in this article, we will describe Quadrature Ensemble Square Root Filter (qEnSRF). The qEnSRF is combined of Quadrature Ensemble Kalman Filter (qEnKF) and Ensemble Square Root Filter (EnSRF). For estimateing and predicting of data in econometric models and in state-space we are going to use Ensemble Kalman Filter. Ensemble Kalman Filter (EnKF) is a method based on assimilation data sequence which is used in a wide range. Then by introducing of the error of Quadrature Ensemble Square Root Filter ...