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:
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:
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.