A Novel Lag Window for Spectrum Estimation of the Ornstein-Uhlenbeck Process

In order to forecast and process the behavior of noisy data, spectral analysis is a crucial area of study in data analysis and interpretation. The goal of this study is to identify the optimal lag window to estimate the continuous-time Ornstein-Uhlenbeck (OU) process’s spectrum. The equivalent difference equation of the OU process was derived, and a consistent estimate of the spectral density function (SDF) was calculated using the most prominent lag window functions in the different parameter cases and time interval segmentation. A parameterized novel lag window (NLW) was proposed. The parameters can be changed to control the kurtosis and skewness of the NLW curve and reduce the influence of the tails of the estimated autocorrelation function on the consistent estimate of the SDF. The simulation results of comparing the SDF and the consistent estimate of the SDF with lag windows showed that the proposed NLW outperformed all other lag windows in estimating the spectrum of the OU process in all parameter cases and in all time-interval segmentation. The promising results of NLW can be used in signal processing and spectral analysis of phenomena subject to the influence of noise.