Time Series Data Cleaning: A Survey <s> B. EVALUATION CRITERIA <s> Preface 1 INTRODUCTION 1.1 Examples of Time Series 1.2 Objectives of Time Series Analysis 1.3 Some Simple Time Series Models 1.3.3 A General Approach to Time Series Modelling 1.4 Stationary Models and the Autocorrelation Function 1.4.1 The Sample Autocorrelation Function 1.4.2 A Model for the Lake Huron Data 1.5 Estimation and Elimination of Trend and Seasonal Components 1.5.1 Estimation and Elimination of Trend in the Absence of Seasonality 1.5.2 Estimation and Elimination of Both Trend and Seasonality 1.6 Testing the Estimated Noise Sequence 1.7 Problems 2 STATIONARY PROCESSES 2.1 Basic Properties 2.2 Linear Processes 2.3 Introduction to ARMA Processes 2.4 Properties of the Sample Mean and Autocorrelation Function 2.4.2 Estimation of $\gamma(\cdot)$ and $\rho(\cdot)$ 2.5 Forecasting Stationary Time Series 2.5.3 Prediction of a Stationary Process in Terms of Infinitely Many Past Values 2.6 The Wold Decomposition 1.7 Problems 3 ARMA MODELS 3.1 ARMA($p,q$) Processes 3.2 The ACF and PACF of an ARMA$(p,q)$ Process 3.2.1 Calculation of the ACVF 3.2.2 The Autocorrelation Function 3.2.3 The Partial Autocorrelation Function 3.3 Forecasting ARMA Processes 1.7 Problems 4 SPECTRAL ANALYSIS 4.1 Spectral Densities 4.2 The Periodogram 4.3 Time-Invariant Linear Filters 4.4 The Spectral Density of an ARMA Process 1.7 Problems 5 MODELLING AND PREDICTION WITH ARMA PROCESSES 5.1 Preliminary Estimation 5.1.1 Yule-Walker Estimation 5.1.3 The Innovations Algorithm 5.1.4 The Hannan-Rissanen Algorithm 5.2 Maximum Likelihood Estimation 5.3 Diagnostic Checking 5.3.1 The Graph of $\t=1,\ldots,n\ 5.3.2 The Sample ACF of the Residuals <s> BIB001 </s> Time Series Data Cleaning: A Survey <s> B. EVALUATION CRITERIA <s> To compensate for the inherent unreliability of RFID data streams, most RFID middleware systems employ a "smoothing filter", a sliding-window aggregate that interpolates for lost readings. In this paper, we propose SMURF, the first declarative, adaptive smoothing filter for RFID data cleaning. SMURF models the unreliability of RFID readings by viewing RFID streams as a statistical sample of tags in the physical world, and exploits techniques grounded in sampling theory to drive its cleaning processes. Through the use of tools such as binomial sampling and π-estimators, SMURF continuously adapts the smoothing window size in a principled manner to provide accurate RFID data to applications. <s> BIB002 </s> Time Series Data Cleaning: A Survey <s> B. EVALUATION CRITERIA <s> We introduce the notion of statistical distortion as an essential metric for measuring the effectiveness of data cleaning strategies. We use this metric to propose a widely applicable yet scalable experimental framework for evaluating data cleaning strategies along three dimensions: glitch improvement, statistical distortion and cost-related criteria. Existing metrics focus on glitch improvement and cost, but not on the statistical impact of data cleaning strategies. We illustrate our framework on real world data, with a comprehensive suite of experiments and analyses. <s> BIB003
The Root Mean Square (RMS) error BIB002 is used to evaluate the effectiveness of the cleaning algorithm. Let x denotes the sequence consisting of the true values of the time series, x denotes the sequence consisting of the observations after the error is added, and x denotes the sequence consisting of the repaired values after the cleaning. Here the RMS error BIB002 is represented as shown in equation BIB001 . The equation BIB001 measures the distance between the true value and the cleaned value. The smaller the RMS error, the better the cleaning effect. Other criteria include error distance between incorrect data and correct data, repaired distance between erroneous data and cleaned results (as shown in equation  referring to the minimum modification principle in data repairing). Dasu and Loh BIB003 propose a statistical distortion method to evaluate the quality of cleaning methods. The proposed method directly observes the numerical distribution in the data set and evaluates the quality according to the variation of the distribution caused by different cleaning methods.