Subject index

  • Absolutely summable, 8, 12, 302, 304, 305
  • Adjoint matrix, 12, 29
  • Aggregation
  • Air pollution, 120–137
  • Amplitude spectrum, 307
  • ARCH models, 203
  • Autoregressive representation of vector processes, 7–9
  • Bandwidth
  • Bartlett’s approximation, 241, 242
  • Cauchy–Schwarz inequality, 4
  • Cholesky decomposition, 315, 317, 318, 333, 334, 337
  • Clustering
    • hierarchical clustering, 460, 463
    • model‐based cluster approach, 443
    • nonhierarchical clustering, 460, 463
    • partitioning around mediods (PAM), 463, 465
    • total within sum of square (TWSS), 461, 463
  • Cointegration, 25
  • Cointegration in vector time series
    • error‐correction representation, 25
    • the trace test, 25
  • Conditional covariance matrix, 204, 207
  • Correlation matrix function
    • partial, 3–7, 24
    • sample, 24, 32
  • Co‐spectrum, 306, 311
  • Covariance matrix function, 12, 23, 304, 320
  • Cross‐spectrum, 306, 312
  • Data
    • body weight of rats (WW7a), 238, 509
    • daily log‐returns of DJIA 30 stocks from 7/1/2006 to 6/30/2010 (WW6c), 225, 509
    • daily log‐returns of SP500, BAC, JPM, and C from 1/4/1994 to 12/30/2005 (WW6b), 222, 509
    • daily mortality and air pollutants, ozone and carbon monoxide, from five California cities from 4/13/1999 to 9/14/1999 (WW3b), 120, 509
    • daily stock returns from the first set of ten stocks from 8/2/2016 to 12/30/2016 (WW4a), 145, 509
    • daily stock returns from the second set of ten stocks from 8/2/2016 to 12/30/2016 (WW5), 166, 173, 509
    • monthly total of vehicular theft data of Philadelphia from 1/2006 to 12/2014 (WW8a), 274, 509
    • monthly unemployment rates for ten states in U. S. from 1/1976 to 8/2010 (WW2c), 58, 509
    • new classified U.S. monthly retail sales from 6/2009 to 11/2016 (WW2b), 36, 320, 325, 327, 509
    • the oral condition of neck cancer patients in 1999 from Mid‐Michigan Medical Center (WW7b), 255, 509
    • U.S. macroeconomic indicators from quarter 1 of 1959 to quarter 4 of 2007 (WW10), 452, 510
    • U.S. monthly consumer price index (CPI) from five different sectors, energy, apparel, commodities, housing, and gas from 1/1986 to 12/2014 in Greater New York City (WW4b), 152, 509
    • U.S. monthly retail sales from 6/2009 to 11/2016 (WW2a), 32, 509
    • U.S. non‐seasonally adjusted labor force count for the 48 contiguous states and Washington D.C. from 1976 to 2014 (WW8b), 279, 509
    • U.S. weekly interest over time on six exercise items from 4/15/2012 to 4/7/2017 (WW6a), 215, 509
    • U.S. yearly retail sales and GDP, JIA, and CPI from 1992 to 2015 (WW3a), 109‐120, 509
    • U.S. yearly sexually transmitted disease morbidity rates from 1984 to 2014 (WW8c), 183, 281, 457, 510
    • weekly log returns of DJIA, NASDQ, and S&P500 from 4/1990 to 12/2011 (WW9), 338, 510
  • Dendrogram, 460, 463–465
  • Diagnostic checking
    • of vector time series models, 24–25
  • Differencing, 21, 36, 47, 145, 152, 265, 274, 329, 452
  • Dimension reduction
    • contemporal aggregation, 437
    • factor analysis, 443–444
    • hierarchical vector autoregressive (HVAR) method, 440–441
    • in high dimensional multivariate time series, 437–505
    • lag‐weighted Lasso method, 440
    • lasso method, 439–440
    • model‐based cluster method, 443
    • multivariate time series, 437
    • principal component analysis, 209
    • regularization methods, 439–441
    • space‐time AR (STAR) model, 442–443
  • Discrete Prolate Spheroidal Sequences (DPSS), 313, 314
  • Distance
    • Canberra distance, 460
    • Euclidian distance, 460
    • Kullback–Leibler (KL) distance, 460
    • Minkowski distance, 460
  • Factor analysis of multivariate time series
    • Bartlett‐corrected test statistic, 172
    • common factors, 163
    • estimation, 165–175
    • ith common factor, 171, 173, 177
    • ith communality, 165, 169
    • loading matrix, 164
    • maximum likelihood method, 169–173
    • orthogonal factor model, 163–165
    • principal component method, 165–166
    • specific factors, 163
  • Factor models with observable factors
    • dynamic factor models, 183
    • forecast equation, 183
  • Factor rotation
    • oblique rotation, 176–177
    • orthogonal rotation, 176
    • varimax, 177
  • Factor scores
    • forecast, 181, 183
    • with observable factors, 181–183
  • Forecast
  • Fourier frequencies, 302, 303, 309, 312, 320, 336, 337
  • Gain function, 307, 311, 312
  • GARCH models, 2, 203–234
  • Generalized least squares (GLS) estimate, 106, 108–109, 114
  • Generalized space‐time autoregressive integrated moving average (GSTARIMA) models, 272
  • GO‐GARCH models
    • estimation, 210–213
    • two step estimation, 210–211
    • weighted scatter estimation, 211–213
  • Granger causality, 18
  • GSTARIMA models, 272
  • Hermitian matrix, 306, 318
  • Heteroscedasticity, 203
  • Hierarchical clustering
    • average linkage, 461
    • complete linkage, 461
    • median linkage, 461
    • single linkage, 461
  • High dimensional problem
    • contemporal aggregation, 437, 466
    • factor analysis, 443–444
    • hierarchical vector autoregressive (HVAR) method, 440–441
    • lag‐weighted lasso method, 440
    • lasso method, 439–440
    • model‐based cluster method, 443
    • multivariate time series, 437, 438
    • regularization methods, 439–441
    • space‐time AR (STAR) model, 442–443
  • Identification of vector time series models, 21–22
  • Information criterion
  • Invertible, 8, 11–14, 16, 19, 20, 27, 209, 210, 225
  • Least squares estimation, 114, 116, 122
  • Log‐likelihood function, 24
  • Longitudinal data, 238, 256
  • MATLAB, 8, 25, 70, 114, 169, 176, 324, 349, 362
  • MINITAB, 169, 176
  • Model‐based cluster approach, 443
  • Moving average representation of vector processes, 7, 11, 15, 17, 23
  • Multivariate analysis of variance (MANOVA), 239–243
  • Multivariate GARCH models
    • BEKK models, 207–208
    • constant conditional correlation (CCC) models, 206
    • DVEC models, 204–206
    • dynamic conditional correlation (DCC) models, 218
    • estimation, 210–213
    • factor models, 208–209
    • GO‐GARCH models, 209
    • O‐GARCH model, 209
    • representations, 204–209
    • two step estimation method, 210–211
    • VEC models, 204–206
    • weighted scatter estimation (WSE) method, 211–213
  • Multivariate multiple time series regression model
    • estimation, 108–114
    • forecast, 115, 116
    • generalized least squares estimator, 106
    • GLS procedure, 108–109
    • VARX models, 114, 115
  • Multivariate normal distribution, 7, 106, 108, 113, 169, 182
  • Multivariate spectral analysis of time series
    • spectral representations, 304–309
  • Multivariate time series analysis
    • issues, 2
  • Multivariate time series outlier
    • multivariate additive outlier (MAO), 28
    • multivariate innovational outlier (MIO), 28
    • multivariate level shift (MLS), 28
    • multivariate temporary change (MTC), 28
  • Nonhierarchical clustering
  • Nonstationary vector autoregressive moving average processes, 21
  • O‐GARCH model, 209–213, 225
  • Ordinary least squares (OLS), 109, 111–113
  • Orthogonal factor model, 163–165
  • Outliers detection
    • likelihood ratio test (LRT), 31
  • Partial autoregression matrix, 6
  • Partial correlation matrix function
  • Partial lag autocorrelation matrix, 36
  • PCA (principal component analysis), 139–142, 145, 147–157, 168–170, 176, 183–188, 209–212
  • Phase spectrum, 306, 307, 311
  • Positive definite matrix, 7, 12, 265, 314, 442
  • Positive semidefinite matrix, 4, 5, 306, 315
  • Principal component analysis (PCA) of multivariate time series
    • based on sample correlation matrix, 154–157
    • based on sample covariance matrix, 153–154
    • implications, 141–142
    • population principal component analysis, 139–141
    • sample principal components, 142–145
  • Projection pursuit, 27, 29–32, 58, 59
  • Projects, 9, 29, 100–101, 137, 160–161, 200–201, 234, 258, 298, 434–435, 505
  • Quadrature spectrum, 306, 311
  • References, 9, 101, 137, 161, 201, 234, 258, 298, 435, 506
  • Regularization methods
    • hierarchical vector autoregressive (HVAR) method, 440–441
    • lag‐weighted lasso method, 440
    • lasso method, 439–440
  • Repeated measurements
    • AR(1) structure, 249
    • ARMA(1,1) structure, 250
    • fixed effects model, 243–247
    • generalization, 254–255
    • heterogeneous AR(1) structure, 250
    • heterogeneous Toeplitz structure, 249
    • identical and independent structure, 247–248
    • independent but non‐identical structure, 248
    • Interaction, 238, 243, 245, 246, 250, 252, 256
    • multivariate analysis of variance (MANOVA), 239–243
      • nested random effects model, 253–254
      • random effects and mixed effects models, 252–253
      • repeated measure analysis of variance, 239–243
    • some common variance‐covariance structures, 247–250
    • structure of common symmetry, 248
    • structure of heterogeneous common symmetry, 248–249
    • Toeplitz structure, 249
    • Treatment group, 237, 241–244, 250
    • Treatment sum of squares, 239, 240
      • unstructured matrix, 247
  • Representation of vector processes
    • autoregressive representation, 7–8
    • moving average representation, 7
  • Sample moments of a vector time series
    • sample correlation matrix function, 23–24
    • sample covariance matrix, 22–23
    • sample mean vector, 22
  • SAS, 8, 25, 43, 44, 47, 58, 113, 115, 116, 118, 122, 129, 169, 176, 218, 242, 243, 251, 252, 255, 256
  • Scree plot, 149, 169
  • Seasonal GSTARIMA model, 272
  • Seasonal STARIMA model, 262–271
  • Seasonal vector time series model
    • nonstationary seasonal vector time series, 26
  • Similarity measures
    • average linkage, 461
    • complete linkage, 461
    • Kullback–Leibler (KL) distance, 460
    • median linkage, 461
    • single linkage, 461
  • Slepian sequences or tapers, 313
  • Smoothed spectrum, 304, 309–313
  • Software code
  • Space‐time series models
    • generalized space‐time autoregressive integrated moving average (GSTARIMA) models, 272
    • space‐time autoregressive integrated moving average (STARIMA) models, 262
    • STARMA models, 266
  • Spatial series, 261, 262
  • Spatial weighting matrix, 262–264
  • Spectral density matrix estimation
    • Bayesian method, 316–317, 325–326
    • multitaper smoothing, 313–314
    • penalized Whittle likelihood, 317–318
    • sample spectrum, 320–325
    • smoothed spectrum matrix, 309–313
    • smoothing spline, 315–316
    • VARMA spectral estimation, 318–320
  • Spectral density matrix function, 305, 306
  • Spectral distribution function, 302, 305
  • Spectral representations
    • of covariance matrix function, 304, 305
    • of multivariate time series processes, 304–309
  • Spectral window
    • Bartlett window, 304
    • Blackman‐Tukey window, 304
    • Daniell, 320
    • Parzen window, 304
    • Rectangular window, 304
  • Spectrum analysis of nonstationary vector time series, 329–337
  • Spectrum matrix
  • Spectrum representation of a nonstationary multivariate process
    • Bayesian methods, 336–337
    • piecewise vector autoregressive model, 334–336
    • smoothing spline ANOVA model, 333–334
    • time‐varying autoregressive model, 332–333
  • SPSS, 25, 169, 176
  • Spurious regression, 109
  • Squared coherency, 307, 311
  • Squared Mahalanobis distance, 212
  • Square summable, 15, 319
  • ST‐ACF and ST‐PACF, 267–271, 273, 279, 281, 284
  • STARIMA models
    • GSTARIMA models, 272
    • iterative model building of, 273
    • seasonal GSTARIMA model, 272
    • seasonal STARIMA model, 265–266
  • STARMA models, 266–267, 273, 279, 442, 443, 445
  • STAR model, 266, 268, 272, 438, 442–443, 445, 457, 484–486
  • STMA model
    • GSTMA model, 273
  • Systematic sampling, 466, 467
  • Temporal aggregation, 437, 466, 467
  • Temporal disaggregation, 467
  • Time series regression, 2, 105–137, 181
  • Toeplitz form, 255
  • Variance–covariance matrix, 4, 108, 109, 112, 113, 116, 124, 127, 142–144, 147, 153, 239, 243, 247, 253, 254, 271, 306, 310, 327, 438
  • VARMA model, 25, 27–29, 216–218, 225, 267, 273, 318, 437, 438, 443
  • VARMAX procedure, 116, 118, 122
  • VAR model, 25, 26, 114–115, 327, 329, 333–335, 439–441, 443–446
  • VARX model, 105, 114–121, 124, 127
  • Vector autoregressive moving average (VARMA) processes
  • Vector autoregressive (VAR) processes
  • Vector autoregressive representation, 8
  • Vector moving average (VMA) processes
  • Vector moving average representation, 7, 17, 23
  • Vector time series model building
    • diagnostic checking, 24–25
    • extended cross‐correlation matrices, 24
    • forecast, 24–25
    • identification, 21–22
    • parameter estimation, 24–25
    • sample correlation matrix function, 23–24
    • sample moments of a vector time series, 22–24
  • Vector time series models
    • vector autoregressive moving (VARMA) processes, 18–20
    • vector autoregressive (VAR) processes, 14–18
    • vector autoregressive representation of, 8
    • vector moving average (VMA) processes, 11–14
    • vector moving average representation of, 17, 23
  • Vector time series regression models, 105, 114–120
  • Vector white noise (VWN) process, 2, 7, 11, 14, 19, 114, 115, 118, 265, 318, 442
  • Volatility, 203–205, 208, 210, 223, 225
  • Volatility model, 204, 205, 210
  • Yule–Walker matrix equations, 16
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3.15.17.50