Exercise

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

Instructions

100 XP
  • Compute the autocorrelation function for each of the three simulated datasets using the plot_acf function with 20 lags (and suppress the confidence intervals by setting alpha=1).