The Bolivian foreign exchange market is explained in terms of the official and parallel exchange rates. The data covers the post hyper inflationary period from 1986 to 1992. The distribution of the rate of depreciation of the official and parallel exchange rates is long tailed and strongly departs from normality due to the existence of outliers. A market interactions model of the autoregressive kind is estimated using robust regression. This procedure produces M-parameter estimates using iteratively reweighted least squares. The robust method handles well the outlier problem and at the same time it reveals the true nature of the statistical properties of the data by not being able to produce white noise in the squared residuals. Both markets show a one-time break in the variance creating two periods of differential behavior, with one of them having GARCH properties. Robust unit root and cointegration tests also fail to produce white noise squared residuals due to the same phenomena. Further research requires the development of a robust procedure that could take care of the outlier and heteroskedasticity problems simultaneously.