Parameter Change Test and Robust Estimation in Integer-Valued Time Series Models
정수값을 가지는 시계열 모형에서의 모수 변화 검정과 로버스트 추정방법
- 자연과학대학 통계학과
- Issue Date
- 서울대학교 대학원
- Poisson autoregressive model; Test for parameter change; Minimum density power divergence estimator
- 학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2014. 2. 이상열.
- In this thesis, we consider the parameter change test and the robust estimation
for integer-valued time series models.
First, we consider the problem of testing for a parameter change in a first order
random coefficient integer-valued autoregressive (RCINAR(1)) model.
For a test, we employ the cumulative sum (CUSUM) test based on the conditional least-squares(CLS)
and modified quasi-likelihood(MQL) estimators. It is shown that under regularity
conditions, the CUSUM test has the same limiting distribution as the supremum of
the squares of independent Brownian bridges. The CUSUM test is then applied to the
analysis of the monthly polio counts data set.
Second, we consider the problem of testing for a parameter change in Poisson
autoregressive models. We suggest two types of CUSUM tests: estimates-based and
residual-based tests. We first demonstrate that the conditional maximum likelihood
estimator (CMLE) is strongly consistent and asymptotically normal and construct the
CMLE-based CUSUM test. It is shown that under regularity conditions, its limiting
null distribution is a functional of independent
Brownian bridges. Next, we construct the residual-based CUSUM test and derive its
limiting null distribution. Simulation results are provided for illustration. A real
data analysis is performed for the polio incidence data and campylobacterosis infections
data. Finally, we study the robust estimation for Poisson autoregressive models.
As a robust estimator, we consider a minimum density power divergence estimator (MDPDE).
It is shown that under regularity conditions, the MDPDE is strongly consistent and
asymptotically normal. We perform a simulation study and a real data analysis to
compare the proposed estimator with MLE.