Statistical analysis with missing data
Statistical analysis with missing data
System parameter estimation with input/output noisy data andmissing measurements
IEEE Transactions on Signal Processing
Autoregressive spectral analysis when observations are missing
Automatica (Journal of IFAC)
Computers and Electronics in Agriculture
Spectral analysis of nonuniformly sampled data -- a review
Digital Signal Processing
Spectral estimation for locally stationary time series with missing observations
Statistics and Computing
Evolutionary spectrum for random field and missing observations
ICISP'12 Proceedings of the 5th international conference on Image and Signal Processing
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The current computational power and some recently developed algorithms allow a new automatic spectral analysis method for randomly missing data. Accurate spectra and autocorrelation functions are computed from the estimated parameters of time series models, without user interaction. If only a few data are missing, the accuracy is almost the same as when all observations were available. For larger missing fractions, low-order time series models can still be estimated with a good accuracy if the total observation time is long enough. Autoregressive models are best estimated with the maximum likelihood method if data are missing. Maximum likelihood estimates of moving average and of autoregressive moving average models are not very useful with missing data. Those models are found most accurately if they are derived from the estimated parameters of an intermediate autoregressive model. With statistical criteria for the selection of model order and model type, a completely automatic and numerically reliable algorithm is developed that estimates the spectrum and the autocorrelation function in randomly missing data problems. The accuracy was better than what can be obtained with other methods, including the famous expectation-maximization (EM) algorithm.