1. (1%) What is the difference between autoregressive and moving average models?
2. Consider an AR(2) model, 𝑦𝑡 = 1 + .5𝑦𝑡−1 + 0.2𝑦𝑡−2 + 𝑢𝑡, where 𝑢𝑡~𝑊𝑁(0, 𝜎2) for t=3,4,…,T. (i) Please rewrite this model using the lag operator L. (ii) Does this model give a stationary process? (iii) Calculate the mean and variance of 𝑦𝑡.
3. Dataset: Assignment2.csv and T=200.
(3%) Please apply Box-Jenkins approach to find a proper ARMA model to fit the dataset Assignment2.csv for the first 196 observations. (2%) Obtain s-step ahead forecast for s=1,2,3. If we set s sufficiently large, what will be your forecast for the variable of interest?