Time Series Data Cleaning: A Survey <s> A. PROBLEM STATEMENT <s> 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. <s> BIB001 </s> Time Series Data Cleaning: A Survey <s> A. PROBLEM STATEMENT <s> Data integrated from multiple sources may contain inconsistencies that violate integrity constraints. The constraint repair problem attempts to find "low cost" changes that, when applied, will cause the constraints to be satisfied. While in most previous work repair cost is stated in terms of tuple insertions and deletions, we follow recent work to define a database repair as a set of value modifications. In this context, we introduce a novel cost framework that allows for the application of techniques from record-linkage to the search for good repairs. We prove that finding minimal-cost repairs in this model is NP-complete in the size of the database, and introduce an approach to heuristic repair-construction based on equivalence classes of attribute values. Following this approach, we define two greedy algorithms. While these simple algorithms take time cubic in the size of the database, we develop optimizations inspired by algorithms for duplicate-record detection that greatly improve scalability. We evaluate our framework and algorithms on synthetic and real data, and show that our proposed optimizations greatly improve performance at little or no cost in repair quality. <s> BIB002 </s> Time Series Data Cleaning: A Survey <s> A. PROBLEM STATEMENT <s> In the statistics community, outlier detection for time series data has been studied for decades. Recently, with advances in hardware and software technology, there has been a large body of work on temporal outlier detection from a computational perspective within the computer science community. In particular, advances in hardware technology have enabled the availability of various forms of temporal data collection mechanisms, and advances in software technology have enabled a variety of data management mechanisms. This has fueled the growth of different kinds of data sets such as data streams, spatio-temporal data, distributed streams, temporal networks, and time series data, generated by a multitude of applications. There arises a need for an organized and detailed study of the work done in the area of outlier detection with respect to such temporal datasets. In this survey, we provide a comprehensive and structured overview of a large set of interesting outlier definitions for various forms of temporal data, novel techniques, and application scenarios in which specific definitions and techniques have been widely used. <s> BIB003
In this study, enlightened by related research BIB003 , BIB001 and  on the classification of time series error types, we summarize the common error in time series into three categories, namely, single point big error, single point small error and continuous errors. This article takes the stock price of a stock for 30 consecutive trading days as an example. As shown in Figure 1 , the characteristics of these three types of errors are described in detail. The red line in the figure indicates the true price of the stock in 30 consecutive trading days, and the blue line indicates the price of the stock crawled by a website. For various reasons, the observed value may not be the same as the actual value. It can be seen that in the four consecutive trading days of 8-11, the observed values are all 0, and the true values are 1.3, 1.2, 1.1 and 1.15, respectively, on the 20th trading day, the observed value is 2.4 and the true value is 1.3, on the 25th trading day, the observed value is 1 and the true value is 1.3. (1) Continuous errors. The so-called continuous errors, that is, in the time series, errors occur in several consecutive time points. Specifically, continuous errors can continue to be subdivided into several types BIB001 , but no longer detailed here. The observed values from the 8th to 11th trading days in Figure 1 are all 0, that is, continuous errors occur here. Continuous errors are common in real life. For instance, when someone is holding a smartphone and walking on the road, nearby tall buildings may have a lasting impact on the collected GPS information. Besides, system errors can also cause continuous errors. (2) A single big error. A single point error is an error that occurs discontinuously in a time series and only occurs on a single data point at intervals. A big error means that the observed value of the data point is far from the true value. Remarkably, the size of the error is relative and closely related to the real situation of the data set. As shown on the 20th trading day in Figure 1 , the observed value differs from the true value by 1.1. Compared with the 25th trading day when the observed value differs from the true value by 0.3, the error of this data point is large, so this data point error is a single big error. The single point big error is also very common in daily life. For instance, the data of motor vehicle oil level recorded by cursors may cause a single big error when bumping on the road. (3) A single small error. Similar to a single point big error, that is, errors do not occur consecutively, only on a single data point at intervals. When the observed value of the data point differs from the true value by a small distance, on the 25th trading day in Figure 1 , it is a single point small error. As stated in BIB002 , the rationale behind single-point small errors is that people or systems always try to minimize possible errors. For instance, people may only have some small omissions when copying files. (4) Translational error. As shown in Figure 2 , where x axis represents time and y axis represents the value of the corresponding time, the red line represents true value, and the blue line represents error value after the translation, the solution to this type of error is not as much as mentioned above. Ignoring time series errors often results in unpredictable consequences for a series of applications such as query analysis. Thereby, time series cleaning algorithms are very important for mining the potential value of data. This paper reviews the cleaning algorithm and anomaly detection algorithm of time series data. By summarizing the existing methods, a reference or guidance is given to scholars interested in time series data cleaning and based on this, the possible challenges and future work of time series cleaning topics are discussed.