my response series as shown is stationary, but I cannot see that reflect on the means and variances for the series at different time points - that is constant mean, variance, and autocorrelation over time. $\endgroup$ Oct 13, 2020 at 0:13
  • $\begingroup$ For (much) more about these topics, please see stats.stackexchange.com/… $\endgroup$
    – whuber
    Oct 13, 2020 at 12:44


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