Reference no: EM132339126

Homework Assignment

Question 1
In class, we discussed the ACF formula for an MA(1) process without an intercept term. Now derive the ACF formula for an MA(1) process with the intercept term (that is, θ₀ ≠ 0).

Question 2
Derive the ACF formula for an MA(2) process with the intercept term (that is, θ₀ ≠ 0).

Question 3
A researcher studies data for the Chinese stock market returns series and finds that it can be modeled as an MA(3) process of the following form (where the standard errors are given in parentheses):

Y^_t = 0.722 + 0.835 e_t-1 + 0.751 e_t-2 + 0.609 e_t-3
         (0.289)  (0.195)       (0.201)       (0.110)

R² = 0.71; n = 185

a. Is the intercept term significant to the model? Conduct a relevant hypothesis test to answer this question.

b. What is the mean-reverting level μ for this data process?

c. Suppose the process is currently at μ. Then, in time period t a shock occurs to the system. In other words, ε_t ≠ 0. For simplicity, assume that there are no other shocks prior to or after this shock. Use relevant equations to trace the impact of this shock from period (t-1) to (t+k).

d. Based on your findings in part (c), show that the above MA(3) process has finite memory. In other words, the impact of the shock fully dissipates after a finite number of periods and the data process will get back to its mean-reverting level μ that you obtained in part (b).

e. Suppose the researcher's advisor says, that fifty years ago, the true underlying data generating process for the Chinese stock returns series was in fact an MA(1) process shown by Y_t = ε_t + 0.65 ε_t-1.

Draw a plot of the Autocorrelation Function (ACF) for this MA(1) process up to 4 lags.