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Detecting ‘potential’ outliers in time series: Some Monte Carlo evidence on dummy variable plot approaches
Abstract
Monte Carlo experiments are employed to examine the small-sample performance of a dummy variable plot procedure. Both the simulation and empirical evidence favour the use of this approach in determining the position of time series outliers.
... In this study, Monte Carlo outlier method was used to detect all the abnormal samples. The detailed detection process was described previously (Cao et al., 2009;Nebebe & Kwan, 1995;Zhang et al., 2016). The main steps were following: Firstly, PLSR model was established with all samples as the correction set, and the RMSECV number was calculated by leave-one-out method. ...
Near infrared hyperspectral imaging (NIR‐HSI) with a spectral range of 900 to 1700 nm was for the first time used to predict the changes of sugar content in Lingwu jujube during storage. Monte Carlo method was adopted to detect outliers, and multiple scattering correction (MSC), standard normal variate transformation (SNV), and Baseline were used to optimize modeling. Competitive adaptive reweighted sampling (CARS), interval variable iterative space shrinkage approach (iVISSA), and interval random frog (IRF) were used to select optimal wavelengths. In addition, partial least square regression (PLSR) and support vector machine (SVM) modeling based on optimal wavelengths were compared. The results showed that 30, 30, and 24 wavelengths were selected by CARS; 106, 87, and 112 feature wavelengths were selected by iVISSA; and 96, 71, and 83 optimal wavelengths were selected by IRF for sucrose, fructose, and glucose, respectively. The CARS–PLSR models provided the best results for fructose and glucose, and iVISSA–SVM model was better for sucrose. The results indicated that NIR–HSI model may be used as a rapid and nondestructive method for the determination of sugar content in jujubes.
... This latter is coincident with the minimum mean squared error linear interpolator, for a Gaussian process, by taking the relationship between the inverse correlations and the autoregressive parameters into account. Nebebe and Kwan (1995), proposed a regression model and dummy variables approach. For each time point t a model with a single dummy at time t is estimated and the Student's statistics is evaluated for the parameter ω t . ...
The detection of multiple outliers in time series is a cumbersome task because of the large number of combinations of the candidate locations. A genetic algorithm is proposed for identifying additive and innovational outliers. The objective function depends on both the likelihood function and the number of outliers. The genetic algorithm allows simultaneous comparison of a great number of outliers' patterns. This way we may hope to overcome the problems of masking and swamping, that are very likely to arise in the context of time series analysis with aberrant observations. We are using the standard genetic algorithm with complete replacement of the past population and elitist strategy. Crossover looks quite a natural operator in the present framework because it accomplishes the task of combining together sets of locations where outlying observations are likely to exist. In the specification of the fitness function we take advantage of the well known relationship between inverse correla...
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ABSTRACT We propose diagnostics for ARIMA model fitting for time series formed by deleting observations from,the data and measuring,the change,in the estimates of the parameters. The use of leave-one-out diagnostics is a well established tool in regression analysis. We,demonstrate,the efficacy of observation deletion based diagnostics for ARIMA models, addressing issues special to the time diagnostics based on the innovations variance. It is shown that the dependency,aspect of time series data gives rise to a "smearing" effect, which confounds the diagnostics for the coefficients. It is also shown that the diagnostics based on the innovations variance are much,clearer and more sensitive than those for the coefficients. A "Ieave-k-out" diagnostics approachis proposed to deal with patches of outliers, and problems caused by "masking" are handled by use of iterative deletion. An overall strategy for ARIMA model fitting is given, and applied to two data sets. Research supported by NASC Contract N00014-86-K-08l9, APL Contract N00014-84-K
This paper investigates whether macroeconomic time series are better characterized as stationary fluctuations around a deterministic trend or as non-stationary processes that have no tendency to return to a deterministic path. Using long historical time series for the U.S. we are unable to reject the hypothesis that these series are non-stationary stochastic processes with no tendency to return to a trend line. Based on these findings and an unobserved components model for output that decomposes fluctuations into a secular or growth component and a cyclical component we infer that shocks to the former, which we associate with real disturbances, contribute substantially to the variation in observed output. We conclude that macroeconomic models that focus on monetary disturbances as a source of purely transitory fluctuations may never be successful in explaining a large fraction of output variation and that stochastic variation due to real factors is an essential element of any model of macroeconomic fluctuations.
The unit root hypothesis is examined allowing a possible one-time change in the level or in the slope of the trend function. When fluctuations are stationary around a breaking trend function, standard tests cannot reject the unit root, even asymptotically. Consistent tests are derived and applied to the Nelson-Plosser data set (allowing a change in level for the 1929 crash) and to the postwar quarterly real GNP series (allowing a change in slope after 1973). The unit root hypothesis is rejected at a high confidence level for most series. Fluctuations are stationary. The only persistent "shocks" are the 1929 crash and the 1973 oil price shock. Copyright 1989 by The Econometric Society.
Outliers and missing observations in time series, paper presented at the NSF/NEER Time Series Seminar Trends and random walks in macroeconomic time series Two issues in time series outlier detection using indicator variables The great crash, the oil price shock and the unit root hypothesis
- I Chang
- G Ljung
Chang, I. (1982), Outliers in time series, Ph.D. thesis, Department of Statistics, University of Wisconsin Madison. Ljung, G. (1989). Outliers and missing observations in time series, paper presented at the NSF/NEER Time Series Seminar, Spain. Nelson, C.R. and C.I. Plosser (1982). Trends and random walks in macroeconomic time series, J. Monetary Economics 10, 139-162. Otto, M.R. and W.R. Bell (1990). Two issues in time series outlier detection using indicator variables, Proc. American Statistical Association. Perron, P. (1989). The great crash, the oil price shock and the unit root hypothesis, Econometrica 57. 1361 1401.
Two issues in time series outlier detection using indicator variables
- Otto
Otto, M.R. and W.R. Bell (1990). Two issues in time series outlier detection using indicator variables, Proc.
American Statistical Association.
Outliers and missing observations in time series
- Ljung
Ljung, G. (1989). Outliers and missing observations in time series, paper presented at the NSF/NEER Time
Series Seminar, Spain.