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The purpose of this project is to investigate the co-movements of Jamaica and Trinidad and Tobago Treasury bill rates, as well as to investigate whether the US Treasury bill rate Granger Cause the movement of the Treasury bill rates of both Caribbean islands.
To study the co-movements between the Treasury rates, we will determine if there is a long run relationship between the two series using co-integration tests. Direct Granger tests will be used to determine the causality between them.
Watson and Teelucksingh (2002) said that the co-integration of two variables occurs when the linear combination of the two does not vary. This means that they tend to move together in the long run. It also described Granger causality as follows, “(A variable) x is a granger cause of (another variable) y, if present y can be predicted with better accuracy by using past values of x rather than by not doing so, ceteris paribus.”
In testing for co-integration, I will be using the Johansen Procedure. Watson and Teelucksingh (2002) describe it as a maximum likelihood approach, based on the factorization Γ=αβ’, and is used for determining the maximum number of co-integrating vectors, (in this case, it would be one since there are only two variables) and obtaining the maximum likelihood estimators of the co-integrating matrix (β) and adjustment parameters (α). If co-integration is established, the error correction model (ECM) is estimated. The two series, however, must be of the same integrating order, namely I(1), before we can test for co-integration. There are three formal tests to determine integrating order; The Dickie-Fuller (DF) test, the Augmented Dickie-Fuller (ADF) test and the Phillips-Perron test. Watson and Teelucksingh (2002) states the Dickie-Fuller (DF) test tests the equation ∆xt=ϕxt-1+μt (ϕ=ρ-1) where the null hypothesis, H0, states that ϕ=0. (ie, the series admits one unit root.). The Augmented Dickie-Fuller (ADF) test is a more generalized variation of the Dickie-Fuller (DF) test that does not require μt being a white noise process. There are other, albeit informal, way of testing for unit roots. One such way is to investigate the autocorrelation function or ACF. If the AC figures start off high and slowly decline over time, then this implies a nonstationary series. Another way is to directly observe the time plot of the data. If the graph appears to fluctuate about a fixed mean, then it is stationary and does not have a unit root. If it appears to generally increase or decrease over time, then it admits at least one unit root. In testing for Granger causality, I will use a Direct Granger test. This test looks at the cases of an “unrestricted” model versus a “restricted” one to determine if any Granger Causality (as described above) exists.
Testing for co-integration on Jamaica and Trinidad and Tobago Treasury Bill Rates. The first step in testing for co-integration is to ensure that both variables are of Integrating Order 1 (I(1)). I will first look at the informal tests on both variables. Looking at the time plot for the Jamaican bill rates (Figure 1) we can see that the graph does not appear to fluctuate about a mean which is an indicator for a unit root existing. Also, when looking at the ACF for Jamaican bill rates (Table 1) we see that it starts off relatively high then gradually declines. This implies non-stationarity. Looking at the time plot for Trinidad and Tobago’s rate (Figure 2), it also appears to not fluctuate about a mean which, again, is an indicator for a unit root existing. Looking at the ACF for Trinidad and Tobago’s rates, it similarly starts off high and then gradually decreases, again implying non-stationarity. I will now move on to the formal tests to confirm...