Learning outcomes

After this module you should be able to:

1. State the three forms of market efficiency and the Grossman–Stiglitz argument precisely, and say which kind of forecast (mean, variance, event probability) each one leaves room for.
2. Derive the stationarity conditions, autocorrelations, Yule–Walker equations and $h$-step forecasts of AR($p$) models, and compute the population $R^2$ of an AR forecast.
3. Define the out-of-sample $R^2$ of Campbell and Thompson, derive the Sharpe ratio a mean-variance investor gains from a predictor with a given $R^2$, and derive the Stambaugh bias of predictive regressions.
4. Derive the unconditional variance, ARMA representation, kurtosis, half-life, multi-step forecasts, log-likelihood and score of GARCH(1,1), and estimate it by maximum likelihood from scratch.
5. Derive the Hamilton filter and the Kim smoother for a two-state Markov-switching model, and explain why smoothed probabilities are look-ahead in a backtest.
6. Build purged k-fold cross-validation with an embargo, triple-barrier labels and meta-labels, and quantify the leakage that ordinary k-fold creates with overlapping labels.
7. Prove that the Brier and logarithmic scores are strictly proper, prove the Murphy decomposition of the Brier score, and score your own probabilistic forecasts in a journal.