Answer the question

Problem 4 (30 marks). a) Inflation, denoted as {X,}, is a key target variable for mon- etary policy and if its forecasts are outside the interval [0.5, 3], then we say that predicted inflation is off-target and the Central Bank needs to intervene. (i) The last T = 100 values of {X} give the following sample autocorrelations p(k) and partial autocorrelations # (k) : The sample mean is X = 2.0593 and sample variance is o? = 2.0658. Using an approximate formula for the 95% confidence intervals for p(k) and i(k) explain why an AR(2) seems to be a reasonable model for {X}. [6 marks] lag k=1 k=2 k=3 k=4 p(k) 0.9144 0.7620 0.5984 0.4500 A (k) 0.9144 -0.4523 0.0883 -0.0258 (ii) Write an AR(2) model for { X} and estimate all its parameters. [12 marks]