Evaluation of Test Statistics for Detection of Outliers and Shifts

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, 62M2

A nonparametric approach to detecting changes in variance in locally stationary time series

This paper proposes a nonparametric approach to detecting changes in variance within a time series that we demonstrate is resilient to departures from the assumption of normality or presence of outliers. Our method is founded on a local estimate of the variance provided by the locally stationary wavelet framework. Within this setting, the structure of this local estimate of the variance will be piecewise constant if a time series has piecewise constant variance. Consequently, changes in the variance of a time series can be detected in a nonparametric setting. In addition, using a simulation study, we explore the robustness of our approach against the typical assumption of normality and presence of outliers. We illustrate the application of the approach to changes in variability of wind speeds at a location in the United Kingdom

Outlier detection in multivariate time series via projection pursuit

This article uses Projection Pursuit methods to develop a procedure for detecting outliers in a multivariate time series. We show that testing for outliers in some projection directions could be more powerful than testing the multivariate series directly. The optimal directions for detecting outliers are found by numerical optimization of the kurtosis coefficient of the projected series. We propose an iterative procedure to detect and handle multiple outliers based on univariate search in these optimal directions. In contrast with the existing methods, the proposed procedure can identify outliers without pre-specifying a vector ARMA model for the data. The good performance of the proposed method is verified in a Monte Carlo study and in a real data analysis

Wavelet-based detection of outliers in volatility models

Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. This paper focuses on these issues and proposes a general detection and correction method based on wavelets that can be applied to a large class of volatility models. The effectiveness of our proposal is tested by an intensive Monte Carlo study for six well known volatility models and compared to alternative proposals in the literature, before applying it to three daily stock market indexes. The Monte Carlo experiments show that our method is both very effective in detecting isolated outliers and outlier patches and much more reliable than other wavelet-based procedures since it detects a significant smaller number of false outliers

OUTLIER DETECTION IN MULTIVARIATE TIME SERIES VIA PROJECTION PURSUIT

This article uses Projection Pursuit methods to develop a procedure for detecting outliers in a multivariate time series. We show that testing for outliers in some projection directions could be more powerful than testing the multivariate series directly. The optimal directions for detecting outliers are found by numerical optimization of the kurtosis coefficient of the projected series. We propose an iterative procedure to detect and handle multiple outliers based on univariate search in these optimal directions. In contrast with the existing methods, the proposed procedure can identify outliers without pre-specifying a vector ARMA model for the data. The good performance of the proposed method is verified in a Monte Carlo study and in a real data analysis.

Identification of Outlying Observations with Quantile Regression for Censored Data

Outlying observations, which significantly deviate from other measurements, may distort the conclusions of data analysis. Therefore, identifying outliers is one of the important problems that should be solved to obtain reliable results. While there are many statistical outlier detection algorithms and software programs for uncensored data, few are available for censored data. In this article, we propose three outlier detection algorithms based on censored quantile regression, two of which are modified versions of existing algorithms for uncensored or censored data, while the third is a newly developed algorithm to overcome the demerits of previous approaches. The performance of the three algorithms was investigated in simulation studies. In addition, real data from SEER database, which contains a variety of data sets related to various cancers, is illustrated to show the usefulness of our methodology. The algorithms are implemented into an R package OutlierDC which can be conveniently employed in the \proglang{R} environment and freely obtained from CRAN

Outliers in Garch models and the estimation of risk measures

In this paper we focus on the impact of additive level outliers on the calculation of risk measures, such as minimum capital risk requirements, and compare four alternatives of reducing these measures' estimation biases. The first three proposals proceed by detecting and correcting outliers before estimating these risk measures with the GARCH(1,1) model, while the fourth procedure fits a Student’s t-distributed GARCH(1,1) model directly to the data. The former group includes the proposal of Grané and Veiga (2010), a detection procedure based on wavelets with hard- or soft-thresholding filtering, and the well known method of Franses and Ghijsels (1999). The first results, based on Monte Carlo experiments, reveal that the presence of outliers can bias severely the minimum capital risk requirement estimates calculated using the GARCH(1,1) model. The message driven from the second results, both empirical and simulations, is that outlier detection and filtering generate more accurate minimum capital risk requirements than the fourth alternative. Moreover, the detection procedure based on wavelets with hard-thresholding filtering gathers a very good performance in attenuating the effects of outliers and generating accurate minimum capital risk requirements out-of-sample, even in pretty volatile periodsMinimum capital risk requirements, Outliers, Wavelets

Outlier Detection and Missing Value Estimation in Time Series Traffic Count Data: Final Report of SERC Project GR/G23180.

A serious problem in analysing traffic count data is what to do when missing or extreme values occur, perhaps as a result of a breakdown in automatic counting equipment. The objectives of this current work were to attempt to look at ways of solving this problem by: 1)establishing the applicability of time series and influence function techniques for estimating missing values and detecting outliers in time series traffic data; 2)making a comparative assessment of new techniques with those used by traffic engineers in practice for local, regional or national traffic count systems Two alternative approaches were identified as being potentially useful and these were evaluated and compared with methods currently employed for `cleaning' traffic count series. These were based on evaluating the effect of individual or groups of observations on the estimate of the auto-correlation structure and events influencing a parametric model (ARIMA). These were compared with the existing methods which included visual inspection and smoothing techniques such as the exponentially weighted moving average in which means and variances are updated using observations from the same time and day of week. The results showed advantages and disadvantages for each of the methods. The exponentially weighted moving average method tended to detect unreasonable outliers and also suggested replacements which were consistently larger than could reasonably be expected. Methods based on the autocorrelation structure were reasonably successful in detecting events but the replacement values were suspect particularly when there were groups of values needing replacement. The methods also had problems in the presence of non-stationarity, often detecting outliers which were really a result of the changing level of the data rather than extreme values. In the presence of other events, such as a change in level or seasonality, both the influence function and change in autocorrelation present problems of interpretation since there is no way of distinguishing these events from outliers. It is clear that the outlier problem cannot be separated from that of identifying structural changes as many of the statistics used to identify outliers also respond to structural changes. The ARIMA (1,0,0)(0,1,1)7 was found to describe the vast majority of traffic count series which means that the problem of identifying a starting model can largely be avoided with a high degree of assurance. Unfortunately it is clear that a black-box approach to data validation is prone to error but methods such as those described above lend themselves to an interactive graphics data-validation technique in which outliers and other events are highlighted requiring acceptance or otherwise manually. An adaptive approach to fitting the model may result in something which can be more automatic and this would allow for changes in the underlying model to be accommodated. In conclusion it was found that methods based on the autocorrelation structure are the most computationally efficient but lead to problems of interpretation both between different types of event and in the presence of non-stationarity. Using the residuals from a fitted ARIMA model is the most successful method at finding outliers and distinguishing them from other events, being less expensive than case deletion. The replacement values derived from the ARIMA model were found to be the most accurate