Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this paper, we use predictive residuals to construct a test statistic to detect threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike i n f o rmation criterion. The nite-sample performance of the proposed test is studied by simulation. The modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost-of-carrying the contracts. In this particular application, thresholds are determined in part by the transaction costs. We also apply the proposed procedure to U.S. monthly interest rates and two river ow series of Iceland.
Outliers, level shifts, and variance changes are commonplace in applied time series analysis. However, their existence is often ignored and their impact is overlooked, for the lack of simple and useful methods to detect and handle those extraordinary events. The problem of detecting outliers, level shifts, and variance changes in a univariate time series is considered. The methods employed are extremely simple yet useful. Only the least squares techniques and residual variance ratios are used. The effectiveness of these simple methods is demonstrated by analysing three real data sets. Outliers and structure changes are commonly encountered in time series data analysis. The presence of those extraordinary events could easily mislead the conventional time series analysis procedure resulting in erroneous conclusions. The impact of those events is often overlooked, however, for the lack of simple yet useful methods available to deal with the dynamic behaviour of those events in the underlying series. The primary goal of this paper, therefore, is to consider unified methods for detecting and handling outliers and structure changes in a univariate time series. The outliers treated are the additive outlier (AO) and the innovational outlier (10). The structure changes allowed for are level shift (LS) and variance change (VC). Level shift is further classified as permanent level change (LC) and transient level change (TC). Several approaches have been considered in the literature for handling outliers in a time series. Abraham and Box (1979) used a Bayesian method, Martin and Yohai (1986) treated outliers as contamination generated from a given probability distribution, and Fox (1972) proposed two parametric models for studying outliers. Chang (1982) adopted Fox's models and proposed an iterative procedure to detect multiple outliers. In recent years, this iterative procedure has been widely used with encouraging results, see Chang and Tiao (1983), HilImer, Bell and Tiao (1983), and Tsay (1986a. The methods mentioned above may be regarded as batch-type procedures for detecting outliers, because the full data set is used in detecting the existence of outliers. On the other hand, Harrison and Stevens (1976), Smith and West (1983), West, Harrison and Migon (1985) and West (1986) have considered sequential detecting methods for handling outliers. These sequential methods assume probabilistic models for outlier disturbances. The third method for handling outliers is the robust procedure advocated
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