Analysis of big dependent data. (2021)

• Record Type: Book
• Further Information: Note: Daniel Peña, Ruey S. Tsay.
• Authors: Peña, Daniel, 1948-; Tsay, Ruey S, 1951-
• Contents: 1 Introduction to Big Dependent Data 1 1.1 Examples of Dependent Data 2 1.2 Stochastic Processes 11 1.2.1 Scalar Processes 11 1.2.1.1 Stationarity 12 1.2.1.2 White Noise Process 14 1.2.1.3 Conditional Distribution 14 1.2.2 Vector Processes 14 1.2.2.1 Vector White Noises 17 1.2.2.2 Invertibility 17 1.3 Sample Moments of Stationary Vector Process 18 1.3.1 Sample Mean 18 1.3.2 Sample Covariance and Correlation Matrices 19 1.3.3 Example 1.1 20 1.3.4 Example 1.2 23 1.4 Nonstationary Processes 23 1.5 Principal Component Analysis 26 1.5.1 Discussion 30 1.5.2 Properties of the Principal Components 30 1.5.3 Example 1.3 31 1.6 Effects of Serial Dependence 35 1.6.1 Example 1.4 37 1.7 Appendix 1: Some Matrix Theory 38 2 Linear Univariate Time Series 43 2.1 Visualizing a Large Set of Time Series 45 2.1.1 Dynamic Plots 45 2.1.2 Static Plots 51 2.1.3 Example 2.1 55 2.2 Stationary ARMA Models 56 2.2.1 The Autoregressive Process 58 2.2.1.1 Autocorrelation Functions 59 2.2.2 The Moving Average Process 60 2.2.3 The ARMA Process 62 2.2.4 Linear Combinations of ARMA Processes 63 2.2.5 Example 2.2 64 2.3 Spectral Analysis of Stationary Processes 65 2.3.1 Fitting Harmonic Functions to a Time Series 65 2.3.2 The Periodogram 67 2.3.3 The Spectral Density Function and its Estimation 70 2.3.4 Example 2.3 71 2.4 Integrated Processes 72 2.4.1 The Random Walk Process 72 2.4.2 ARIMA Models 74 2.4.3 Seasonal ARIMA Models 75 2.4.3.1 The Airline Model 77 2.4.4 Example 2.4 78 2.5 Structural and State Space Models 80 2.5.1 Structural Time Series Models 80 2.5.2 State-Space Models 81 2.5.3 The Kalman Filter 85 2.6 Forecasting with Linear Models 88 2.6.1 Computing Optimal Predictors 88 2.6.2 Variances of the Predictions 90 2.6.3 Measuring Predictability 91 2.7 Modeling a Set of Time Series 92 2.7.1 Data Transformation 93 2.7.2 Testing for White Noise 95 2.7.3 Determination of the Difference Order 95 2.7.4 Example 2.5 96 2.7.5 Model Identification 97 2.8 Estimation and Information Criteria 97 2.8.1 Conditional Likelihood 97 2.8.2 On-line Estimation 99 2.8.3 Maximum Likelihood Estimation 100 2.8.4 Model Selection 101 2.8.4.1 The Akaike Information Criterion 102 2.8.4.2 The BIC Criterion 103 2.8.4.3 Other Criteria 103 2.8.4.4 Cross-Validation 104 2.8.5 Example 2.6 104 2.9 Diagnostic Checking 107 2.9.1 Residual Plot 107 2.9.2 Portmanteau Test for Residual Serial Correlations 107 2.9.3 Homoscedastic Tests 109 2.9.4 Normality Tests 109 2.9.5 Checking for Deterministic Components 109 2.9.6 Example 2.7 110 2.10 Forecasting 111 2.10.1 Out-of-Sample Forecasts 111 2.10.2 Forecasting with Model Averaging 112 2.10.3 Forecasting with Shrinkage Estimators 113 2.10.4 Example 2.8 114 2.11 Appendix 2: Difference Equations 115 3 Analysis of Multivariate Time Series 125 3.1 Transfer Function Models 126 3.1.1 Single Input and Single Output 126 3.1.2 Example 3.1 131 3.1.3 Multiple Inputs and Multiple Outputs 132 3.2 Vector AR Models 133 3.2.1 Impulse Response Function 135 3.2.2 Some Special Cases 136 3.2.3 Estimation 137 3.2.4 Model Building 139 3.2.5 Prediction 141 3.2.6 Forecast Error Variance Decomposition 143 3.2.7 Example 3.2 144 3.3 Vector Moving-Average Models 152 3.3.1 Properties of VMA Models 153 3.3.2 VMA Modeling 153 3.4 Stationary VARMA Models 157 3.4.1 Are VAR Models Sufficient? 157 3.4.2 Properties of VARMA Models 158 3.4.3 Modeling VARMA Process 159 3.4.4 Use of VARMA Models 159 3.4.5 Example 3.4 160 3.5 Unit Roots and Co-integration 165 3.5.1 Spurious Regression 165 3.5.2 Linear Combinations of a Vector Process 166 3.5.3 Co-integration 167 3.5.4 Over-Differencing 167 3.6 Error-Correction Models 169 3.6.1 Co-integration Test 170 3.6.2 Example 3.5 171 4 Handling Heterogeneity in Many Time Series 179 4.1 Intervention Analysis 180 4.1.1 Intervention with Indicator Variables 182 4.1.2 Intervention with Step Functions 184 4.1.3 Intervention with General Exogenous Variables 185 4.1.4 Building an Intervention Model 185 4.1.5 Example 4.1 186 4.2 Estimation of Missing Values 187 4.2.1 Univariate Interpolation 187 4.2.2 Multivariate Interpolation 192 4.2.3 Example 4.2 193 4.3 Outliers in Vector Time Series 194 4.3.1 Multivariate Additive Outliers 195 4.3.1.1 Effects on Residuals and Estimation 195 4.3.2 Multivariate Level Shift or Structural Break 197 4.3.2.1 Effects on Residuals and Estimation 197 4.3.3 Other Types of Outliers 198 4.3.3.1 Multivariate Innovative Outliers 198 4.3.3.2 Transitory Change 199 4.3.3.3 Ramp Shift 200 4.3.4 Masking and Swamping 200 4.4 Univariate Outlier Detection 201 4.4.1 Other Procedures for Univariate Outlier Detection 203 4.4.2 Example 4.3 204 4.4.3 New Approaches to Outlier Detection 205 4.4.4 Example 4.4 207 4.4.5 Example 4.5 209 4.5 Multivariate Outliers Detection 210 4.5.1 VARMA Outlier Detection 210 4.5.2 Outlier Detection by Projections 212 4.5.3 A Projection Algorithm for Outliers Detection 214 4.5.4 The Nonstationary Case 215 4.5.5 Example 4.6 216 4.5.6 Example 4.7 217 4.6 Robust estimation 218 4.6.1 Example 4.8 220 4.7 Heterogeneity for Parameter Changes 221 4.7.1 Parameter Changes in Univariate Time Series 221 4.7.2 Covariance Changes in Multivariate Time Series 223 4.7.2.1 Detecting Multiple Covariance Changes 224 4.7.2.2 LR test: 225 4.8 Appendix 4: Cusum Algorithms 227 5 Clustering and Classification of Time Series 235 5.1 Distances and Dissimilarities 236 5.1.1 Distance Between Univariate Time Series 236 5.1.2 Dissimilarities Between Univariate Series 239 5.1.3 Example 5.1 241 5.1.4 Dissimilarities Based on Cross-Linear Dependency 247 5.1.5 Example 5.2 250 5.2 Hierarchical Clustering of Time Series 252 5.2.1 Criteria for Defining Distances Between Groups 253 5.2.2 The Dendrogram 254 5.2.3 Selecting the Number of Groups 254 5.2.3.1 The Height and Step Plots 254 5.2.3.2 Silhouette Statistic 255 5.2.3.3 The Gap Statistic 258 5.2.4 Example 5.3 260 5.3 Clustering by Variables 270 5.3.1 The K-means Algorithm 271 5.3.1.1 Number of Groups 273 5.3.2 Example 5.4 273 5.3.3 K-Mediods 277 5.3.4 Model Based Clustering by Variables 279 5.3.4.1 ML Estimation of the AR Mixture Model 280 5.3.4.2 The EM Algorithm 282 5.3.4.3 Estimation of Mixture of Multivariate Normals 283 5.3.4.4 Bayesian Estimation 284 5.3.4.5 Clustering with Structural Breaks 285 5.3.5 Example 5.5 286 5.3.6 Clustering by Projections 287 5.3.7 Example 5.6 290 5.4 Classification with Time Series 292 5.4.1 Classification Among a Set of Models 293 5.4.2 Checking the Classification Rule 295</p&
• Edition: 1st
• Publisher Details: Hoboken : John Wiley & Sons, Inc
• Publication Date: 2021
• Extent: 1 online resource
• Subjects: 005.7; Big data -- Mathematics; Time-series analysis; Data mining -- Statistical methods; Forecasting -- Statistical methods
• Languages: English
• ISBNs: 9781119417415; 9781119417392
• Related ISBNs: 9781119417385
• Notes: Note: Description based on CIP data; resource not viewed.
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