VaR-Forecasting-with-ARMA-GARCH

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VaR-Forecasting-with-ARMA-GARCH

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# ARMA-GARCH-Models

This repo documents my general exploration of ARMA-GARCH models, and how I created a Python module for fitting them with Quasi-Maximum Likelihood estimation. I used my findings to run a simple historical backtest to create a one-day-ahead estimate of Value-at-Risk (VaR).

## 1: Exploring Distribution of Stock Returns

This notebook goes through some of the key characteristics and statistical distributions of stock returns.

## 2: Theoretical Background of ARMA-GARCH

Here I go through the basic theory of Autoregressive Moving-Average (ARMA) and General Autoregressive Conditional Heteroscedastic (GARCH) processes and why they are relevant.

## 3: ARMA-GARCH Maximum Likelihood Estimation

I demonstrate how Maximum Likelihood Estimation can be applied using various likelihood functions.

## 4: Forecasting Value at Risk

Here, I bring all the theory and code from the previous notebooks and perform a backtest of the model. to estimate one day 5% VaR values. I also demonstrate how the results show that the model is not as predictive/ accurate as it may seem.

VaR-Forecasting-with-ARMA-GARCH

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