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Abstract
Time series data are often subject to uncontrolled or unexpected interventions, from which various types of outlying observations are produced. Outliers in time series, depending on their nature, may have a moderate to significant impact on the effectiveness of the standard methodology for time series analysis with respect to model identification, estimation, and forecasting. In this article we use an iterative outlier detection and adjustment procedure to obtain joint estimates of model parameters and outlier effects. Four types of outliers are considered, and the issues of spurious and masking effects are discussed. The major differences between this procedure and those proposed in earlier literature include (a) the types and effects of outliers are obtained based on less contaminated estimates of model parameters, (b) the outlier effects are estimated simultaneously using multiple regression, and (c) the model parameters and the outlier effects are estimated jointly. The sampling behavior of the test statistics for cases of small to large sample sizes is investigated through a simulation study. The performance of the procedure is examined over a representative set of outlier cases. We find that the proposed procedure performs well in terms of detecting outlets and obtaining unbiased parameter estimates. An example is used to illustrate the application of the proposed procedure. It is demonstrated that this procedure performs effectively in avoiding spurious outliers and masking effects. The model parameter estimates obtained from the proposed procedure are typically very close to those estimated by the exact maximum likelihood method using an intervention model to incorporate the outliers.
... Once AO is apparent in the part of the GARCH model, the Equation could be transformed into Eq. (7), as shown by Chen and Liu (1993b). ...
... Since the outliers could affect the mean and standard deviation as the central tendency and dispersion, respectively, therefore, Hampel (1974) proposed the MAD as a more robust estimate than the sample standard deviation. Chen and Liu (1993b) also examined the MAD approach to achieve a better estimate and considered it an appropriate option (Simpson & Montgomery, 1998) and more robust dispersion (Leys et al., 2013;Ruppert & Matteson, 2015). ...
Dispersion measurement and tuning constants are critical aspects of a model's robustness and efficiency. However, in the presence of outliers, the standard deviation is not a reliable measure of dispersion in Huber's weight. This research aimed to assess the efficacy of the Huber weight function in terms of dispersion measurement and tuning constant. The simulation study was conducted on a hybrid of the autoregressive (AR) model and the generalized autoregressive conditional heteroscedasticity (GARCH) model with 10% and 20% additive outlier contamination. In the simulation analysis, three dispersion measurements were compared: median absolute deviation (MAD), interquartile range (IQR), and IQR/3, with two tuning constant values (1.345 and 1.5). The numerical simulation results showed that during contamination with 10% and 20% additive outliers, the IQR/3 outperformed the MAD and IQR. Our findings also showed that IQR/3 is a potentially more robust dispersion measurement in Huber's weight. The tuning constant of 1.5 revealed a decrease in resistance to outliers and increased efficiency. The proposed IQR/3 model with a constant tuning value (h) of 1.5 outperformed the AR(1)-GARCH(1,2) model while minimising the effect of additive outliers.
... Then to assess the impact government intervention has on prices, we fit an autoregressive integrated moving average (ARIMA) model to the data with exogenous regressors and indicators of 'events.' This modeling approach is known as transfer function modeling or intervention analysis (Box and Tiao 1975;Brockwell and Davis 1991;Chen and Liu 1993). The events in which we are interested are government attempts to intervene or outright regulate the cryptocurrency markets. ...
... Identifying these change points and comparing them to events or interventions -news, political events, regulatory actions -we can estimate the effect of any such action. To study the outlier events, we used the "tsoutlier" package in R (Chen and Liu 1993) to identify the timing and type of events. ...
Cryptocurrencies have gained popularity over the past five to six years. Most recently, events like the FTX bankruptcy fueled the interest in regulation. Moreover, it is possible that the FTX event disrupting the cryptocurrency market was a factor in Silicon Valley Bank's failure. While several countries consider regulation, from soft regulation, like Japan, to more rigid standards, like the total ban in China, we study the effect of other news or events on cryptocurrency prices. This paper looks at historical closing prices for Bitcoin, the largest of the cryptocurrencies, and how prices react to various events. Then we focus on modeling the time series considering an 'event,' China's ban on cryptocurrency exchanges, using intervention analysis. We find that intervention analysis provides a reliable approach to quantifying the impact regulation may have on cryptocurrency pricing.
... In the same year, Chang and Chen (1988) introduced two new types of abnormal fluctuations based on Tsay, namely additive abnormal values (AO) and innovative abnormal values (IO). Subsequently, Chen and Liu (1993) introduced temporary change (TC) and horizontal displacement (HD) abnormal fluctuations into time series and discussed their roles in modeling and estimating time series parameters. They further demonstrate that the sensitivity of the prediction interval is mainly caused by AO, and discuss the prediction problem when outliers appear near abnormal fluctuations or at the prediction starting point. ...
In the analysis of agricultural product price time series, the detection of abnormal fluctuations is the primary task. Accurately judging the abnormal fluctuations of agricultural product prices can help farmers avoid potential economic losses in a timely manner and improve the circulation efficiency of agricultural products. This paper introduces a convolutional neural network (CNN) classification model based on time series images (TSI), and identifies abnormal fluctuations in agricultural product prices using improved standard deviation–slope judgment. First, a standard deviation–slope (SDS) time series abnormal fluctuation criterion is proposed. Second, the Markov Transfer Field (MTF) method is used to convert the sparse one-dimensional time series of agricultural product prices into a two-dimensional dense image. Third, the CNN model is used to automatically extract features from time series images containing abnormal fluctuations, and they are divided into two categories: “normal” and “abnormal”; Finally, the performance of the proposed model was evaluated using China’s corn and wheat price dataset. Comparing with other abnormal fluctuation judgment methods, the accuracy of the proposed algorithm is about 20% higher on average. This confirms the applicability of the standard deviation–slope time series Image-Resnet-34 (SDS-TSI-Resnet34) model in practical scenarios. At the end of the paper, some feasible suggestions for the efficient development of agricultural economy are proposed based on the abnormal fluctuation judgment method.
... To identify potential associations between the start of the COVID-19 pandemic in 2020 and changes in antipsychotic drug prescribing, we conducted a prespecified outlier analysis in the seasonal autoregressive integrated moving average models based on the method described by Chen and Liu. 23 We identified additive outliers, level shifts, or transitory changes using the R package tsoutlier, 24 with timepoints identified as outliers if the t-statistic exceeded 3·5. We presented demographic data with absolute values and percentages and medians with IQRs. ...
Background:
Concerns have been raised that antipsychotic drug prescribing, which has been associated with increased mortality in people with dementia, might have increased during the COVID-19 pandemic due to social restrictions imposed to limit the spread of SARS-CoV-2. We used multisource, routinely collected health-care data from Wales, UK to investigate prescribing and mortality variations in people with dementia before and during the COVID-19 pandemic.
Methods:
In this retrospective cohort study, we used individual-level, anonymised, population-scale linked health data to identify adults aged 60 years and older with a diagnosis of dementia in Wales, UK. We used the CVD-COVID-UK initiative to access Welsh routinely collected electronic health record data from the Secure Anonymised Information Linkage (SAIL) Databank. Patients who were alive and registered with a SAIL general practice on Jan 1, 2016, and who received a dementia diagnosis before the age of 60 years and before or during the study period were included. We explored antipsychotic drug prescribing rate changes over 67 months, between Jan 1, 2016, and Aug 1, 2021, overall and stratified by age and dementia subtype. We used time-series analyses to examine all-cause and myocardial infarction and stroke mortality over the study period and identified the leading causes of death in people with dementia between Jan 1, 2020, and Aug 1, 2021.
Findings:
Of 3 106 690 participants in SAIL between Jan 1, 2016 and Aug 1, 2021, 57 396 people (35 148 [61·2%] women and 22 248 [38·8%] men) met inclusion criteria for this study and contributed 101 428 person-years of follow-up. Of the 57 396 people with dementia, 11 929 (20·8%) were prescribed an antipsychotic drug at any point during follow-up. Accounting for seasonality, antipsychotic drug prescribing increased during the second half of 2019 and throughout 2020. However, the absolute difference in prescribing rates was small, ranging from 1253 prescriptions per 10 000 person-months in March, 2019, to 1305 per 10 000 person-months in September, 2020. All-cause mortality and stroke mortality increased throughout 2020, while myocardial infarction mortality declined. From Jan 1, 2020, to Aug 1, 2021, 1286 (17·1%) of 7508 participants who died had COVID-19 recorded as the underlying cause of death.
Interpretation:
During the COVID-19 pandemic, antipsychotic drug prescribing in people with dementia in the UK increased slightly; however, it is unlikely that this was solely related to the pandemic and this increase was unlikely to be a major factor in the substantial increase in mortality during 2020. The long-term increase in antipsychotic drug prescribing in younger people and in those with Alzheimer's disease warrants further investigation using resources with access to more granular clinical data. Although deprescribing antipsychotic medications remains an essential aspect of dementia care, the results of this study suggest that changes in prescribing and deprescribing practices as a result of the COVID-19 pandemic are not required.
Funding:
British Heart Foundation (via the British Heart Foundation Data Science Centre led by Health Data Research UK), and the Scottish Neurological Research Fund.
... As mentioned by 27 To overcome the effect of an innovative outlier, researchers, for example, Huber, have suggested using different types of measures instead of regular mean and variance as the basis for modelling the time series. Such measures were next to be discussed. ...
The unstable and uncertain nature of natural rubber prices makes them highly volatile and prone to outliers, which can have a significant impact on both modeling and forecasting. To tackle this issue, the author recommends a hybrid model that combines the autoregressive (AR) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models. The model utilizes the Huber weighting function to ensure the forecast value of rubber prices remains sustainable even in the presence of outliers. The study aims to develop a sustainable model and forecast daily prices for a 12-day period by analyzing 2683 daily price data from Standard Malaysian Rubber Grade 20 (SMR 20) in Malaysia. The analysis incorporates two dispersion measurements (IQR/3 and Sn) and three levels of IO contamination 0%, 10%, and 20%. The results indicate that using the Huber weighting function with the IQR/3 measurement to build the AR(1)-GARCH(2,1) model leads to better sustainability. These findings have the potential to enhance the GARCH model by modifying the weighting function of the M-estimator
... Four types of outliers are proposed in the literature on univariate time series: additive outliers, innovation outliers, level shifts, and temporal changes. Additive outliers are quite common in practical problems and are more dangerous than the other outlier types in Gaussian and Non-Gaussian processes (Chen & Liu, 1993). For example, in the standard structure of Box-Jenkins models, Ledolter (1989) showed that the predictions in integrated autoregressive moving average (ARMA) models are quite sensitive to additive outliers. ...
M-regression and quantile methods have been suggested to estimate generalized autoregressive conditionally heteroscedastic (GARCH) models. In this paper, we propose an M-quantile approach, which combines quantile and M-regression to obtain a robust estimator of the conditional volatility when the data have abrupt observations or heavy-tailed distributions. Monte Carlo experiments are conducted to show that the M-quantile approach is more resistant against additive outliers than M-regression and quantile methods. The usefulness of the method is illustrated on two financial datasets.
... Collectively, these records suggest that the seasonal precipitation and temperature cycles are in phase with one another, with a wet and warm season (December-April) followed by a colder and drier season (May-November). An outlier analysis was run on the monthly cumulative precipitation data (Chen and Liu, 1993) to capture anomalously high months of precipitation within the timespan over which the snails were collected (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). This revealed four anomalously high precipitation months in Moue ( Here these months of very high precipitation did not obviously match with any records of historical tropical storms in the region from the International Best Track Archive for Climate Stewardship (IBTrACS) database, suggesting that sources of high precipitation months can be various in the region, and not necessarily related to extreme punctual events. ...
The stable oxygen (δ18Oshell) and carbon (δ13Cshell) isotope ratios retrieved from the carbonate shell of terrestrial gastropods can be used as an environmental proxy and are thought to reflect dietary composition and ambient climatic conditions (e.g. precipitation amount, humidity, temperature). Here, we generate high-resolution isotopic profiles of nine modern land snails of the genus Placostylus, collected from two locations in New Caledonia and one location in New Zealand. We found that snails from New Zealand had, on average, higher δ18Oshell values than their counterparts in New Caledonia, which surprisingly runs counter to the expected relationship based on the isotopic composition of rainwater between these two regions. Specimens from New Caledonia exhibit ephemeral decreases in their δ18Oshell values, which could be linked to extreme precipitation events in this region, while snails from New Zealand have less variation in their δ18Oshell values. Snails from New Zealand had, on average, slightly higher δ13Cshell than their counterparts in New Caledonia, but a large difference in carbon isotopes was sometimes observed between snails collected at the same location. Most snails exhibit a temporal trend in their δ13Cshell values, indicating potential shifts in diet through to maturity.
Purpose:
To evaluate if changes in preterm birth (PTB, <37 weeks of gestation) incidence differed between non-Hispanic (NH) Black and NH white births following the July 1995 Chicago heat wave-among the most severe US heat waves since 1950.
Methods:
We used an ecologic study design. We obtained birth data from January 1990-December 1996 from the National Vital Statistics File to calculate the mean monthly PTB incidence in Chicago's Cook County, Illinois. Births between July 1995-February 1996 were potentially exposed to the heat wave in utero. We generated time series models for NH Black and NH white births, which incorporated synthetic controls of Cook County based on unexposed counties. We ran a secondary analysis considering socioeconomic status (SES).
Results:
From 1990-1996, the mean monthly PTB incidence among NH Black births was 18.6% compared to 7.8% among NH white births. The mean monthly PTB incidence among NH Black births from August 1995-January 1996 was 16.7% higher than expected (3 additional PTBs per 100 live births per month [95% CI: 1, 5]). A similar increase occurred among low-SES NH Black births. No increase appeared among NH white births.
Conclusions:
Severe heat waves may increase racial disparities in PTB incidence.
Outliers in time series can be regarded as being generated by dynamic intervention models at unknown time points. Two special cases, innovational outlier (IO) and additive outlier (AO), are studied in this article. The likelihood ratio criteria for testing the existence of outliers of both types, and the criteria for distinguishing between them are derived. An iterative procedure is proposed for detecting IO and AO in practice and for estimating the time series parameters in autoregressive-integrated-moving-average models in the presence of outliers. The powers of the procedure in detecting outliers are investigated by simulation experiments. The performance of the proposed procedure for estimating the autoregressive coefficient of a simple AR(l) model compares favorably with robust estimation procedures proposed in the literature. Two real examples are presented.
Two models are considered for outliers and their effects in time series. Likelihood ratio and approximate likelihood ratio criteria are derived for these models and the power functions are compared with that of the approach generally applied in the past.
Time series analysis, particularly intervention analysis, is commonly employed in impact studies of environmental data. Environmental time series are susceptible to exogenous variations and often contain various types of outliers. Outliers, depending upon the time of their occurrences and nature, can have substantial impact on the estimates of intervention effects and their test statistics. Hence, outlier detection and adjustment should be an indispensable part of an intervention analysis. In this paper, an iterative procedure for the joint estimation of model parameters and outlier effects is employed with the intervention analysis. We find that this joint estimation procedure not only produces more reliable estimates of intervention effects, but also provides information on outliers, which is valuable in many respects. As a special case of outlier adjustment, this joint estimation procedure can also be used to estimate the values of missing data in a time series. Two data sets are used to illustrate the application of intervention analysis with outlier adjustment. We find the results under the new approach more meaningful and informative than those of traditional analyses. A third data set is used to illustrate time series modeling with missing data and outliers. Outlier analysis is not only useful in providing information for retroactive investigation of unusual observations in a time series, but more importantly, it can be used in conjunction with data collection and thus improve the quality of the data.
This article discusses the effect of interventions on a given response variable in the presence of dependent noise structure. Difference equation models are employed to represent the possible dynamic characteristics of both the interventions and the noise. Some properties of the maximum likelihood estimators of parameters measuring level changes are discussed. Two applications, one dealing with the photochemical smog data in Los Angeles and the other with changes in the consumer price index, are presented.
Two models, the aberrant innovation model and the aberrant observation model, are considered to characterize outliers in time
series. The approach adopted here allows for a small probability α that any given observation is ‘bad’ and in this set-up
the inference about the parameters of an autoregressive model is considered.
This paper examines the effect of correlation of observations on estimators of a mean which are designed to guard against the possibility of spurious observations (that is, observations generated in a manner not intended). The mean squared error, premium and protection of these estimators are evaluated and discussed for some specific correlation structures.
The effect of an additive outlier upon the accuracy of forecasts derived from extrapolative methods is investigated. It is demonstrated that an outlier affects not only the accuracy of the forecasts at the time of occurrence but also subsequent forecasts. Methods to adjust for additive outliers are discussed. The results of the paper are illustrated with two examples.
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.