Modeling the Distribution of Exchange Rate Time Series and Measuring the Tail Area: An Empirical Application of the Colombian Flexible Exchange Rate

Modeling the unconditional distribution of returns on exchange rate and measuring its tails area are issues in the finance literature that have been studied extensively by parametric and non-parametric estimation procedures. However, a conflict of robustness is derived from them because the time series involved in this process are usually fat tailed and highly peaked around the center. Moreover, it has been an empirical fact that the initial phase of a freely floating exchange rate regime has experienced high volatility across many economies. The purpose of this paper is twofold. First, we try to capture the behavior of the Colombian exchange rate under the flexible system by fitting special types of distributions in order to obtain a new insight of the underlying distribution. Secondly, we measure the tail area through the Hill estimator. This strategy requires the number of extreme observations in the tails to be known. Therefore, the decision rule of choosing an optimal cutting observation based on the idea of spacing statistics is implemented by using a Monte Carlo simulation under different underlying distributions. The decision model is formulated in such a way that the mean squared error is minimized.

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