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978-1-5090-6126-6/16/$31.00 2016 IEEE 426

A SURVEY OF RESEARCH ON ANOMALY DETECTION FOR TIME SERIES

HU-SHENG WU

Materiel Engineering College, Armed Police Force Engineering University, Xi'an 710086, China

E-MAIL: wuhusheng0421@163.com

Abstract:

Time series is an important class of temporal data objects

and it can be easily obtained from scientific and financial

applications, and anomaly detection for time series is

becoming a hot research topic recently. This survey tries to

provide a structured and comprehensive overview of the

research on anomaly detection. In this paper, we have

discussed the definition of anomaly and grouped existing

techniques into different categories based on the underlying

approach adopted by each technique. And for each category,

we identify the advantages and disadvantages of the

techniques in that category. Then, we provide a briefly

discussion on the representative methods recently.

Furthermore, we also point out some key issues about

multivariate time series anomaly. Finally, some suggestions

about anomaly detection are discussed and future research

trends are also summarized, which is hopefully beneficial to

the researchers of time series and other relative domains.

Keywords:

Time series; anomaly detection; big data; data mining;

multivariate time series

1. Introduction

Date have proliferated over with the development of

information technology. According to the latest research of

University of Southern California in 2016, since 1980s, the

scale of data has increased sharply and doubled every year

or even a few months. All of the global data information

has reached 295EB until 2007, 1.8ZB until 2011, and will

reach more than 40ZB in 2020. Therefore, big data era has

arrived. And how to abstract potential information from the

plentiful data needs to be solved urgently [1]. A big part of

these data is time series. The so-called time series is a

sequence records according with the chronological order.

Time series is so widely applied in many fields, such as

military, economy and scientific observations that it has

aroused great attention concern from researchers.

For normal time series data, although the number of

abnormal data is very small, it does not mean that the

abnormal data is not important. On the contrary, some

important data may be hided behind these few abnormal

data. In medical field, the abnormal heart beat should be

detected so that doctors can find the disease in time by the

ECG observation. In addition, the anomaly detection of

time series can be widely used in the engine condition

monitoring, network intrusion detection, anti-money

laundering, network public opinion monitoring, credit card

fraud, stock market analysis, improper tax behavior

monitoring, major construction projects inspection, natural

disaster analysis and so on. Obviously, the study of

abnormal detection of time series has important theoretical

value and practical significance.

2. Definition of time series anomaly detection

Time series widely exist in various large financial,

medical, engineering and social science database. There are

two features between time series and other data types.

Firstly, the time attribute, the records of each variable must

have time dimension and should be arranged in

chronological order, and some date types like market basket

data do not have such attributes. Secondly, the sequence

attribute, the record values are a continuous one in a certain

period of time and in certain laws. Time series can be

divided into univariate time series and multivariate time

series according to the number of variables, the specific

definition is as follows:

Definition 1 Time Series A sequence records

according with the chronological order

 

(1), (2), , ( ), , ( )

i i i i

S v v v t v n …… ……

is defined as the time series.

In which t (t=1,2,…,n)

is defined as time,

(

1,2, ,im

)

is defined as variable.

()

is defined as the record of the

variable

on time

. When m=1,

is defined as

univariate time series (UTS). When m>1,

is defined as

multivariate time series (MTS).

At the same time, in order to make the anomaly

detection of MTS meaningful, MTS needs to meet the three

requirements as follows: (1) For the MTS data set, the

variable dimension of each sequence is identical, and the

variables which have the same meaning are one-to-one

match. (2) For one MTS sample, the recording time of each

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