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tion results (i.e Ordinary Least Square) will be biased and misleading when the time series is found to be non-stationary and exhibits spurious regression.

Testing for relevance of PPP in the long run involves examining whether the real exchange rate revert to its own mean, a condition necessary to ensure that long run PPP holds. In the face of a series of disappointing results, researchers began to adopt another approach to investigating the PPP theory. Instead, they test the null hypothesis that the real exchange rate does not revert to its mean but instead follows a random walk (Roll (1979), Darby (1983) and Edison (1985)). Some authors argued that the existence of random walk in real exchange rate signifies a well-functioning international market where all available information is reflected in the prices and exchange rate while arbitrage opportunities are efficiently taken advantage of. In all, there are several methods utilised to test if the real exchange rate follows a random walk;

Firstly, the Dickey Fuller and Augmented Dickey Fuller (ADF) tests were used to determine whether a particular time series contains a unit root and subsequently follow a random walk. Moreover, the ADF test has been able to distinguish from 3 possible scenarios; has unit root, has unit root plus drift and has unit root plus drift and time trend.

where is a real exchange rate at time t, is a pth order polynomial function of lag operator L with coefficients: , ,… , and is a white noise disturbance. The null hypothesis will not be rejected if, and where the process has a unit root. But if the null hypothesis is rejected (), this implies that PPP theory holds. Studies from Hakkio (1984), MacDonald (1985), Edison (1987), Meese and Rogoff (1988), Taylor (1988), Roll (1979), Mark (1990) have consecutively used unit root test for their analysis but were coherent in their conclusion where they failed to reject the unit root hypothesis. Their failure to prove the validity of PPP could have been due to the low power of the ADF tests. This meant that even when we do not reject the null hypothesis of a random walk; it might not imply that the time series is in actual fact non-stationary.

Another approach used to investigate the presence of random walk is the variance ratios method.

Where is a real exchange rate at time t, T is the sample size, i = 2, 3 … T-1. If the null hypothesis of random walk holds, the variance of the real exchange rate should grow linearly and k(i) should be the same for all i. Conversely, if k(i) tends to zero when i increases , the series will instead follow a random walk. Glen (1988) found that contrasting results when testing the variance ratios on the monthly and annual sample. He could reject the random walk for monthly data but failed to find similar evidences for mean reversion while finding proof of mean reversion and not able to reject the random walk hypothesis for the annual data. Huizinga (1987) employed this approach and found a positive auto-correlation in real exchange rate of the US Dollar for time up to two years.

Frankel (1986, 1990) argues that even when the null hypothesis of a random walk is not rejected at a certain significance level; it might not mean that the results should be accepted. This is because of the lack of power of the statistical tests especially for studies covering less than 15 years or since 1973. To prove his poin