University of Illinois Urbana-Champaign

Specification testing of ARCH and nonlinear time-series models

Higgins, M.L.

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Description

Title
Specification testing of ARCH and nonlinear time-series models
Author(s)
Higgins, M.L.
Issue Date
1989
Department of Study
Economics
Discipline
Economics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Economics, General
Language
eng
Abstract
  • Since the introduction of autoregressive conditional heteroscedasticity (ARCH) by Engle, there has been considerable interest in econometrics in models in which the variance of the current observation is a function of past observations. A difficulty in applying the ARCH model and other types of nonlinear time series models is lack of specification test for determining the appropriate model. This dissertation proposes several new tests to aid the selection of ARCH and nonlinear time series models.
  • It is shown that the standard Lagrange multiplier test for ARCH and the portmanteau test for nonlinearity are asymptotically equivalent under the null hypothesis of a linear model. A statistic for simultaneously testing for the presence of ARCH and bilinearity is proposed. This test is applied to an estimated inflation equation and indicates that the test increases the possibility of detecting nonlinearity.
  • A general nonlinear ARCH (NARCH) model is suggested which encompasses many of the functional forms frequently used for ARCH models. A test for the appropriateness of Engle's original linear ARCH model is developed when the alternative is the NARCH model. Finally, a test is derived for the presence of ARCH when the alternative is the NARCH model. This test is applied to six monthly exchange rates. The results indicate that the test has considerable power to detect nonlinear ARCH processes.
Type of Resource
text
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Copyright and License Information
Copyright 1989 Higgins, Matthew Lawrence

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