Abstract: For the problem of predicting the capacity degradation of capacitors at elevated temperatures, based on the auto-regressive integrated moving average (ARIMA) model and the auto-regressive fractionally integrated moving average (ARFIMA) model, time series analysis methods are introduced to predict the degradation path of capacity. For the ARIMA model, when the degradation process of the capacitors obeys Wiener distribution, the over-differential prediction method (OPM) can be used to predict the difference order of the original time series that cause over-difference. According to the calculation results from unit root test, auto-correlation function and partial auto-correlation function, it will be verified that whether the time series can become stationary through the first order difference. For the ARFIMA model, the re-scaled range analysis is used to determine whether the degradation data has long-term memory. The orders and related parametric estimated values are obtained by using minimum information criterion and maximum likelihood estimation. Finally, the residual test is used to verify the ability of the OPM-ARIMA model and the ARFIMA model for extracting valuable information and accurate prediction. Furthermore, the feasibility and effectiveness of two models are also analyzed.

Key words: time series analysis； capacitors； degradation prediction； auto-regressive moving average model； fractional difference