There is a problem that AXt = f (AXt-i), which can make Dt = g(Dt-i) where i = 1, 2,..,.,n so transformation is done in equation (20) to break up this relationship in the residuals the augmented form is created.
AXt = a0 + PXm + Xt +EQiAXt-1-i + Dt — (21)
Ho; p = 0 (non-stationary series I and a=1) Hi; p Ф 0 (stationary series, I and aФ 1)
This hypothesis on p does not have standard T-distribution, so this parameter is checked against special critical values that depend upon the number of dynamics, data length and specifications like trend and intercept.
The Augmented Dickey Fuller test represented that for all the variables except Bond Rate of USA, test statistic shows the acceptance of the null hypothesis concluding that these series are non-stationary in nature and are integrated to order I. There is no hint of presence of trend in these series too. For the case of the Bond Rate of USA it showed hint of stationarity at only 10% level, but using 5% level ad benchmark and the significant trend, the Bond Rate of USA can be considered as non-stationary. These variables are tested in another class of test, these set of tests are used to form the robust form of results.
5.7.1.2 Phillips Peron test
(Phillips & Peron, 1988) builds on the Augmented Dickey Fuller Test by using non-parametric corrected test statistic to correct for the unspecified autocorrelation and hetroscedasticity. The results of Philips Peron Test are following; The results of this Philips Peron test show that using the 5% criteria, all the variables that are going to be used, have non-stationary behavior, which confirms the results of previous test.
Here again like Augmented Dickey Fuller test the Bond Rate of USA is a border line case, sorting this out, needs a robust method that is independent of this issue. As all the variables found are non-stationary with order of integration 1 i.e. I and Bond Rate of USA being a border line case, Ordinary Least Square Method (OLS) to estimate causality will not be appropriate, so another method is used that estimates long run perimeters and short run dynamics and suitable for I variables called Co-integration and Error Correction Model.
Table 7. Correlation analysis of exchange rate using UIP
BondRate of Pakistan | Bond Rate ofUSA | ||
Change in the Exchange Rate | PearsonCorrelation | 0.085 | -.0.033 |
Significance (2 – tailed) | 0.197 | 0.615 | |
Self calculated using Spss 16 |
Figure 8. Price differential and exchange rate change
Table 8. Augmented dickey fuller test
Series | Intercept | Lag level Parameter | Timeparameter | No of Dynamics | TestStatistic | P-Value |
Exchange rate | 0.06* | – 0.016 | 0.0001 | 0 | -1.474 | 0.838 |
Price level of Pakistan | 0.03 | – 0.007 | 0.000 | 3 | -1.109 | 0.927 |
Price level of USA | 0.15 | -0.036 | 0.000 | 2 | -1.587 | 0.797 |
Bond Rate of Pakistan | 0.06 | -0.028 | 0.000 | 1 | -1.286 | 0.891 |
Bond Rate of USA | 0.17** | -0.088** | – 0.0002** | 2 | -3.278 | 0.070* |
Table 9. Phillips Peron test
Series | Intercept | Lag level Parameter | Timeparameter | Newey-westLags | TestStatistic^{z(t)} | TestStatisticz(rho) | P-Value for z(t) |
Exchangerate | 0.06* | 098*** | 0.000 | 4 | -1.600 | -4.332 | 0.838 |
Price level of Pakistan | 0.02 | _{–}099 *** | 0.000 | 4 | –1.000 | -2.226 | 0.944 |
Price level of USA | 0.13 | 097*** | 0.000 | 4 | -1.722 | -9.159 | 0.741 |
Bond Rate of Pakistan | 0.11* | 0.95*** | –0.000 | 4 | -1.704 | -7.273 | 0.749 |
Bond Rate of USA | 014*** | _{–}0 92*** | 0.0001*** | 4 | -3.318* | -21.475** | 0.063* |
There is a problem that AXt = f (AXt-i), which can make Dt = g(Dt-i) where i = 1, 2,..,.,n so transformation is done in equation (20) to break up this relationship in the residuals the augmented form is created. AXt = a0 + PXm + Xt +EQiAXt-1-i + Dt — (21) Ho; p = 0 (non-stationary series I and a=1) Hi; p Ф 0 (stationary series, I and aФ 1) This hypothesis on p does not have standard T-distribution, so this parameter is checked against special critical values that depend upon the number of dynamics, data length and specifications like trend and intercept. The Augmented Dickey Fuller test represented that for all the variables except Bond Rate of USA,