zt3=vector(length = 100) zt3[1:3]=e[1:3] for(i in 3 :100){ zt3[i]=zt3[i]-0.9*zt3[i-1]+0.3*zt3[i-2] } zt3 acf(zt3) plot(zt3)

This code generates a time series vector zt3 of length 100 and sets the first three values to the first three elements of another vector e. Then, it creates a for loop that iterates from 3 to 100, and for each iteration, calculates the current value of zt3 based on the previous two values using a specific formula. Finally, it plots the autocorrelation function and a plot of zt3.

The formula used to calculate the new value of zt3[i] involves subtracting 0.9 times the previous value zt3[i-1] and adding 0.3 times the value two periods ago zt3[i-2]. This is a simple autoregressive moving average (ARMA) model with a lag of 1 and 2.

The acf(zt3) function plots the autocorrelation function of zt3, which shows the correlation between the time series and its lagged values. The plot(zt3) function shows a simple line plot of the values of zt3 over time.