In the first chapter the performance of two of the long memory tests, the Modified Rescaled Range Test and Geweke and Porter-Hudak Test for persistence in small samples is examined using Monte-Carlo methods. Some possible candidates for persistence in volatility are Autoregressive Conditional Heteroskedasticity (ARCH), Markov Regime Switching ARCH, and long memory. The long memory series are simulated through a Semi-Markov process with Pareto waiting times and lognormal realizations. The persistence in volatility arising from transition waiting probabilities for a Markov Regime Switching process, and from the tail index of the waiting time distribution for the Semi-Markov process is established through simulations with different parameter values. There is evidence that persistence in a regime switching process is closely linked to state transition probabilities and waiting times.;The second chapter re-examines what structural vector autoregressive modeling of real exchange rates with differenced variables tells us about interesting macroeconomic questions. Using quarterly data from G-7 countries in the post Bretton-Woods period, the evidence suggests that shock identification is not an easy process in a Blanchard and Quah decomposition framework with long run restrictions. Confidence bands do not find significant impulse responses and the signs of the estimated impulse responses are very sensitive to the lag selection criteria adopted. Possible cointegration effects seem to be the main driving force behind the unsatisfactory performance of the structural approach.;Chapter three extends the structural vector autoregression model by incorporating cointegration effects. Using the method of Warne (1993), in a simple four-variable vector autoregression (VAR) characterized by cointegration, the response of real exchange rates to various economic shocks are investigated with economically plausible long-run restrictions. The long-run relations and driving stochastic trends of the real exchange rate between United States and other G-7 countries are analyzed in a structural cointegrated framework. Productivity shocks depreciate the real exchange rate and the perverse sign effect of supply shock is corrected for most countries in the sample. More significant impulse responses are observed through confidence intervals. The structural vector error correction decompositions are also found to be not robust to estimating with different lag lengths owing to additional cointegration effects.