Financial Econometrics
Unit 1: Statistical Properties of Financial Returns & Univariate Time Series and Applications to Finance
Asset Returns
A Foundation of Financial Econometrics Asset returns are fundamental to financial econometrics, r...
Discrete vs. Continuously Compounded Returns
A Comparison As discussed before, asset returns can be calculated in two primary ways: discrete (...
Numericals
Discrete vs. Continuously Compounded Returns Here are a few problems illustrating the concepts of...
Empirical Properties of Financial Returns
Financial returns exhibit several stylized facts, or empirical properties, that distinguish them...
Introduction to Univariate Time Series
A time series is a sequence of data points, measured typically at successive points in time or o...
Real life Example
Analyzing and Modeling a Stock's Daily Returns Suppose you have a time series of daily continuous...
Autoregressive (AR), Moving Average (MA), and ARMA Processes
These models are fundamental building blocks in time series analysis. They describe the evolutio...
Numerical Problem
Identifying and Estimating an ARMA Model Suppose you have the following sample autocorrelations (...
The Box-Jenkins Approach
A Methodology for Time Series Modeling The Box-Jenkins approach, also known as the ARIMA (Autoreg...
Unit 2: Modelling Volatility – Conditional Heteroscedastic Models
Introduction to Modelling Volatility
Volatility, a measure of the dispersion of returns for a given security or market index, is a ke...
Numerical Example
EWMA Volatility Calculation Step 1: Given Data Decay factor (λ): 0.94 Yesterday's estimated va...
Autoregressive Conditional Heteroscedasticity (ARCH) Models
ARCH models, introduced by Engle (1982), are a class of statistical models for time series data ...
Numerical Example
Comparison: With a positive return yesterday (2%), today's conditional variance was 0.000...
Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Models
GARCH models, introduced by Bollerslev (1986), are an extension of ARCH models that allow the co...
Numerical
Estimation of GARCH Models
The estimation of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models invol...
Forecasting with GARCH Models
Introduction to Forecasting with GARCH Models One of the primary uses of GARCH models is forecas...
Numericals
These calculations give us a basic understanding of how volatility is forecasted using a GA...
Unit 3: Modelling Volatility and Correlations – Multivariate GARCH Models
Introduction to Modelling Volatility and Correlations
While univariate GARCH models focus on modeling the volatility of a single asset, multivariate G...
Multivariate GARCH (MGARCH) Models
Multivariate GARCH (MGARCH) models are extensions of univariate GARCH models designed to model t...
VECH, Diagonal VECH, and BEKK Models
Specific MGARCH Specifications The VECH, Diagonal VECH, and BEKK models are three essential types...
Estimation of a Multivariate Model
Estimating multivariate GARCH (MGARCH) models involves determining parameter values that best fit...
Unit 4: Vector Autoregressive Models (VAR), Granger Causality Test (GCT) and Johansen Cointegration Test (JCT)
Estimating a Multivariate GARCH Model
Estimating multivariate GARCH (MGARCH) models involves determining parameter values that best de...
Granger Causality Test (GCT)
The Granger Causality Test (GCT), developed by Clive Granger, is a statistical hypothesis test u...
Johansen Cointegration Test (JCT)
The Johansen Cointegration Test (JCT), developed by Søren Johansen, is a statistical test used to...