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Who is afraid of missing data in spectral analysis
System Identification, Volume # 14 | Part# 1
Authors
Piet M. T. Broersen
Identifier
10.3182/20060329-3-AU-2901.00109
Index Terms
ARMA model,autoregressive model,autocovariance estimation,missing observations,order selection,parametric model,spectral estimation
Abstract
The program ARMAsel automatically selects a single time series model for given stationary stochastic data. Three model types are candidates for selection. The type can be AR or autoregressive, MA or moving average and the combined ARMA type. The parameters of that selected model accurately represent the power spectral density and the autocorrelation function of the data. The reduced statistics ARMAsel-rs algorithm uses a long AR model as only input to compute models of the other types and to select the best. ARMAsel-mis is a new program that can handle missing data. It computes AR models with a numerically stable maximum likelihood algorithm and uses ARMAsel-rs to determine MA and ARMA models. The order and the type of the best candidate are automatically selected with dedicated missing data criteria, supposing that data are randomly missing. Missing less than 10 % of the data has not much influence on the accuracy, missing 50 % generally looses a factor two in the accuracy in comparison with the model estimated from the same number of contiguous observations. Low order time series models can be computed as long as the product of the remaining fraction and the remaining number of observations is greater than about 10.
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