1. Consider the monthly log returns of CRSP equal-weighted index from January 1962 to
December 1999 for 456 observations. You may obtain the data from the file hw1.txt.
(a) Plot the time series.
(b) Build an AR model for the series and check the fitted model.
(c) Build an MA model for the series and check the fitted model.
(d) Compute 1- and 2-step-ahead forecasts of the AR and MA models built in the
previous two questions.
(e) Compare the fitted AR and MA models.
(f) Use diagnostic tools to identify the possible order(s) of ARMA model(s) that most
likely describes the series.
(g) Use some form of search to identify what form of ARMA(p,q) model best
describes the log index returns.
(h) Write out the best model

2. Please write out the process to get the mean, variance and autocorrelation function for the
following models
(a) MA(1) model: = 0 + − 1−1 in which is a white noise time series.
(b) AR(1) model: = ∅0 + ∅1−1