Time-Series Finance — Final Exam

This is the capstone. Six lessons built the machinery for modeling returns through time — from the gate every technique must pass to the discipline that keeps you from fooling yourself. You learned why prices are non-stationary (a unit root, shocks that never decay) while returns are roughly stationary; how the ACF and PACF read a series’ memory against the white-noise band and identify a model; how AR, MA, and ARIMA turn those patterns into fitted equations for the mean; how volatility clustering breaks the constant-variance assumption and GARCH(1,1) forecasts the variance with three parameters; how EWMA is the IGARCH special case that powers RiskMetrics VaR; and how look-ahead bias, overfitting, and data-snooping make a backtest lie. No formula sheet, no hints, no take-backs: every answer locks the instant you submit, the wrong options are the exact traps that fool real desks, and your score stays hidden until the end.

Big picture

Time-Series Finance — the whole ladder

Time-Series Finance
- Stationarity & returns
  - Constant mean, variance, lag-only autocovariance
  - Prices: unit root (φ=1), non-stationary
  - Returns ≈ I(0); ADF tests, logs & differencing fix it
- Autocorrelation, ACF & PACF
  - White-noise band ±2/√n
  - AR cuts off in PACF, MA in ACF
  - Ljung–Box: joint test, clean on residuals
- AR, MA & ARIMA
  - AR: past values; MA: past shocks
  - ARIMA(p,d,q): difference d times then ARMA
  - Choose by AIC/BIC; models the mean, not variance
- Volatility clustering & GARCH
  - Flat return ACF, persistent squared-return ACF
  - GARCH(1,1): ω + α·ε² + β·σ²
  - Persistence α+β; long-run ω/(1−α−β)
- EWMA & RiskMetrics
  - σ²=λσ²+(1−λ)r²; half-life ln0.5/lnλ
  - IGARCH: ω=0, α+β=1, no mean reversion
  - λ=0.94 daily; VaR ≈ 2.33·σ·position
- Backtesting pitfalls
  - Look-ahead bias: one-bar-lag rule
  - Overfitting: in-sample up, out-of-sample falls
  - Data-snooping: 1 − 0.95^N; walk-forward

From the stationarity gate to honest backtesting: six lessons, one continuous thread of modeling returns through time.

How this exam works

This is a graded exam. Questions arrive one at a time. Once you submit an answer it is final — there is no going back, no second try, and a wrong answer simply fails that question. Your score stays hidden until the very end, where you need 70% to pass. Read every option before you commit.

Question 1 of 27

What does it mean for a time series to be (weakly) stationary?

It always trends steadily upward with a fixed slopeIts mean and variance are constant over time and its autocovariance depends only on the lag, not on when you lookIts values never change from one period to the nextIt has exactly zero autocorrelation at every lag

Select an answer to continue.

Passed? Here's what you now own

You can take a raw price series and do the whole pipeline a quant does: test it for a unit root, difference it into stationary returns, read the ACF and PACF to identify a model, fit and validate an ARIMA for the mean, layer a GARCH or EWMA on top for the time-varying variance and VaR, and — most importantly — evaluate the result with enough suspicion that look-ahead bias, overfitting, and data-snooping don’t fool you. You know which tool fits which job, and why a beautiful backtest is guilty until proven innocent.

That’s the time-series toolkit, end to end — the statistical language of returns over time, and the discipline to use it without deceiving yourself. You now own both the models and the judgment to know when to trust them.