• Descriptive Statistics and Statistical Inference
• Deterministic phenomena vs. Stochastic phenomena
• Modeling: First principles
Matrix Algebra Review
• Matrix and vector operations, the determinant and the inverse, rank of a matrix, quadratic forms, the eigensystem of a matrix, vector and matrix differentiation. Idempotent matrices, Kronecker product, partitioned matrices.
Probability, random variables and probability distributions
• Probability theory, random experiments, the probability space, the statistical space.
• The notion of a random variable, the cumulative and density functions, the probability model, parameters and moments, univariate probability models.
• Random vectors, joint distributions, marginal distributions, conditional distributions.
• The notion of a random sample: independence, identical distributions, the simple statistical model in empirical modeling.
• Functions of random variables
• The notion of a non-random sample.
Probabilistic Concepts and Real Data
• Graphic Displays: a t-plot
• Assessing Distribution Assumptions
• Independence and the t-plot
• Homogeneity and the t-plot.
• Conditioning and regression, regression and skedastic functions.
• Stochastic conditioning, weak exogeneity.
• The notion of a statistical generating mechanism and regression models.
• The concept of a stochastic process. Dependence restrictions, heterogeneity restrictions.
• Elementary stochastic processes, Markov processes, random walk processes, martingale processes, the Wiener process, the Brownian motion process.
• Defining an estimator, finite sample properties, large sample properties.
• Methods of estimation. Least squares estimation method, method of moments, maximum likelihood estimation method.
• Test statistics, hypothesis testing and confidence intervals, size and power of a test.
• Specification, misspecification testing, re-specification, specification testing.
• Applications using Eviews.