Explorative paper on conditional heteroskedasticity in financial market data and other applications. Discuss theory of modeling autocorrelation within these systems through specialized time series models (ARCH) and provide insight into forecasting methodology. (Specifically within risk analysis and volatility forecasting). Short accompanying talk given at Worcester Polytechnic Institute as a part of a smaller project.
In this paper, we explore the development, identification, and motivations behind a fundamental class of time series models: autoregressive conditional heteroskedasticity (ARCH) models. First introduced by Robert Engle in his seminal work, ARCH models have given way to a rich class of econometric inquiry. Concerned with conditional-level fluctuations in variance, this unique class of models allows us to analyze dependence in residual series data. Finding particular applications within financial time series, ARCH modeling has shown continued success in risk analysis and volatility forecasting. They have especially seen applications within asset pricing, where risk is a central concern in making optimal financial decisions. We examine these considerations and more while discussing the motivations behind such models. By looking at the historical returns of one asset in particular, we provide a demonstrative analysis of the ARCH modeling process. We identify distinct effects in our data that suggest an ARCH process and go on to introduce a parsimonious model that fits our data well and forecasts future volatility