Modeling Flat Stretches, Bursts Outliers in Time Series Using Mixture Transition Distribution Models
作者:
NhuD. Le,
R.Douglas Martin,
AdrianE. Raftery,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 436
页码: 1504-1515
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476718
出版商: Taylor & Francis Group
关键词: Autocorrelation;Autoregressive integrated moving average model;EM algorithm;Mixture transition distribution;Non-Gaussian time series;Stationarity
数据来源: Taylor
摘要:
The class of mixture transition distribution (MTD) time series models is extended to general non-Gaussian time series. In these models the conditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the lastpobservations. They can capture non-Gaussian and nonlinear features such as flat stretches, bursts of activity, outliers changepoints in a single unified model class. They can also represent time series defined on arbitrary state spaces, univariate or multivariate, continuous, discrete or mixed, which need not even be Euclidean. They perform well in the usual case of Gaussian time series without obvious nonstandard behaviors. The models are simple, analytically tractable, easy to simulate readily estimated. The stationarity and autocorrelation properties of the models are derived. A simple EM algorithm is given and shown to work well for estimation. The models are applied to several real and simulated datasets with satisfactory results. They appear to capture the features of the data better than the best competing autoregressive integrated moving average (ARIMA) models.
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