Time series playground
ACF and PACF plots finally make sense when you can move the coefficients yourself. Pick a model, drag φ and θ, re-roll the randomness, and watch the correlograms do exactly what the identification rules promise. Then hit Test me and identify hidden models from the correlograms alone — the actual exam skill.
Simulated path (500 observations)
Sample ACF (theoretical in gold)
Sample PACF
The purple band is the ±1.96/√n significance band: bars inside it are consistent with zero. The identification rules to memorise: an MA(q) has an ACF that cuts off dead after lag q; an AR(p) has a PACF that cuts off dead after lag p; mixtures tail off in both. Push φ₁ towards 1 on AR(1) and watch the path start wandering and the ACF refuse to die out: that slow decay is the classic sign of non-stationarity, and differencing is the exam's fix. When the rules feel solid, hit “Test me”.
The identification game
CS2 hands you a correlogram and asks which model produced it. The playbook: a sharp cut-off in the ACF after lag q says MA(q); a sharp cut-off in the PACF after lag p says AR(p); geometric tailing-off in both says ARMA. The sample bars here never match the theory exactly, and that is the real lesson: with a couple of hundred observations, sampling noise is loud, which is what the significance band is for. Re-roll a few times on the same parameters and notice how much the picture moves.
Make it stick. Time series shares CS2 with Markov chains and ruin theory; the no-claims discount simulator and ruin theory simulator cover those. Memori is a flashcard app built by actuarial students, with a ready-made CS2 set in the shop. Join the beta.
For education only, not financial advice.