Compare the ACF for Several AR Time Series
The autocorrelation function decays exponentially for an AR time series at a rate of the AR parameter. For example, if the AR parameter, \(\small \phi = +0.9\), the first-lag autocorrelation will be 0.9, the second-lag will be \(\small (0.9)^2 = 0.81\), the third-lag will be \(\small (0.9)^3 = 0.729\), etc. A smaller AR parameter will have a steeper decay, and for a negative AR parameter, say -0.9, the decay will flip signs, so the first-lag autocorrelation will be -0.9, the second-lag will be \(\small (-0.9)^2 = 0.81\), the third-lag will be \(\small (-0.9)^3 = -0.729\), etc.
The object simulated_data_1 is the simulated time series with an AR parameter of +0.9, simulated_data_2 is for an AR parameter of -0.9, and simulated_data_3 is for an AR parameter of 0.3
This exercise is part of the course
Time Series Analysis in Python
Exercise instructions
- Compute the autocorrelation function for each of the three simulated datasets using the
plot_acffunction with 20 lags (and suppress the confidence intervals by settingalpha=1).
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Import the plot_acf module from statsmodels
from statsmodels.graphics.tsaplots import plot_acf
# Plot 1: AR parameter = +0.9
plot_acf(___, alpha=1, lags=___)
plt.show()
# Plot 2: AR parameter = -0.9
plot_acf(___, alpha=___, lags=20)
plt.show()
# Plot 3: AR parameter = +0.3
plot_acf(___, alpha=___, lags=___)
plt.show()