Assessing influence in time series

Abstract

This paper studies influential observations on the spectrum of a stationary stochastic process. We introduce a leave-one-out procedure in spectral density estimation to identify influential points. A simulated envelope is proposed to assess the magnitude of influence when the data follow an autoregressive integrated moving average model. Practical illustrations are discussed in two examples.

Spectral density estimation with amplitude modulation and outlier detection

“…For example, one may also identify influential cases by employing the estimated spectral curve in (2.6) and the methods mentioned in Subba Rao (1989) and Hui and Lee (1992). [-i(s-t) …”

“…The leave-k-out diagnostic has been widely used in regression analysis (see Cook and Weisberg (1982) and Atkinson (1985)). Bruce and Martin (1989) and Hui and Lee (1992) also studied the leave-oneout approach in the time series context. We expect that our diagnostic approach based on deletion and the proposed spectral density estimation identifies outliers (especially innovation outliers) without masking and smearing effects.…”

“…The original RESEX dataset is given in Martin et al (1983), and consists of Bell Canada inward movement of residential telephone extensions in a fixed geographic area from January 1966 to May 1973. As pointed out by Hui and Lee (1992), several common diagnostic approaches suffer from masking and smearing phenomena, which motivated Jiang et al (1999) to use the robust Ll-norm fit of the dataset. Here we use the proposed diagnostic procedure to identify outliers in the data.…”

“…Several authors have proposed regarding the missing observations or outliers as zeros, and then estimating the spectral density from the "zeroed" data series. See for example Jones (1962), Parzen (1961Parzen ( , 1963, Priestley (1981), and Hui and Lee (1992) among others. A remarkable work in this field is that of Parzen (1963) in which amplitude modulation mechanics is proposed.…”