Spectral density estimation with amplitude modulation and outlier detection

Abstract

Amplitude modulation, local linear regression, missing observations, outlier detection, spectral density,

Efficient Non‐parametric Estimation of the Spectral Density in the Presence of Missing Observations

“…For these settings, consistent spectral density estimators have been proposed. Further references and developments in time‐series analysis with missing data can be found in Dunsmuir and Robinson (,b), Jiang and Hui (), Lee (), Robinson (), Vorotniskaya (), and Quevedo et al . ().…”

Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations

“…Typical practical examples are when a recording apparatus is faulty or liable to failure, or observations cannot be collected due to poor weather conditions; see a discussion in Parzen (1963), Efromovich (1999), Bloomfield (2004) and Tarczynski and Allay (2004). In the modern missing data literature R t would be referred to as the indicator of observing the data at time t and the missing mechanism would be called missing completely at random (MCAR), see Little and Rubin (2002). The stochastic time series {Z t } defines the amplitude-modulating mechanism.…”

“…The made assumption allows us to conclude that only time series {R t } defines the missing mechanism and that the non-zero mean of Z t does not change in time. There are numerous examples of amplitude-modulated times series discussed, for instance, in Parzen (1963), Dunsmuir and Robinson (1981), Efromovich (1999), Jiang and Hui (2004), and Vorotniskaya (2008). Now, following Efromovich (1999), let us introduce the shape of spectral density…”

Nonparametric inference with generalized likelihood ratio tests

“…For example, Wahba (1980) considered spline approximations to the log-periodogram using the least-square method; Pawitan and O'Sullivan (1994) and Kooperberg et al (1995aKooperberg et al ( , 1995b used Whittle's likelihood to estimate parameters in the spline models; Fan and Kreutzberger (1998) studied automatic procedures for estimating spectral densities, using the local linear fit and the local Whittle's likelihood; Jiang and Hui (2004) proposed a generalized periodogram and smoothed it using local linear approximations when missing data appeared.…”