In 2016 I attended Stanislav Anatolyev's graduate course in time series econometrics and took my notes by hand on a tablet. These pages are those notes, reworked into slides. The structure and the choice of results follow his lectures; the slides, the examples, the code and any errors are mine. Lecture 8, and a few individual slides elsewhere, cover material that is missing from my notes; they are written from the standard texts and marked as such on the slide.
Each deck opens with a short film that gives the idea before the formalism; it is narrated by a synthetic copy of my voice. The slides are interactive: sliders redraw the figures, the quiz questions check themselves, and every number comes from R code that runs on real data from FRED, shipped with the deck. Open a deck in a browser; the arrow keys move between slides, and F gives full screen.
Foundations
| | Lecture | What it covers | Materials |
|---|
| 1 | Stationarity, Ergodicity and White Noise | Why one trajectory can stand in for many: strict stationarity, three strengths of white noise, ergodicity, and the law of large numbers that needs both. | |
| 2 | Ergodic Theorem, CLT and the Long-Run Variance | Averages of dependent data: the ergodic theorem, the CLT for martingale differences and in general, the long-run variance, and why the naive estimator fails while Newey–West works. | |
| 3 | Time-Series Regression and HAC Inference | OLS on time series: when White standard errors suffice, when HAC is needed, Mishkin's inflation regressions with overlapping horizons; structural versus non-structural models. | |
Choosing and judging models
| | Lecture | What it covers | Materials |
|---|
| 4 | What to Model, and How to Choose a Model | The objects of modelling — conditional mean, variance, quantiles, density — and the tools for choosing a model: diagnostics, general-to-specific testing, AIC, BIC and Hannan–Quinn. | |
| 5 | In-Sample Fit, Out-of-Sample Forecasts, Diebold–Mariano | In-sample fit against out-of-sample forecasting, fixed, rolling and recursive schemes, and the Diebold–Mariano test of equal predictive ability. | |
| 6 | Data Snooping, Superior Predictive Ability, Model Confidence Sets | Searching over many models: data snooping, White's Reality Check, Hansen's SPA test and the model confidence set. | |
Linear models for the mean
| | Lecture | What it covers | Materials |
|---|
| 7 | Linear Projection, Innovations and the Wold Decomposition | Linear projection on the infinite past, innovations, the Wold decomposition, impulse responses, and invertibility of moving averages. | |
| 8 | ARMA Models: Identification, Estimation, Forecasting | ARMA models: roots, ACF and PACF, estimation by least squares and likelihood, the Box–Jenkins cycle, and h-step forecasts with their uncertainty. | |
| 9 | Trends, Unit Roots and Brownian Motion | Deterministic and stochastic trends, OLS rates of convergence, the unit-root limit, Brownian motion and the functional CLT. | |
| 10 | Dickey–Fuller, Phillips–Perron and ADF Tests | Testing for a unit root: the Dickey–Fuller distributions, deterministic terms, Phillips–Perron and augmented Dickey–Fuller, and why power is low near one. | |
Nonlinear models for the mean
| | Lecture | What it covers | Materials |
|---|
| 11 | Nonlinear Models and Threshold Autoregression | Why nonlinear models; bilinear and threshold autoregressions, regimes, stationarity with an explosive regime, and estimation by concentrated least squares. | |
| 12 | Threshold Inference and Smooth Transition | Inference on the threshold: Hansen's likelihood-ratio confidence set, testing linearity with sup-F and the fixed-regressor bootstrap, and smooth transition (LSTAR, ESTAR). | |
| 13 | Markov Switching and State-Space Models | Linearity tests against STAR, Markov-switching autoregressions, the Hamilton filter and maximum likelihood, and state-space models. | |
Several series at once
| | Lecture | What it covers | Materials |
|---|
| 14 | Vector Autoregressions, Impulse Responses and Cointegration | Vector autoregressions: estimation, impulse responses, variance decompositions, Granger causality, spurious regression and cointegration. | |
Volatility, stability and risk
| | Lecture | What it covers | Materials |
|---|
| 15 | Volatility — ARCH and GARCH | Conditional variance: ARCH and GARCH, Gaussian quasi-maximum likelihood with robust standard errors, the ARCH-LM test, multivariate GARCH and stochastic volatility. | |
| 16 | Structural Breaks and Parameter Stability | Breaks at known and unknown dates: Chow and sup-Wald tests, Andrews' critical values, Bai–Perron multiple breaks, and CUSUM monitoring. | |
| 17 | Realized Volatility, Durations, Direction and Value-at-Risk | Measuring risk: RiskMetrics, realized volatility, duration models, direction-of-change models, Value-at-Risk and its backtest, and CAViaR. | |
Reading
- Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.
- Tsay, R. S. (2010). Analysis of Financial Time Series, 3rd ed. Wiley.
- Franses, P. H. and van Dijk, D. (2000). Non-Linear Time Series Models in Empirical Finance. Cambridge University Press.
- Anatolyev, S. Syllabus of Applied Time Series Econometrics, New Economic School, for the current reading list and the original papers.
