State-space multitaper time-frequency analysis

Significance Rapid growth in sensor and recording technologies is spurring rapid growth in time series data. Nonstationary and oscillatory structure in time series is commonly analyzed using time-varying spectral methods. These widely used techniques lack a statistical inference framework applicable to the entire time series. We develop a state-space multitaper (SS-MT) framework for time-varying spectral analysis of nonstationary time series. We efficiently implement the SS-MT spectrogram estimation algorithm in the frequency domain as parallel 1D complex Kalman filters. In analyses of human EEGs recorded under general anesthesia, the SS-MT paradigm provides enhanced denoising (>10 dB) and spectral resolution relative to standard multitaper methods, a flexible time-domain decomposition of the time series, and a broadly applicable, empirical Bayes’ framework for statistical inference. Time series are an important data class that includes recordings ranging from radio emissions, seismic activity, global positioning data, and stock prices to EEG measurements, vital signs, and voice recordings. Rapid growth in sensor and recording technologies is increasing the production of time series data and the importance of rapid, accurate analyses. Time series data are commonly analyzed using time-varying spectral methods to characterize their nonstationary and often oscillatory structure. Current methods provide local estimates of data features. However, they do not offer a statistical inference framework that applies to the entire time series. The important advances that we report are state-space multitaper (SS-MT) methods, which provide a statistical inference framework for time-varying spectral analysis of nonstationary time series. We model nonstationary time series as a sequence of second-order stationary Gaussian processes defined on nonoverlapping intervals. We use a frequency-domain random-walk model to relate the spectral representations of the Gaussian processes across intervals. The SS-MT algorithm efficiently computes spectral updates using parallel 1D complex Kalman filters. An expectation–maximization algorithm computes static and dynamic model parameter estimates. We test the framework in time-varying spectral analyses of simulated time series and EEG recordings from patients receiving general anesthesia. Relative to standard multitaper (MT), SS-MT gave enhanced spectral resolution and noise reduction (>10 dB) and allowed statistical comparisons of spectral properties among arbitrary time series segments. SS-MT also extracts time-domain estimates of signal components. The SS-MT paradigm is a broadly applicable, empirical Bayes’ framework for statistical inference that can help ensure accurate, reproducible findings from nonstationary time series analyses.