Examine whether the two series G10 and TB3MS are co integrated. Carry out an Angle-Granger co integration test;

The expectation theory of the term structure of interest rates implies that if two interest rates
of different maturities are I(1), then they will be cointegrated with a cointegrating coefficient
of one; that is, the spread between the two rates will be stationary. The series SPREAD is
calculated by subtracting the short-term rate from the long-term rate.
The aim of this exercise is to test the above theory. The data for this exercise are given for
the United States and are contained in the file Data Coursework 19-20.xlsx, where G10 is
the 10-Year Treasury Constant Maturity Rate (Quarterly Average of Monthly Values), and
TB3MS is the 3-Month Treasury Bill (Quarterly Average of Monthly Values). The period in
consideration is from 1957 to 2013 (source: Bloomberg).
Answer the following question:
a) Generate an appropriate Eview workfile. Create the new series SPREAD as
explained above. Graph and show the descriptive statistics of the time series and
comment briefly; [14 marks]
b) Test whether the series G10 is a random walk or a martingale and briefly comment;
[22 marks]
c) Investigate the order of integration of the series G10 and TB3MS;
[28 marks]
d) Examine whether the two series G10 and TB3MS are cointegrated. Carry out an
Angle-Granger co integration test;
[14 marks]
e) Estimate and explain the results of the following two vector error correction models
of the two interest rates:
∆𝑇𝐵3𝑀𝑆𝑡 = 𝛼1 + 𝛼2∆𝑇𝐵3𝑀𝑆𝑡−1 + 𝛼3∆𝑇𝐵3𝑀𝑆𝑡−2 + 𝛼4∆𝐺10𝑡−1+𝛼5∆𝐺10𝑡−2 +
𝛼6𝑆𝑃𝑅𝐸𝐴𝐷𝑡−1 + 𝜀𝑡
(1)
∆𝐺10𝑡 = 𝛽1 + 𝛽2∆𝑇𝐵3𝑀𝑆𝑡−1 + 𝛽3∆𝑇𝐵3𝑀𝑆𝑡−2 + 𝛽4∆𝐺10𝑡−1+𝛽5∆𝐺10𝑡−2 +
𝛽6𝑆𝑃𝑅𝐸𝐴𝐷𝑡−1 + 𝜀𝑡
(2)