The paper titled, “Empirical properties of asset returns: stylized facts and statistical issues”, by Rama Cont presents 11 stylized facts applicable to wide set of assets that should be always in a quant’s working memory. These stylized facts should shape one’s thinking in building financial models. Stylized facts are the statistical properties of asset prices that are common across a wide range of instruments, markets and time periods. They are usually formulated in terms of qualitative properties of asset returns and may not be precise enough to distinguish among different parametric models.

Joel Hasbrouck in his paper, “Security Bid/Ask Dynamics with Discreteness and Clustering” , uses Gibbs sampling for estimating the parameters of a stylized market microstructure model. For any model, there are many ways to estimate parameters. One of the common methods is the likelihood approach. Even though this approach makes sense intuitively, the computational complexity explodes as the number of parameters increase. The curse of dimensionality kicks in and hence parameters become notoriously unstable.

[youtube https://www.youtube.com/watch?v=r-ERajkMXw0?rel=0]

When I first encountered Kalman Filter technique, I was overwhelmed by the ton of approaches taken by various authors to explain it. It can be explained from an engineering vocabulary but I wanted to understand it from a stats point of view . One typically reads either the Frequentist approach( where Gaussian multivariate normal distribution is used to derive all the formulae) or the Bayesian approach where the usual prior-posterior stuff is used to derive Kalman Filter.