Linear Time Series with MATLAB and OCTAVE

Description

Preface Software Installation References Contents 1 Quick Introduction to SSMMATLAB 1.1 ARIMA Models 1.2 Transfer Function Models 1.3 Univariate Structural Models 1.4 VARMA and VARMAX Models 1.5 Innovations State Space Models and Likelihood Evaluation Reference 2 Stationarity, VARMA, and ARIMA Models 2.1 Stationarity and VARMA Models 2.1.1 Simulation of VARMA Models 2.1.2 Sample Autocorrelations and PartialAutocorrelations 2.1.3 VAR Models 2.1.4 VAR Least Squares Estimation and Identification 2.1.5 Multiplicative VARMA Models: Preliminary Estimation and Model Simplification 2.1.6 Multiplicative VARMA Model Identification 2.1.7 Innovations State Space Models 2.1.8 Fixing of Parameters 2.1.9 Model Estimation Using the Kalman Filter 2.1.10 Missing Observations 2.1.11 Recursive Residuals and OLS Residuals 2.1.12 Forecasting 2.1.13 VARMA Models in Echelon Form 2.1.14 VARMA Models in State Space Echelon Form 2.1.15 Identification and Estimation of VARMA Models in Echelon Form 2.2 ARMA and ARIMA Models 2.2.1 State Space Form 2.2.2 Complex Seasonal Patterns 2.2.3 Model Identification 2.2.4 Model Estimation 2.2.5 Fixing of Parameters 2.2.6 Simplified ARIMA Estimation 2.2.7 Missing Values 2.2.8 Residuals 2.2.9 Residual Diagnostics 2.2.10 Tests for Residual Seasonality 2.2.11 ARIMA Forecasting 2.2.12 Forecasting Transformed Variables 2.2.13 Trading Day, Easter, and Leap Year Effects 2.2.14 Automatic Outlier Detection 2.2.15 Automatic ARIMA Model Identification and Estimation 2.2.16 Simplified Automatic ARIMA Specification and Estimation References 3 VARMAX and Transfer Function Models 3.1 VARMAX Models 3.1.1 State Space Models With Inputs 3.1.2 VARX Models 3.1.3 VARX Identification and Least SquaresEstimation 3.1.4 Identification and Estimation of VARMAX(p,q,r) Models 3.1.5 VARMAX Models in Echelon Form 3.1.6 VARMAX Models in State Space Echelon Form 3.1.7 Identification and Estimation of VARMAX Models in Echelon Form 3.1.8 VARMAX Estimation Using Regression Techniques: The Hannan–Rissanen Method 3.1.9 Model Simplification Using Stepwise Regression 3.1.10 The Conditional Method for VARMAXEstimation 3.1.11 The Exact ML Method for VARMAX Estimation 3.1.12 Forecasting VARMAX Models 3.2 Transfer Function Models 3.2.1 TF Model Specification and Estimation 3.2.2 TF Model Identification 3.2.3 Automatic TF Model Identificationand Estimation 3.2.4 Missing Values 3.2.5 Residual Diagnostics, Forecasting, and Outliers 3.2.6 Simplified Automatic TF Identification and Estimation References 4 Unobserved Components in Univariate Series 4.1 Structural Models 4.1.1 Model Specification and Estimation 4.1.2 Simplified Model Specification and Estimation 4.1.3 Model Identification 4.1.4 Missing Values 4.1.5 Residual Diagnostics and Forecasting 4.1.6 Smoothing 4.2 Structural Models with Complex Seasonal Patterns 4.3 Structural Models with Interventions 4.4 AMB Unobserved Components Models 4.4.1 Canonical Decomposition 4.4.2 Estimation of the Canonical Components 4.4.3 Estimation of Smooth Trends and Cycles 4.5 A Business Cycle Estimated with Both a Structural Model and the AMB Method References 5 Spectral Analysis 5.1 The Periodogram 5.2 The Cross Spectrum and Its Estimation 5.3 Autocovariances and Spectral Factorization References 6 Computing Echelon Forms by Polynomial Methods 6.1 VARMA and VARMAX Models 6.2 Time Invariant State Space Models Reference 7 Multivariate Structural Models 7.1 A Macroeconomic Model with a Common Cycle 7.2 Temporal Disaggregation 7.3 A Structural Model with Common Slopes 7.4 Estimation of the Business Cycle Using a Multivariate Band-Pass Filter References 8 Cointegrated VARMA Models 8.1 Parametrizations and Preliminary Estimation 8.2 Obtaining the Number of Unit Roots in the Model 8.3 Estimation Using the Kalman Filter 8.4 Forecasting References 9 Simulation of Common Univariate and Multivariate Models 10 The State Space Model 10.1 Kalman Filter and Likelihood Evaluation 10.2 Maximum Likelihood Estimation and Residual Diagnostics 10.2.1 Maximum Likelihood Estimation 10.2.2 Recursive and OLS Residuals 10.2.3 Residual Diagnostics 10.3 Forecasting and Smoothing 10.3.1 Forecasting 10.3.2 Smoothing 10.4 Square Root Covariance Filtering and Smoothing References 11 SSMMATLAB Examples by Subject 11.1 Automatic ARIMA and TF Identification and Estimation 11.1.1 arimatf1_d 11.1.2 arimatf2_d 11.1.3 arimatf3_d 11.1.4 arimatf4_d 11.1.5 arimatf5_d 11.1.6 arimatf6_d 11.1.7 arimatf7_d 11.1.8 arimatf8_d 11.1.9 arimatf9_d 11.1.10 arimatf10_d 11.2 TRAMO/SEATS Examples 11.2.1 TRAMO/SEATSex1_d.m 11.2.2 TRAMO/SEATSex2_d.m 11.3 BIC with Nonstationary Series 11.3.1 btozoneprof_d.m 11.4 Multiplicative VARMA Models 11.4.1 Tsayex61_d.m 11.4.2 Tsayex61ident_d.m 11.4.3 Tsayex61missing_d.m 11.4.4 armapq_d.m 11.4.5 armapqPQ_d.m 11.4.6 varmapqPQ_d.m 11.4.7 varmapqPQ2_d.m 11.5 Simulation 11.5.1 whitenoise_d.m 11.5.2 arimasimul_d.m 11.5.3 arimasimul2_d.m 11.5.4 arimasimul3_d.m 11.5.5 tfsimul_d.m 11.5.6 tfsimul2_d.m 11.5.7 usmsimul_d.m 11.5.8 varmasimul_d.m 11.5.9 varmasimul2_d.m 11.5.10 varmasimul3_d.m 11.5.11 varmaxsim_d.m 11.5.12 Tsayex11p23_d.m 11.6 Covariance Computation for a VARMA Model 11.6.1 TsayEx37_d.m 11.7 Canonical Decomposition 11.7.1 candec_d.m 11.7.2 USIPIcdstcl_d.m 11.7.3 TRAMO/SEATSex1_d.m 11.7.4 TRAMO/SEATSex2_d.m 11.8 Estimation of Smooth Trends and Cycles 11.8.1 btozone3cdstcl_d.m 11.8.2 USIPIcdstcl_d.m 11.8.3 unicycusgdp_hpb_d.m 11.8.4 mulcycuswcv_d.m 11.8.5 mulcycus2wcv_d.m 11.9 Multivariate Structural Models 11.9.1 usa4vcv_d.m 11.9.2 agtrimanssbs_d.m 11.9.3 viviusa_d.m 11.9.4 mulcycuswcv_d.m 11.9.5 mulcycus2wcv_d.m 11.10 Spectral Analysis 11.10.1 spec1_d.m 11.10.2 spec2_d.m 11.10.3 spec3_d.m 11.11 Covariance Factorization 11.11.1 CovFac_d.m 11.12 Structural Models 11.12.1 usmdk1_d.m 11.12.2 usmdk2_d.m 11.12.3 usmdk3_d.m 11.12.4 usmdk4_d.m 11.12.5 usmdk5_d.m 11.12.6 usm_d.m 11.12.7 usm2_d.m 11.12.8 usmc_d.m 11.12.9 usmc2_d.m 11.12.10 USIPIstscl_d.m 11.13 Structural Models with Simplified Specification 11.13.1 usmbjsgairl 11.13.2 usmbtozone 11.13.3 usmbtozonem 11.13.4 usmcgdp 11.13.5 usmcgwage 11.13.6 usmcslopeint 11.13.7 usmmelanoma 11.13.8 usmSeatbelt 11.13.9 usmSeatbelti 11.13.10 usmseriee 11.13.11 usmUSIPI 11.13.12 usmUSIPIHP 11.14 Structural Models with Complex Seasonal Patterns 11.14.1 usmcsp_d.m 11.15 VARMA and VARMAX Models in Echelon Form 11.15.1 TsayEx461_d.m 11.15.2 TsayPa472_d.m 11.15.3 TsayEx62kro_d.m 11.15.4 mkhrcestim_d.m 11.15.5 varmapqPQ3_d.m 11.15.6 lutkepohlex1235_d.m 11.15.7 ReinselMinkMuskrat_d.m 11.16 Computation of Echelon Forms of VARMA and VARMAX Models 11.16.1 varmax2echelon_d.m 11.17 Identification and Estimation of VARX and VARMAX Models 11.17.1 TsayEx23_d.m 11.17.2 TsayEx25_d.m 11.17.3 TsayEx26_d.m 11.17.4 TsayEx27_d.m 11.17.5 TsayEx31_d.m 11.17.6 TsayEx32_d.m 11.17.7 TsayEx33_d.m 11.17.8 TsayEx34_d.m 11.17.9 TsayEx39_d.m 11.17.10 TsayPa315_d.m 11.17.11 TsayPa315hm_d.m 11.17.12 TsayEx441_d.m 11.17.13 TsayEx62_d.m 11.17.14 TsayEx62c_d.m 11.17.15 reinselex52_d.m 11.17.16 reinselex66_d.m 11.17.17 reinselex82_d.m 11.17.18 tf2_d.m 11.18 Cointegrated VARMA Models 11.18.1 TsayPa511_d.m 11.18.2 TsayPa595_d.m 11.18.3 TsayPa62_d.m 11.18.4 Tsayex11p23_d.m 11.18.5 reinselex64_d.m 11.18.6 reinselex65_d.m 11.18.7 reinselp307_d.m 11.18.8 lutkepohlex146_d.m 11.18.9 lutkepohlex726_d.m 11.19 Temporal Aggregation 11.19.1 agtrimanssbs_d.m 11.20 Two Stage Kalman Filter (TSKF) with SRIBF 11.20.1 tskfsribfEx1_d.m 11.20.2 tskfsribfEx2_d.m 11.21 Estimation of the Profile Likelihood: BIC and AIC for Nonstationary Series 11.21.1 btozoneprof_d.m 11.22 Square Root Covariance Filter and Smoother 11.22.1 mulcycus2wcv_d.m 11.22.2 TsayPa595_d.m 11.23 Testing all the Kalman Filtering and Smoothing Functions 11.23.1 testskfs_d.m References Author Index Subject Index