The paper titled, Temporal Aggregation of GARCH processes, by Drost and Njiman is a classic paper that introduces three forms of GARCH processes: Strong form of GARCH, Semi-strong form of GARCH and Weak form of GARCH. Only the Weak form of GARCH is appropriate for connecting volatility estimates and parameters of models built at various frequencies. In most of the literature on volatility estimation from high frequency data, the authors assume Weak form of GARCH.

Link to book summary Takeaway : Most of the phenomena in our world are periodic in nature. Yet, econometric courses at undergraduate / graduate level inevitably start from the time domain instead of frequency domain. This book is a great introduction for some one looking to get an overview of frequency domain analysis. All the principles are explained from a regression standpoint in the initial chapters. Discrete Fourier Transforms are gradually introduced to connect various ideas.

[youtube https://www.youtube.com/watch?v=LvfEgQ6pPdE?rel=0]

The paper titled, “Intraday periodicity and volatility persistence in financial markets”, by Andersen and Bollerslev is a 44 page analysis on volatility modeling and has close to 75 references. This paper is one of the widely quoted papers on intraday volatility modeling. In this post, I will give a brief summary of the main sections of the paper. Introduction Return volatility varies systematically over the trading day and this pattern is highly correlated with the intraday variation of trading volume and bid-ask patterns.