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We introduce and analyze a general bivariate non-linear dynamic system in order to assess the non-linearities and non-normalities in economic time series data that cannot be accounted for by non-linear models like ARCH, Bilinear or TAR. The system is in state space form with an unobservable state variable. Its most crucial property is conditional non-normality. For the estimation of the unobserved variable that may change at each time period, we derive a set of non-linear filters which is more general than the extended Kalman filter. We show that if the true system is conditionally Gaussian, the filter equations collapse to the Kalman filter. We introduce three models with non-linearity, non-normality complications and assess the performance of the non-linear filter via simulation. The simulation results indicate that as non-linearity in the system plays a more important role, the extended Kalman filter's performance deteriorates substantially, while the non-linear filter performs consistently well. The filter is successful in extracting the unobserved variable for many different non-linear non-normal systems. However, this cannot be generalized for all non-linear models and all parameter values. The estimation of the system parameters are also discussed. The non-linear filtering methodology is used to discover the behavior of exchange rates that are assumed to be generated by a subordinate stochastic process. The parameters are estimated by the Generalized Method of Moments and the information variable series are estimated via the non-linear filters. The directing process extracted through non-linear filtering easily lends itself to be interpreted as information flow; it increases during high volatility clusters and levels off during calm periods. The effect of liquidity constraints on firm behavior is also analyzed. For estimation, we use Kitagawa's filtering technique which utilizes the spline method for linear but non-normal models. We find that liquidity constr