Estimation of time series noise covariance using correlation technology

Covariance of clean signal and observed noise is necessary for extracting clean signal from a time series. This is transferred to calculate the covariance of observed noise and clean signal's MA process, when the clean signal is described by an autoregressive moving average (ARMA) model. Using the correlations of the innovations data from observed time series to form a least-squares problem, a concisely autocovariance least-square (CALS) method has been proposed to estimate the covariance. We also extended our work to the case of unknown MA process coefficients. Comparisons between Odelson's autocovariance least-square (ALS) estimation algorithm and the proposed CALS method show that the CALS method could get a much more exact and compact estimation of the covariance than ALS and its extended form.