Research On Outlier Detection Of Two Kinds Of Time Series Models

Outlier detection of time series is an important issue in time series analysis, which can provide a lot of valuable information for the real world problems in many lines of work. Easiliy found in transportation, medicine, finance and many other fields, integer-valued time series and multivariate time series are crucial parts of time series. Therefore, study of outlier detection of integer-valued time seriese and multivariate time series has great theoretical and pratical significance both for the development of outlier detection theories per se and for solving real world problems. However, result of a broad and in-depth survey of the literature shows that most of the mainstream outlier detection methods of time series are proposed for ARMA or ARIMA models, that is, most researches are focusing on univariat continuous time series, leaving the outlier detection of many non-univariate and discrete time series in the real world, integer-valued and univariate time series included, largely unattended.The first-order integer-valued autoregressive(INAR(1)) model and the vector autoregressive(VAR) model are respectively the most successful model for integer-valued time series and multivariate time series analysis. Their simplicity and explanability single themselves out as the most critical tools for integer-valued time series and multivariate time series analysis.Due to the above-mentioned reasons, the outlier detection of INAR(1) and VAR time series models will be the focus of this paper. This paper has done the following research:Firstly, we introduce and compare the existing outlier detection methods in time series. The concept and features of common time series, as well as those of the outlier detection, are introduced. It is followed by the introduction of three often-used outlier detection methods, i.e., the likelihood ratio detection method, the influential observation detection method, and the Bayesian method. After that, a simulation experiement comparing the three methods has been done and finally their advantages and disadvantages are illustrated.Secondly, we consider the problem of INAR(1) model contaminated with both additive outliers(AO) and innovational outliers(IO). We first define an INAR(1) model contaminated with AO and IO outliers. Then we suppose the model contaminated by only one AO and one IO, and the time points of the two outliers are known and not neighbouring. Under these assumptions, the conditional least squares(CLS) estimation of some parameters of the model was calculated and we proved the CLS estimator is unique, strongly consistent and asymptotically normal. Finally we proved this result can be generalized to cases with finite number of AO and IO.Thirdly, we propsed a Bayesian outliers detection and parameter estimation method for INAR(1) model. This method can detect time points of outliers and classify them as either additive or innovational outliers. It can also estimate the parameters of model and the size of the outliers. Notably, the method can be used without knowing the type of outlier or the number of outliers. Extensive simulation studies and an experiment with real-world IP dataset both show that the proposed method can always deliver promising result.Finally, we propose a Bayesian method to detect outliers for VAR model. We generalize a Bayesian method for AR model to VAR model. Then we design a simulation experiment of outlier detection of VAR model to compare the performance of our Bayesian method and the likelihood ratio test method. The result shows that our method outperforms the likelihood ratio test method. We also use our method to real world macroeconomic data, and the result checks out the feasibility of our method.