Outlier detection and estimation in nonlinear time series. (English) Zbl 1092.62081

Battaglia, Francesco; Orfei, Lia

J. Time Ser. Anal. 26, No. 1, 107-121 (2005).

The paper deals with the problem of identifying the time location and estimating the amplitude of outliers in nonlinear time series. A model based method is proposed for detecting the presence of additive or innovation outliers when the stationary zero-mean time series is generated by a nonlinear model of the type \(x_t=f(x^{(t-1)}; \varepsilon^{(t-1)})+ \varepsilon_t\), where \(f\) is a nonlinear function containing the unknown parameters, \(x^{(t-1)}= (x_{t-1}, x_{t-2},\dots, x_{t-p})'\), \(\varepsilon^{(t-1)}= (\varepsilon_{t-1}, \varepsilon_{t-2},\dots, \varepsilon_{t-p})'\), where \(\varepsilon_t\) is a zero-mean Gaussian white-noise series with \(E(\varepsilon^2_t)=\sigma^2\). The authors use this method for identifying and estimating outliers in bilinear, self exciting threshold autoregressive (SETAR) and exponential autoregressive models. A simulation study is performed to test the proposed procedures and comparing them with methods based on linear models and linear interpolators. This approach is applied to detecting outliers in the Canadian lynx trapping and in sunspot numbers data.

Reviewer: N. M. Zinchenko (Kyïv)

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C05	Monte Carlo methods

Keywords:

bilinear models; exponential autoregressive models; outliers; self-exciting threshold autoregressive models; state-dependent models; sunspot numbers

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