This is the fourth part of the series on volatility modelling. For other parts of the series follow the tag volatility. In this exercise set we will explore GARCH-M and E-GARCH models. We will also use these models to generate rolling window forecasts, bootstrap forecasts and perform simulations. Answers to ... [Read more...]

This is the third part of the series on volatility modelling. For other parts of the series follow the tag volatility. In this exercise set we will use GARCH models to forecast volatility. Answers to the exercises are available here. Exercise 1 Load the rugarch and the FinTS packages. Next, load ... [Read more...]

This is the second part of the series on volatility modelling. For other parts of the series follow the tag volatility. In this exercise set we will use the dmbp dataset from part-1 and extend our analysis to GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models. Answers to the exercises are available ... [Read more...]

Volatility modelling is typically used for high frequency financial data. Asset returns are typically uncorrelated while the variation of asset prices (volatility) tends to be correlated across time. In this exercise set we will use the rugarch package (package description: here) to implement the ARCH (Autoregressive Conditional Heteroskedasticity) model in ... [Read more...]

Bias vs Variance tradeoff is always encountered in applying supervised learning algorithms. Least squares regression provides a good fit for the training set but can suffer from high variance which lowers predictive ability. To counter this problem, we can regularize the beta coefficients by employing a penalization term. Ridge regression ... [Read more...]

Lease Absolute Shrinkage and Selection Operator (LASSO) performs regularization and variable selection on a given model. Depending on the size of the penalty term, LASSO shrinks less relevant predictors to (possibly) zero. Thus, it enables us to consider a more parsimonious model. In this exercise set we will use the ... [Read more...]

The standard OLS (Ordinary Least Squares) model explains the relationship between independent variables and the conditional mean of the dependent variable. In contrast, quantile regression models this relationship for different quantiles of the dependent variable. In this exercise set we will use the quantreg package (package description: here) to implement ... [Read more...]

This is the third part of the series on Instrumental Variables. For other parts of the series follow the tag instrumental variables. In this exercise set we will use Generalized Method of Moments (GMM) estimation technique using the examples from part-1 and part-2. Recall that GMM estimation relies on the ... [Read more...]

This is the second part of the series on Instrumental Variables. For other parts of the series follow the tag instrumental variables. In this exercise set we will build on the example from part-1. We will now consider an over-identified case i.e. we have multiple IVs for an endogenous ... [Read more...]

One of the most frequently encountered issues in econometrics is endogeneity. Consider the simple Ordinary Least Squares (OLS) regression setting in which we model wages as a function of years of schooling (education): One of the main assumption of OLS is that the independent variables are not correlated with the ... [Read more...]