Brainstormin

So I find myself at the start of my third year in grad school with nearly all my required coursework completed about to embark upon my first piece of significant academic research. After two years of punishing qualifying exams and field requirements I stand ready to contribute to the total sum of human knowledge. What that contribution is exactly remains to be seen, but here's what I've got so far.

A couple of professors got me thinking about the relationship between volume and volatility in financial time series. Now one of the most well documented features of financial data is the fact that asset returns exhibit volatility clustering. This means that large changes in asset prices tend to be followed by large changes (and likewise for small changes), resulting in periods of high volatility and low volatility.

In order to capture this phenomena, a statistical model called ARCH was developed in the early 80's by Robert Engle, currently a professor at the Stern School of Business (NYU). ARCH (and its variants) parameterizes the conditional variance of a stationary time series (typically an asset return) as an autoregressive process, thereby allowing for serial dependence in volatility. Now this points to a deeper, more economic question. Why does ARCH exist? More specifically, what are the economic mechanisms which cause the magnitude of price changes to be serially correlated?

Perhaps a plausible explaination for the presence of ARCH is the idea that volatility clustering is merely a manifestation of the rate of information arrival in financial markets. The existing research indicates that information itself may be a serially correlated process, so that market participants receive information in temporal 'lumps' as opposed to an independent random stream. The reaction of market participants to these information lumps cause asset prices to fluctuate thereby resulting in volatility clustering. Therefore, to understand the information arrivals process is to understand ARCH. The problem faced by the economist and econometrician is the fact that the rate of information arrival is largely an unobservable (latent) process which introduces difficulties in econometric modelling (how does one devise a statistical model for something that one cannot observe?).

That said, the idea of information flow also points to the behavior of trade volume. Unlike volatility, the issue of trade volume has not been well explored but it is clear that the two are inextricably linked. One need only think about the basic ideas of supply and demand to see this.

So my first step is to get my hands dirty and have a look at some volume data. Wish me luck!