Compute the ACF for Several MA Time Series
Unlike an AR(1), an MA(1) model has no autocorrelation beyond lag 1, an MA(2) model has no autocorrelation beyond lag 2, etc. The lag-1 autocorrelation for an MA(1) model is not \(\small \theta\), but rather \(\small \theta / (1+\theta^2)\). For example, if the MA parameter, \(\small \theta\), is = +0.9, the first-lag autocorrelation will be \(\small 0.9/(1+(0.9)^2)=0.497\), and the autocorrelation at all other lags will be zero. If the MA parameter, \(\small \theta\), is -0.9, the first-lag autocorrelation will be \(\small -0.9/(1+(-0.9)^2)=-0.497\).
You will verify these autocorrelation functions for the three time series you generated in the last exercise.
Diese Übung ist Teil des Kurses
Time Series Analysis in Python
Interaktive Übung
Vervollständige den Beispielcode, um diese Übung erfolgreich abzuschließen.
# Import the plot_acf module from statsmodels
from statsmodels.graphics.tsaplots import plot_acf
# Plot 1: MA parameter = -0.9
plot_acf(___, lags=20)
plt.show()