Title page for ETD etd-053105-143724

Document Type thesis

Author Name Ursan, Alina Maria

URN etd-053105-143724

Title A Robust Cusum Test for SETAR-Type Nonlinearity in Time Series

Degree MS

Department Mathematical Sciences

Advisors
Joseph D. Petruccelli, Advisor
Jayson D. Wilbur, Co-Advisor

Keywords
robust
cusum test
setar
nonlinearity

Date of Presentation/Defense 2005-05-31

Availability unrestricted

Abstract
As a part of an effective SETAR (self-exciting threshold autoregressive) mod-
eling methodology, it is important to identify processes exhibiting SETAR-type non-
linearity. A number of tests of nonlinearity have been developed in the literature,
including those of Keenan (1985), Petruccelli and Davies (1986), Tsay (1986, 1989),
Luukkonen (1988), and Chan and Tong (1990). However, it has recently been shown
that all these tests perform poorly for SETAR-type nonlinearity detection in the
presence of outliers.
In this project we develop an improved test for SETAR-type nonlinearity in
time series. The test is an outlier-robust variant of the Petruccelli and Davies (1986)
test based on the cumulative sums of ordered weighted residuals from generalized
maximum likelihood fits (which we call CUSUM-GM).
The properties of the proposed CUSUM-GM test are illustrated by means of
Monte Carlo simulations. The merits, in terms of size and power, of the proposed test
are evaluated relative to the test based on ordered residuals from the ordinary least
squares fit (which we call CUSUM-LS) and also to that of other tests for nonlinearity
developed in literature. The simulations are run for uncontaminated data and for
data contaminated with additive and innovational outliers. The simulation study
strongly supports the validity of the proposed robust CUSUM-GM test, particularly
in situations in which outliers might be a problem.

Files
AlinaUrsan.pdf

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Document Type	thesis
Author Name	Ursan, Alina Maria
URN	etd-053105-143724
Title	A Robust Cusum Test for SETAR-Type Nonlinearity in Time Series
Degree	MS
Department	Mathematical Sciences
Advisors	Joseph D. Petruccelli, Advisor Jayson D. Wilbur, Co-Advisor
Keywords	robust cusum test setar nonlinearity
Date of Presentation/Defense	2005-05-31
Availability	unrestricted
Abstract As a part of an effective SETAR (self-exciting threshold autoregressive) mod- eling methodology, it is important to identify processes exhibiting SETAR-type non- linearity. A number of tests of nonlinearity have been developed in the literature, including those of Keenan (1985), Petruccelli and Davies (1986), Tsay (1986, 1989), Luukkonen (1988), and Chan and Tong (1990). However, it has recently been shown that all these tests perform poorly for SETAR-type nonlinearity detection in the presence of outliers. In this project we develop an improved test for SETAR-type nonlinearity in time series. The test is an outlier-robust variant of the Petruccelli and Davies (1986) test based on the cumulative sums of ordered weighted residuals from generalized maximum likelihood fits (which we call CUSUM-GM). The properties of the proposed CUSUM-GM test are illustrated by means of Monte Carlo simulations. The merits, in terms of size and power, of the proposed test are evaluated relative to the test based on ordered residuals from the ordinary least squares fit (which we call CUSUM-LS) and also to that of other tests for nonlinearity developed in literature. The simulations are run for uncontaminated data and for data contaminated with additive and innovational outliers. The simulation study strongly supports the validity of the proposed robust CUSUM-GM test, particularly in situations in which outliers might be a problem.
Files	AlinaUrsan.pdf