We will concentrate on the modeling and analysis of a class of nonstationary time series, called correlation coefficient stationary series, which commonly exists in practical engineering. First, the concept and scope of correlation coefficient stationary series are discussed to get a better understanding. Second, a theorem is proposed to determine standard deviation function for correlation coefficient stationary series. Third, we propose a moving multiple-point average method to determine the function forms for mean and standard deviation, which can help to improve the analysis precision, especially in the context of limited sample size. Fourth, the conditional likelihood approach is utilized to estimate the model parameters. In addition, we discuss the correlation coefficient stationarity test method, which can contribute to the verification of modeling validity. Monte Carlo simulation study illustrates the authentication of the theorem and the validity of the established method. Empirical study shows that the approach can satisfactorily explain the nonstationary behavior of many practical data sets, including stock returns, maximum power load, China money supply, and foreign currency exchange rate. The effectiveness of these processes is addressed by forecasting performance. 1. Introduction Time series methods have been generally accepted as one of the most important means in an increasing number of real-world applications including finance. In the past several decades, considerable efforts have been made for time series analysis and prediction [1–3]. Time series approaches [4], regression models [5], artificial intelligence method [6], and Grey theory [7] are the commonly used techniques [8]. Many analyses are based on the assumption that the probabilistic properties of the underlying process are time invariant; that is, the series to be analyzed is covariance stationary. Modeling this stationary time series, one frequently chooses time series methods because of their high performance and robustness, which mainly include autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), and Box-Jenkins models. Although the stationary assumption is very useful for the construction of simple models, it does not seem to be the best strategy in practice, and sometimes such stationarity assumptions are often questionable [9], because time series with time-varying means and variances are commonly seen in economic forecast [10], fault diagnosis [11], quality control [12], signal processing
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