Seasonal trends in unequally spaced data: Confidence intervals for spectral estimates

摘要

Confidence intervals for spectral estimates are found for the case when the data are unequally spaced and exhibit a seasonal trend. The trend is estimated and removed using a procedure developed by the authors. This procedure is a modification of the Buys-Ballot filter where Hamming averaging is used to account for missing values. The effectiveness of this procedure in removing seasonal trends is examined. Both theoretical and Monte Carlo results are presented for confidence intervals of the spectral estimates based on the resulting residuals. Several decimation processes are considered —some that are independent of the trend, some that depend on the value of the trend, such as censoring of the data.