Question

1. Cointegration

For the macro data file consider interest rates of different maturities from 3 months to 10 years: USTB3M USTB6M USTB3Y USTB5Y USTB10Y

1. Test for unit root each variable and perform the Engle Granger test of cointegration for

1. 3 month and 6 month interest rates
2. 3 month and 10 year interest rates
3. Explain results in (a) and (b). What can you say about the spread between the rates?

2. Would you use a VAR (Vector Autoregression) or VEC (Vector Error Correction) for further modelling of interest rates in cases (a) and (b) above? Explain in words (no computer work needed).

Answer 1

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(a) 3 month and 6 month interest rates

(i) USTB 3 month = alpha + (Beta)USTB 5 month

(ii) Yes p value is very small,

Cointegration test

Graph of 3Month and 6 Monthvariable

l Both 3 month and 6 month variables have a unit root

n 3 month: -1.90 > -2.57, do not reject the null, unit root by Unit Root Test

n 6 month: -1.40 > -2.57, do not reject the null, unit root by Unit Root Test

(b) 3 month and 10 year interest rates

Contegration Test

Graph of 3 Months and 10 years variable

Both 3 month and 10 year variables have a unit room

10 year: -1.48 > -2.57, do not reject the null, unit root by Unit Root Test.

(c) Explain results in (a) and (b). What can you say about the spread between the rates?

Graph from (a) looks like it has cointegration because they have similar curve in the graph, but graph in from (b) looks like it does not a cointegration.

In (a) both tau-statistic from 3 month and 6 month variables are > -2.57, it means reject the null. (a) has cointegration, null hypothesis was series are not cointegrated.

Both tau-statistics from 3 month and 10 year variables are higher than -2.57, which accept the null hypothesis. (b) has no cointegration as accept the null hypothesis.

The graph and comparing tau-statistic came out with same results; (a) has cointegration and (b) has no cointegration.

Moreover, 10 year variable do not have Unit Root, so it is not right to find cointegration with 3 month variable.

Would you use a VAR (Vector Autoregression) or VEC (Vector Error Correction) for further modelling of interest rates in cases (a) and (b) above? Explain in words (no computer work needed).

Essentially, we use a vector error correction when we find a cointegration. On the other hand, we use a vector autoregression when there is no cointegration. As stated earlier, in the case of (a), we have a cointegration. Therefore, it is appropriate to use VEC (vector error correction). In the case of B, we have no cointegration. Therefore, it is appropriate to use a VAR (vector autoregression).