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Ridge Estimation for Uncertain Autoregressive Model with Imprecise Observations

The objective of time series analysis is to study the relationship between the data over time and to predict future values. Traditionally, statisticians assume that the observation data are precise, and we can get some exact values. However, in many cases, the imprecise observation data are available. We assume that these data are uncertain variables in the sense of uncertainty theory. In this paper, the ridge method is used to compute the unknown parameters in the uncertain autoregressive model. First, the ridge estimation of the parameters is given. The shrinkage parameter in the ridge estimation is obtained by ridge trace analysis. Based on the fitted autoregressive model, the forecast value and confidence interval of the future data are derived. Then two numerical examples are presented to verify the feasibility of this approach. Finally, the effectiveness of our model in reducing the influence of the outliers is shown by the comparative analysis.