This is an intermediate course in Statistics and is intended for students who have already taken an exam in Probability and/or Statistics. It is divided into two parts: statistical inference and an introduction to time series analysis The following topics are treated during the lectures:
- Marginal and conditional probability, the Bayes theorem;
- Random variables and the expected value, the bernoulli, binomiale, poisson, exponential, uniform and normal distributions;
- Sampling distributions, the distributions of the sample mean, variance and proportion, the central limit theorem;
- The chi-square, Students t and Fisher F distributions;
- Point estimates and their properties, maximum likelihood estimation, the Cramer-Rao bound, interval estimates;
- The theory of hypothesis testing with particular attention to hypotheses on the means, variances and proportions of one and two populations;
- Testing the independence between two random variables;
- Exponential smoothing;
- An analysis of the trend and seasonal components in economic time series: methods for detrending and deseasonalization;
- Statistical properties of finantial time series;
- Time series analysis through ARCH-GARCH models.
The objective of this course if that of offering the student useful tools for the analysis of economic data with particular interest in time series.