ECON30401 · Time series econometrics

Time series econometrics
study notes & exercises

A complete set of free study notes for ECON30401, a third-year time series econometrics module. The material runs from the foundations of stationary processes, through estimation, inference and forecasting, to an introduction to vector autoregression and system modelling — each topic written up thoroughly with derivations, worked examples and self-check questions.

These notes cover the univariate time series toolkit — stationarity, white noise, MA/AR/ARMA models, the sample autocorrelation function, estimation and model selection, hypothesis testing, forecasting and seasonality — and an introduction to multivariate VAR system modelling, all with worked exercises and an EViews computer lab.

What the module covers

Time series econometrics is the study of data indexed by time: GDP, inflation, interest rates, stock returns. Its distinctive challenge is that we usually observe only a single run of history and must infer the underlying process from it. The course builds the toolkit for doing so, in a natural sequence.

It begins with the foundations: what stationarity means, why it matters, and how the moving-average and autoregressive models — MA(q), AR(p) and ARMA(p,q) — encode dependence through their autocorrelation functions, with the Wold decomposition tying everything together. It then turns to practice: estimating these models, reading the correlogram, testing hypotheses about autocorrelations and coefficients, choosing the model order with information criteria, and forecasting, including how to handle the seasonal swings in quarterly and monthly data. Finally it opens up system modelling, extending the autoregression to several series at once with the vector autoregression (VAR). Two applied strands — a set of worked exercises and an EViews computer lab on UK GDP — keep the theory anchored to real data.

The notes

Note 1Stationarity, white noise & MA processesProcess vs realisation, weak stationarity, white noise, and the moments and ACF of moving-average models.Read the note → Note 2AR, ARMA & the Wold decompositionThe AR(1) as an MA(∞), the Wold decomposition, the lag operator, and stationarity via the characteristic roots.Read the note → Note 3Estimation, the sample ACF & model selectionThe correlogram and its bands, the Ljung-Box Q-test, OLS and ML estimation, AIC/SIC and diagnostic testing.Read the note → InferenceHypothesis testing & inferenceThe logic of testing from first principles: sampling distributions, p-values, size, critical values and the z-test.Read the note → Note 4Forecasting & seasonalityOptimal AR forecasts and forecast-error variance, seasonal dummies, seasonal ARMA and seasonal adjustment.Read the note → SystemsVAR models & system modellingFrom simultaneous-equations models to Sims' VAR: vector white noise, vector stationarity and the VMA form.Read the note → PracticeExercises & worked solutionsMA(2) and AR(2) properties, MA(∞) to ARMA(1,1), and AR(2) forecasting — each with a full worked solution.Read the note → Computer labARMA in EViews: the GDP labA step-by-step EViews practical modelling UK real GDP growth: correlograms, ARMA estimation and model selection.Read the note →

Downloads

The lecture slides, written notes and exercise sheets behind these pages are free to download.

Lecture 1: introduction, stationarity & white noise
Slides for the foundations note.
PDF
Lecture 2: ARMA processes & stationarity
MA(∞), Wold decomposition, lag operator and the stationarity condition.
PDF
Lecture 3: estimation, model selection & testing
Sample ACF, Q-tests, estimation, AIC/SIC and diagnostics.
PDF
Lecture 4: prediction & seasonality
AR forecasting, forecast-error variance and seasonal models.
PDF
Lecture 5: VAR models & system modelling
Introduction to vector autoregressions and the VMA representation.
PDF
Written notes: inference in time series
Full written derivations for estimation, the sample ACF and testing.
PDF
Time series lecture notes, Weeks 1–2
Comprehensive written notes for the MA, AR and ARMA material.
PDF
Problem set 1 & worked solutions
ARMA properties and derivations, with full video solutions.
Video exercise 2 & solutions: prediction & seasonality
AR(2) forecasting and seasonal ARMA, worked step by step.
Exercise sheet 3: seasonal ARMA prediction
Forecasting a seasonal ARMA and its mean-square errors.
PDF
PC lab 1: time series in EViews (UK real GDP)
The EViews computer practical on UK GDP growth.
PDF

Related resources on this site

All teaching materials →
Lecture notes, slides and exercises across econometrics and time series.
Time series econometrics guide →
A plain-English companion covering unit roots, ARIMA and cointegration.
Econometrics explained →
A concise map of the whole subject, from OLS to GARCH.

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