Course Map: Inference for Relationships and Time

Welcome to the course where the statistics finally starts to move.

Until now, inference has been about a single quantity: estimate a volatility, bound it, test whether it could be chance (SVI 201). But markets are not single numbers — they are relationships (implied vol bends with moneyness; one asset leans on another) and processes in time (today's turbulence breeds tomorrow's). SVI 202 is where you learn to model both. It is the bridge from "is this number real?" to "how does this number depend on that one, and on its own past?"

The course has two halves that meet in the middle. The first is regression — the machinery for fitting one variable to others and, crucially, deciding which of those relationships are evidence and which are noise. Regression is not a new idea so much as a payoff: it is the conditional expectation of 102 made estimable, and the covariance of 101 turned into a slope you can test. The second half is time series — stationarity, autocorrelation, the AR and MA building blocks, and then the model this entire program has been pointing at since Tier 100: GARCH, the formal account of why volatility clusters and how to forecast it.

Here is the road through the six modules and the SVQ output each is anchored to:

1. Simple Linear Regression (OLS) — fitting a line and testing its slope. Anchored to SVQ's wing slope, the regression of implied vol on log-moneyness that measures the smile's skew.
2. Multiple Regression & Its Assumptions — many inputs at once, and the assumptions the method quietly rests on. Anchored to the crash-o-meter's wing-slope regressions.
3. Diagnostics: Heteroskedasticity & Autocorrelation — reading the residuals to catch a misspecified model, the two failures that matter most in finance.
4. Time Series: Stationarity, AR & MA — the grammar of a series that depends on its own past. Anchored to the HAR decomposition of realized variance (daily / weekly / monthly).
5. Volatility Clustering & GARCH(1,1) — the formal model of the clustering you first saw in Tier 100, fit by maximum likelihood. Anchored to SVQ's GARCH(1,1) volatility model.
6. Monte Carlo Simulation — generating thousands of possible futures when no formula will do. Anchored to SVQ's forecast Monte-Carlo paths.

The course ends with a graded assessment spanning regression through simulation. Pass it and 202 counts toward your Tier 200 credential; earn honors and you are flagged for the honors track.

When you finish, you will hold the full intermediate inference toolkit — and you will understand, from the inside, the volatility models the platform runs. Tier 300 then takes the leap into continuous time: stochastic calculus and the mathematics of options.

Let's begin with the straight line — the simplest relationship, and the foundation of everything that follows.