The research paper is devoted to developing a mathematical approach for dealing with time-varying parameters in rolling window logit models for credit risk assessment. Forecasting coefficients yields a better model accuracy than a trivial approach of using computed past statistics parameters for the next time period. In this paper, a new method of dealing with time-varying parameters of scoring models is proposed, which is aimed at computing the default probability of a borrower. It was empirically shown that in a continuously changing economic environment factors’ influence on a target variable is also changing. Therefore, forecasting coefficients yields a better financial result than simply applying parameters obtained by accumulated statistics over past time periods. The paper develops a new theoretical approach, incorporating a combination of the ARIMA class model, the DCC-GARCH model and the state–space model, which is more accurate, than using only the ARIMA model. Rigorous simulation testing is provided to confirm the efficiency of the proposed method.