## Quantitative Methods

25-01-12 0 comment

Quantitative Methods

COURSE OUTLINE

Introduction
•    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.

Regression
•    Conditioning and regression, regression and skedastic functions.
•    Stochastic conditioning, weak exogeneity.
•     The notion of a statistical generating mechanism and regression models.

Stochastic Processes
•    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.

Statistical Inference
•    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.