From the synopsis: > It's important to use dynamic measures in a dynamic system. I often see the mistake of using a static value for mean or kurtosis, unaware

From the synopsis: > It's important to use dynamic measures in a dynamic system. I often see the mistake of using a static value for mean or kurtosis, unaware of how it changes over time. This is both important to note, and unavoidable. You can account for changes in volatility in pure data analysis, but when developing mathematical models of time series, data stationarity has to be assumed for closed form solutions. Even if the volatility itself followed its own model (say garch could model it accurately), it can be iteratively reduced to a stationary series (I'm not sure if there's proof of this, but that's how most time series courses teach it - take first diff, second diff, log etc). Markets are a similar level of complexity, but to compare anything to a reflexive system such as a market is kinda skirting the main issue of markets - reflexivity. You cannot find a closed form solution for it using current mathematics. Finance developed a distribution based mathematics called stochastic calculus (used in other fields, but it's the backbone of finance) to deal with this, but even there, the assumptions are highly restrictive compared to real world conditions.