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**Category:**A COMPANION TO Theoretical Econometrics (continued)- The General Multivariate Parametric Problem
- LR, W, and LM tests
- Asymtotically normal estimators
- Nonlinear Models and Nonlinear Inequality Restrictions
- Nonparametric Tests of Inequality Restrictions
- Tests for stochastic dominance
- Definitions and tests
- 1 Introduction, History, and Definitions
- Simulations
- Spurious Regressions with Stationary Processes
- Forecasting Economic. Time Series
- Economic Forecasting: A Theoretical Framework
- Model selection using information criteria
- Prediction intervals
- Forecast comparison and evaluation
- Salient Features of US Macroeconomic Time Series Data
- Univariate Forecasts
- Differencing the data
- Empirical examples
- Multivariate Forecasts
- Vector autoregressions
- Forecasting with leading economic indicators
- Discussion and Conclusion
- Time Series and Dynamic Models
- Time series: a brief historical introduction
- A PROBABILISTIC FRAMEWORK FOR TIME SERIES
- Autoregressive Models: Univariate
- AR(1): the probabilistic reduction perspective
- Extending the autoregressive AR(1) model
- Moving Average Models
- MA(q): the probabilistic reduction perspective
- ARMA Type Models: Multivariate
- The probabilistic reduction perspective
- Time Series and Linear Regression Models
- Dynamic linear regression models
- Unit Roots
- The Gaussian AR(1) Case without Intercept: Part 1
- Weak convergence of random functions
- The Gaussian AR(1) Case with Intercept under the Alternative of Stationary
- General AR Processes with a Unit Root, and the Augmented Dickey-Fuller Test
- ARIMA Processes, and the Phillips-Perron test
- Unit Root with Drift vs. Trend Stationarity
- Cointegration
- Preliminaries: Unit Roots and Cointegration
- Estimation and testing for cointegration in a single equation framework
- System-Based Approaches to Cointegration
- The Johansen's method
- Common trends representation
- Further Research on Cointegration
- Higher order cointegrated systems
- Fractionally cointegrated systems
- Nearly cointegrated systems
- Nonlinear error correction models
- Seasonal Nonstationarity and Near-Nonstationarity*
- Properties of Seasonal Unit Root Processes
- Asymptotic properties
- Deterministic seasonality
- Testing the Seasonal Unit Root Null Hypothesis
- Testing complex unit roots
- The Hylleberg-Engle-Granger-Yoo test
- Extensions to the HEGY approach
- Multiple tests and levels of significance
- Characteristics of variables
- Alternative models and model representations
- Estimation of unrestricted VARs and VECMs
- Estimation of restricted models and structural forms
- Model Specification and Model Checking
- Model checking
- Uses of Vector Autoregressive Models
- Forecasting VAR processes
- Granger-causality analysis
- Impulse response analysis
- Forecast error variance decomposition
- Conclusions and Extensions
- Applications of Test Principles to Econometrics
- Models and Their Specification

**Category:**Advanced Econometrics Takeshi Amemiya- Advanced Econometrics Takeshi Amemiya
- Classical Least Squares Theory
- Model 1
- Implications of Linearity
- Matrix Notation
- Theory of Least Squares
- Least Squares Estimator of a Subset of fi
- The Mean and Variance of 0 and a2
- Definition of Best
- Least Squares as Best Linear Unbiased Estimator (BLUE)
- Model 1 with Normality
- Cram6r-Rao Lower Bound
- Least Squares Estimator as Best Unbiased Estimator (BUE)
- The Cramer-Rao Lower Bound for Unbiased Estimators of cr2
- Model 1 with Linear Constraints
- Constrained Least Squares Estimator (CLS)
- An Alternative Derivation of the Constrained Least Squares Estimator
- Constrained Least Squares Estimator as Best Linear Unbiased Estimator
- Test of Linear Hypotheses
- The F Test
- A Test of Structural Change when Variances Are Equal Suppose we have two regression regimes
- A Test of Structural Change when Variances Are Unequal
- Prediction
- Recent Developments in Regression Analysis
- Statistical Decision Theory
- Bayesian Solution
- Theil’s Corrected Я2
- Prediction Criterion
- Optimal Significance Level
- Ridge Regression and Stein’s Estimator
- Canonical Model
- Multicollinearity and Principal Components
- Stein’s Estimator: Homoscedastic Case
- Stein’s Estimator: Heteroscedastic Case
- Monte Carlo and Applications
- Stein’s Estimator versus Pre-Test Estimators
- Robust Regression
- Independent and Identically Distributed Case
- Regression Case
- Large Sample Theory
- Random Variables
- Distribution Function
- Various Modes of Convergence
- Laws of Large Numbers and Central Limit Theorems
- Relationships among lim E, AE, and plim
- Consistency and Asymptotic Normality of Least Squares Estimator
- Asymptotic Properties of Extremum Estimators
- General Results
- Asymptotic Normality
- Maximum Likelihood Estimator
- Concentrated Likelihood Function
- Nonlinear Least Squares Estimator
- Bootstrap and Jacknife Methods
- Tests of Hypotheses
- Methods of Iteration
- Newton-Raphson Method
- The Asymptotic Properties of the Second-Round Estimator in the Newton-Raphson Method
- Gauss-Newton Method
- Asymptotic Tests and Related Topics
- Akaike Information Criterion
- Tests of Separate Families of Hypotheses
- Least Absolute Deviations Estimator
- Asymptotic Normality of the Median
- Consistency of Least Absolute Deviations Estimator
- Asymptotic Normality of Least Absolute Deviations Estimator
- Time Series Analysis
- Stationary Time Series
- Autocovariances
- Autoregressive Models
- Second-Order Autoregressive Model
- Autogressive Models with Moving-Average Residuals
- Asymptotic Properties of Least Squares and Maximum Likelihood Estimator in the Autoregressive Model
- Distributed-Lag Models
- The Almon Lag
- Generalized Least Squares Theory
- Generalized Least Squares Estimator
- Efficiency of Least Squares Estimator
- Consistency of the Least Squares Estimator
- A Singular Covariance Matrix
- The Case of an Unknown Covariance Matrix
- Asymptotic Normality of the Least Squares Estimator
- Estimation of p
- Feasible Generalized Least Squares Estimator
- A Useful Transformation for the Calculation of the Feasible Generalized Least Squares Estimator
- Durbin-Watson Test
- Joint Presence of Lagged Endogenous Variables and Serial Correlation
- Seemingly Unreleted Regression Model
- Heteroscedasticity
- Unrestricted Heteroscedasticity
- Model of Lee
- Two-State Models with Exogenous Variables
- Constant Variance in a Subset of the Sample
- General Parametric Heteroscedastidty
- Variance as a Linear Function of Regressors
- Variance as an Exponential Function of Regressors
- Three Error Components Models
- Two Error Components Model
- Balestra-Nerlove Model
- Two Error Components Model with a Serially Correlated Error
- Two Error Components Model with Endogenous Regressors
- Random Coefficients Models
- The Kelejian and Stephan Model
- Hsiao’s Model
- Swamy’s Model
- Other Models
- Linear Simultaneous Equations Models
- Full Information Maximum Likelihood Estimator
- Limited Information Model
- Limited Information Maximum Likelihood Estimator
- Asymptotic Distribution of the Limited Information Maximum Likelihood Estimator and the Two-Stage Least Squares Estimator
- Exact Distributions of the Limited Information Maximum Likelihood Estimator and the Two-Stage Least Squares Estimator
- Interpretations of the Two-Stage Least Squares Estimator
- Consider regression equations
- Three-Stage Least Squares Estimator
- Further Topics
- Nonlinear Simultaneous Equations Models
- Box-Cox Transformation
- Nonlinear Limited Information Maximum Likelihood Estimator
- Estimation in a System of Equations
- Nonlinear Three-Stage Least Squares Estimator
- Nonlinear Full Information Maximum Likelihood Estimator
- Tests of Hypotheses, Prediction, and Computation
- Prediction
- Qualitative Response Models
- Univariate Binary Models
- Global Concavity of the Likelihood Function in the Logit and Probit Models
- Iterative Methods for Obtaining the Maximum Likelihood Estimator
- Berkson’s Minimum Chi-Square Method
- Comparison of the Maximum Likelihood Estimator and the Minimum Chi-Square Estimator
- Tests of Hypotheses
- Discriminant Analysis
- Aggregate Prediction
- Multinomial Models
- Multinomial Logit Model
- Multinomial Discriminant Analysis
- Nested Logit Model
- Higher-Level Nested Logit Model
- Generalized Extreme-Value Model
- Universal Logit Model
- Multinomial Probit Model
- Sequential Probit and Logit Models
- Multivariate Models
- Multivariate Nested Logit Model
- Log-Linear Model
- Multivariate Probit Model
- Choice-Based Sampling
- Results of Manski and Lerman
- Results of Manski and McFadden
- Results of Cosslett: Part I
- Results of Cosslett: Part II
- Distribution-Free Methods
- Maximum Score Estimator—A Binary Case
- Maximum Score Estimator—A Multinomial Case