Abstract
Existence of outliers and structural breaks having mutually unknown nature, in time series data, offer challenges to data analysts in model identification, estimation and validation. Detection of these outliers has been an important area of research in time series since long. To analyze the impact of these structural breaks and outliers on model identification, estimation and their inferential analysis, we use two data generating processes: MA(1) and ARMA(1,1). The performance of the test statistics for detecting additive outlier(AO), innovative outlier(IO), level shift(LS) and transient change(TC) is investigated using simulation strategy through power of a test, empirical level of significance, empirical critical values, misspecification frequencies and sampling distribution of estimators for the two models. The empirical critical values are found higher than the theoretical cut-off points, empirical power of the test statistics is not satisfactory for small sample size, large cut-off points and large model coefficient. We have explored confusion between LS, AO, TC and IO at different critical values(c) by varying sample size. We have also collected empirical evidence from time series data for Pakistan using 3-stage iterative procedure to detect multiple outliers and structural breaks. We find that neglecting shocks lead to wrong identification, biased estimation and excess kurtosis.
 JEL Classification Codes: C15, C18, C63, C32, C87, C51, C52, C82
 AMS Classification Codes: 62, 65, 91, DI, 62-08, 62J20, 00A72, 91-08, 91-10, 91-11 62P20, 91B82, 91B84, 62M07, 62M09, 62M10, 62M15, 62M20
Highlights
Time series variables are extensively used to study aggregate fluctuations in the characteristics of any phenomenon
This is achieved by focusing on the performance of these test statistics for different choices of parameters in MA(1) and ARMA (1, 1) models through simulations. The choice of these two models is postulated on the argument that these commonly used nonlinear models provide parsimonious representation of data, make easier to spot trend and remove short term noise along with AR(1) model. The performance of these test statistics for outlier detection in AR(1) process is already evaluated by Urooj and Asghar (2017), while we look at existence, impact and detection of various types of outliers in some nonlinear models
We evaluate the performance of test statistics in detecting the outliers in some nonlinear models via simulations
Summary
Time series variables are extensively used to study aggregate fluctuations in the characteristics of any phenomenon. Another objective is to analyze the behavior of time series data having structural breaks and outliers and to identify the best possible model in the presence of various types of disturbances This is achieved by focusing on the performance of these test statistics for different choices of parameters in MA(1) and ARMA (1, 1) models through simulations. The occurrence of TC affects the time series for several lags depending upon the decay parameter δ with the size of outlier with magnitude ωTC. This decay is sharper in ARMA(1,1) than MA(1).
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