Ridge estimation for uncertain autoregressive moving average model with imprecise observations

An uncertain time series is a sequence of imprecisely observed values arranged in chronological order, whose main purpose is to predict future values based on previously observed values. It is significant to select an appropriate parameter estimation method in uncertain time series analysis. Firstly, the paper transforms a one-order uncertain autoregressive moving average model into an uncertain autoregressive model by the iterative method. Secondly, the ridge method is used to estimate the unknown parameters in the uncertain autoregressive moving average model, in which the shrinkage parameter is determined by ridge trace analysis. Thirdly, the forecast value and confidence interval are acquired by the residual analysis of the fitted model. Finally, two examples are provided to verify the validity and feasibility of the method. The result shows that the ridge method can effectually cut down the affection of outliers and improve the prediction accuracy compared with the least square estimation.