Estimation of the State Space Models: An Application in Macroeconomic Series of Ecuador

This paper develops a framework for the analysis of state-space models combined with Kalman and smoothed Kalman filters for the estimation of unknown states, and parameters, determining the accuracy of the algorithms, with the purpose of analyzing some time series of the macroeconomy of Ecuador. This methodology plays an important role in the area of economics and finance and has many advantages because it allows describing how observed macroeconomic variables can be related to potentially unobserved state variables, determining the evolution in real time, estimating unobserved trends, changes of structures and make forecasts in future times. To achieve the objectives, three models are proposed: the first model is used to estimate the Ecuador's gross domestic product. The second model combines a state space model with the classic ARIMA (p, q, r) model to adjust the GDP rate and finally it is considered a model for the simultaneous stress time series analysis related to: consumer price index, industrial production index and active interest rate. In all the cases studied, the estimates obtained reflect the real behavior of the Ecuadorian economy. The square root of the mean square error was used as a measure of goodness of fit to measure the quality of estimation of the algorithms, obtaining small errors.