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Courses → Financial Econometrics
Financial Econometrics
Master statistical methods for financial data analysis, from time series modelling to panel data techniques, with Python and R implementations.
What you’ll learn
- ✓ Apply time series models (ARIMA, GARCH) to financial data
- ✓ Build and interpret panel data regression models
- ✓ Conduct cross-sectional and survey data analysis
- ✓ Synthesise evidence with meta-analysis, bibliometrics and systematic reviews
- ✓ Implement econometric models in Python and R
- ✓ Run diagnostic tests and handle model violations
Prerequisites
- • Undergraduate-level Statistics
- • Linear Algebra fundamentals
- • Basic Python or R programming
8 Learning Tracks
Time Series
Stationarity, ARMA, GARCH family, long memory, VAR, cointegration, Markov-switching, structural breaks, the Kalman filter, VaR/ES backtesting.
Stationarity & Unit-Root Testing
ACF and PACF: AR(2) Process, Identifying the Model Order
ACF, Autocorrelation Function
PACF, Partial Autocorrelation Function
ACF: exponential decay → AR process. PACF: cuts off at lag 2 → AR(2). Use for Box-Jenkins identification.
Motivation
Every time-series technique you'll learn, ARMA, GARCH, VAR, cointegration, VaR backtesting, rests on whether the input series is stationary. Run OLS on two unrelated random walks and you'll find a "highly significant" relationship with R² above 0.7. This is the spurious regression problem (Granger & Newbold, 1974), and it is the reason every empirical finance paper that uses prices, yields, or exchange rates first reports a unit-root test.
Key Equations
Intuition
A random walk has no "centre of gravity", knowing today's value tells you nothing about where the series will be in 10 years. Stock prices look like this. Returns, by contrast, fluctuate around zero with stable variance. The ADF test asks: if you ran a one-period regression of changes on lagged levels, would the coefficient on the lagged level be statistically less than zero? If yes, the series mean-reverts; if no, it wanders. The non-standard distribution arises because, under the null, the regressor y_{t-1} is itself non-stationary.
Assumptions
- 1.DGP can be written as AR(p+1) with possible deterministic terms
- 2.εt is iid with finite variance
- 3.Lag length p is large enough to whiten residuals
Diagnostic Checks
| Test | H₀ | If rejected |
|---|---|---|
| ADF | Unit root | Reject → mean-reverting; proceed with ARMA |
| Phillips-Perron | Unit root (non-parametric correction) | Use alongside ADF as robustness |
| KPSS | Stationarity (reverse!) | Reject → unit root present; differences needed |
| Ljung-Box on residuals of ADF | White noise residuals | Reject → increase lag length p |
Practitioner Pitfalls
- ▶Running ARMA on prices (levels) instead of returns, always first-difference I(1) series.
- ▶Structural breaks masking stationarity: Perron (1989) test for known break dates, Zivot-Andrews for unknown.
- ▶Low power with small samples, failing to reject unit root ≠ proof of unit root.
- ▶Daily vs monthly: same series may give different conclusions due to sample size change.
- ▶Fractional integration: I(d), 0 < d < 1, needs ARFIMA testing (Lesson 05).
References