|
Abstract:
|
A common approach for characterizing the properties of time series data that are evenly sampled in time is to estimate the power spectrum. As an estimator of the spectrum, the periodogram is (1) inconsistent, (2) biased for finite samples, and (3) suffers from spectral leakage. In cases where the measurement of time series cannot be controlled, such as astronomy, data are often unevenly sampled. In these cases, Scargle (1982) and Lomb (1976) specify an estimator (LS periodogram) that accounts for the uneven sampling. Unfortunately, the LS Periodogram suffers the same problems as the classical periodogram and has even worse spectral leakage.
The multitaper spectral estimator (Thomson 1982) is well-known in the statistics and engineering literature. It is an attractive approach for evenly sampled time series because it directly trades off bias and variance for frequency resolution. We describe a multitapered version of the LS periodogram. We show examples in which this new approach has improved properties compared to the LS periodogram for unevenly sampled time series. Finally, we demonstrate its advantages in studying stellar brightness data collected by the Kepler spacecraft.
|
