Advanced Statistics and Alternative Data Types

Introduction

Understanding and correctly applying modern data science techniques requires a solid background in statistics. In the first part of this course we will review important concepts in probability and statistical inference to provide the required basic framework. In the second part, we will study the linear regression model (and some extensions) as well as time series analysis. 

This course is in four parts:

1) - An introduction to probability
2) - The idea of statistical inference
3) - The linear regression model & extensions in the cross-sectional context
4) - The statistical analysis of time series data

In this course, we will first first review probability, the goals of statistical analysis and the basics of statistical inference. Following this we will cover regression analysis from a statistical perspective and then introduce time series and standard (ARMA) models used to analyse such data.

Course content

An introduction to probability

    Probability and random variables
    Expectations
    Conditioning and independence
    Classical limit theorems

The idea of statistical inference

    The basic idea of statistical inference
    Estimators, tests
    Evaluation of statistical procedures

The (linear) regression model

    The linear regression model
    Bias/variance trade-off & Regularisation
    Prediction
    Generalised linear models [if time allows]

Time series data
    Stationarity and autocorrelation
    Fundamental time series processes
        Random Walk
        ARMA models
    Estimation and inference
    Out-of-sample forecasting