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root hypothesis for each of the auction variables of interest These tests are presented in Aron and Elbadawi (1994): in all four countries, the data series for each of the thtee exchange rate variables (the auction, bureaux rates and the premium) was found to have a unit root non-ationary process. Noting that the distinction between a random walk (unit root) and a trend-stationary series is extreme, Cochrane (1988) argues that there are many cases where a stationary but a slow trendreverting series could be confounded with unit root series. To address this problem with unit root tests, he proposed a variance ratio test that basically asks the following question: How large is the variance of shocks to the random walk or permanent component of the series compared with the variance of the growth rates of -the series? Or, equivalently, How big is the random walk in the series? The ratio is given by l " X . For a stationary series the ratio will eventually converge to zero as k goes to infinity, the speed of this convergence reflects the extet to which the stationary time series stucture is doser to either of the two polar cases: the stationary (zero root) or the random walk (unit root). On the other hand a unit root series will have a ratio that settle down to the share of the variance of the shock to the random walk component in the total variance (> 0). Figure 3 shows the plots of the Cochrane ratio for the auction equilibrium exchange rates against k for each of the four auctions. The auction rate is much closer to the unit root case in both the Ghana and Uganda, where the shares of the random walk in total variance settle down to approximately 77 percent in Ghana and 96 percent in Uganda24 Particularly in the case of Ghana, the ratios have in fact diverged for a prolonged time before sarting to converge at k = 62. On the other hand, random walk components account for about 54 percent of total variance of the auction rate in Zambia, and only about 6 percent of total variance in Nigeria. Furtermore, convergence of the varimae ratios have strted rather rapidly (at k = 2) in both countries. This finding is again fairly consistent with the stochastic reserve price<sup>3</sup> that has had a significant effect on the auction rates in Ghana and UgaXlda, as opposed to the frequent and direct policy inteventions that characterized the Nigerian and Zambian auctions. Therefore it is obvious that the auction rate is chacterized by high persistence (random walk component), which agrees with the unit root tests in Aron and Elbadawi (1994). But Figure?v also shows the presence of substantial temporary components in the innovation v=arices of these series, especially in the case of Nigeria and Zambia. This is also in general agreement with the prevalence of detrministic trends and regime shifts.in auction rates and auction data (Figure 1).

The lawge sarmpl standard error for the ratio is given by ' tarQC_) 1d) where T is the number of observations., 7' The cboice of the temminal k is rathcr arbiray. but following Cochmne we chose the maximunm k to be the ine of one Iounh to a third of ihe total number of observations.

- The reserve prc closely fosilow the evolution of the burauz or paradel rates in Ghana and Ugmada which are shown to be l(l) scries Table 4).