Estimating error correction mechanism

Question

This coursework uses a data set from Stock and Watson’s ‘Introduction to Econometrics’ textbook. The two variables are a three-month interest rate (R90_t) and a one-year interest rate (R1yr_t). Use of the GRETL econometrics software is required. The data set is on the class MyPlace page. Using data for 1964Q1 to 1999Q4 throughout:
(a) Obtain time series plots of R90t,  R90t, R1yr_t, and  R1yr_t. Obtain plots of R90t against R1yr_t and of  R90t against  R1yr_t. Comment.
Consider the equation
 ΔX_t =α +  ρX_t−1 + γ1 ΔX_t−1 + γ2 ΔX_t−2 + γ3 ΔX_t−3 + u_t.
(b) Run the regression corresponding to (1) when Xt is R90_t (the three month interest rate) and test H0 : ρ = 0 against Ha : ρ< 0 using appropriate Dickey-Fuller critical values.
(c) Repeat step (b) but for R1yr_t (the one year interest rate).
(d) Repeat step (b) but for R90_t − R1yr_t.
(e) Discuss the implications of your estimations and your tests in parts (b),
(c), and (d).
(f) Estimate and discuss an ‘error correction mechanism’ type equation to explain ΔR90_t, reporting tests for both (i) autocorrelation and (ii) parameter stability, as well as parameter estimates and standard errors.