Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression

Economic Fundation for Time Series Regression Models

Outline
I. Time Series Regression and Concept of Martingale Di¤erence Sequence
II. A Motivating Example: E¢ cient Market Hypothesis
III. A General Framework: Rational Expectations
IV. Applications
a. Consumption Smoothing
b. Martingale Theory of Stock Price
c. Dynamic CAPM
d. Derivatives Pricing
V. Conclusion

Detecting for Smooth Structural Changes in GARCH Models

Detecting and modelling structural changes in GARCH processes have attracted increasing
attention in time series econometrics. In this paper, we propose a new approach to testing struc-
tural changes in GARCH models. The idea is to compare the log likelihoods of a time-varying
parameter GARCH model and a constant parameter GARCH model, where the time-varying
GARCH parameters are estimated by a local quasi-maximum likelihood estimator (QMLE) and
the constant GARCH parameters are estimated by a standard QMLE. The test does not require
any prior information about the alternatives of structural changes. It has an asymptotic N(0,1)
distribution under the null hypothesis of parameter constancy and is consistent against a vast
class of smooth structural changes as well as abrupt structural breaks with possibly unknown
break points. A consistent parametric bootstrap is employed to provide a reliable inference in
…nite samples and the simulation study highlights the merits of our approach.