Financial and Economic Time Series — Course Guide

A matrix-based course in returns, volatility, persistent predictors, cointegration, structural dynamics, nowcasting, and forecast evaluation.

Financial and Economic Time Series

What this course adds

The Classical Time Series course begins with stochastic processes, Toeplitz covariance matrices, ARMA equations, linear projection, and likelihood. This course keeps that mathematical spine but changes the question:

How should a time-series model change when the decision concerns financial risk, an economic forecast, or a policy intervention?

The answer is not “use a larger ARIMA model.” Financial and economic data introduce different clocks, transformations, losses, and identification problems:

a stock price is observed almost continuously, but a national-account series is revised long after its first release;
return means are weak and volatility is highly persistent, while macroeconomic levels often contain trends and cointegrating relations;
a risk manager cares about tail losses, whereas a central-bank forecaster may care about a quarterly nowcast and the response to a policy shock;
a forecasting relation need not be a causal or structural relation.

This is therefore an applied time-series econometrics course, not a replacement for the classical theory course and not a trading-strategy cookbook.

Preparation

Before starting, you should be able to:

write OLS as $(X^\top X)^{-1}X^\top y$ and interpret a covariance matrix;
recognise a stationary AR process and a unit root;
read an ARMA equation and a first-order state equation;
use logarithms, conditional expectation, likelihood, and matrix multiplication;
run a self-contained base-R example.

If these are unfamiliar, complete the first five modules of Classical Time Series first.

Ten-minute readiness check

Why do we usually model a liquid asset's return rather than its price level?
If $x_t$ and $y_t$ are both $I(1)$ , when can a regression in levels still be meaningful?
Why does an $h$ -period overlapping return create serially correlated regression errors?
What extra assumption turns a reduced-form VAR innovation into a named policy shock?
Why is a revised GDP series inappropriate for evaluating a historical real-time forecast?

Short answers: returns are closer to stationary and directly measure gains or losses; when a stationary linear combination exists; adjacent outcomes share observations; an identification restriction; the revised value was unavailable when the forecast was made.

Learning outcomes

By the end, you will be able to:

choose defensible transformations for prices, returns, yields, macroeconomic levels, growth rates, and revised releases;
derive predictive regressions and Newey–West covariance estimators in matrix form;
estimate and diagnose ARCH/GARCH models and convert conditional variance forecasts into risk measures;
distinguish unit-root, cointegration, error-correction, and spurious-regression arguments;
derive reduced-form VAR forecasts and explain what additional restrictions identify structural shocks;
implement a Kalman filter for missing and mixed-frequency observations;
compare point, density, and tail-risk forecasts with losses matched to the decision;
state clearly whether a result is descriptive, predictive, or structural;
reproduce each core calculation in browser-based base R.

One mathematical spine, two applied tracks

Let $\mathcal F_{t-1}$ denote information available before time $t$ . Both tracks use

y_t=\mu_t+\varepsilon_t,\qquad E(\varepsilon_t\mid\mathcal F_{t-1})=0,\qquad \operatorname{Var}(\varepsilon_t\mid\mathcal F_{t-1})=H_t.

They emphasise different parts:

Track	Typical observation	Dominant uncertainty	Decision
Finance	daily or intraday return, spread, yield	time-varying $H_t$ , heavy tails, market timing	hedge, allocate, price, limit risk
Economics	monthly or quarterly level/growth release	persistent $\mu_t$ , revisions, latent current state	forecast, nowcast, explain, evaluate policy

Finance is not “only variance,” and economics is not “only the mean.” The distinction tells us where model failure is most costly.

Course map

Module	Central question	Matrix object	Main output
1. Three versions of time series	what changes across statistics, finance, and economics?	covariance, information set, loss	method-selection memo
2. Data and transformations	what is the estimand after transforming raw observations?	differencing and aggregation operators	auditable data transformation
3. Predictive regressions	does a persistent variable improve a forecast?	projection and HAC covariance	horizon-specific forecast regression
4. Volatility and risk	how does conditional risk evolve?	variance recursion and likelihood	volatility, VaR, and ES forecast
5. Unit roots and cointegration	is a level relation genuine or spurious?	long-run rank and error correction	equilibrium-and-adjustment argument
6. VAR and identification	what propagates through a system, and what is a shock?	companion matrix and impact matrix	identified impulse-response analysis
7. State space and nowcasting	how do we estimate an unobserved current state?	prediction/update covariance recursion	ragged-edge nowcast
8. Forecast evaluation	is one forecast useful for the actual decision?	loss differential and long-run variance	comparative evaluation report
9. R laboratory	can the complete workflow be reproduced?	reusable matrix checks	finance and economics mini-cases
10. Capstone and readings	can evidence support a bounded decision?	end-to-end audit trail	finance or economics project

How every module works

Each module has four layers:

Prepare: identify the data clock, transformation, information set, and decision.
Derive: express the model as a projection, covariance, companion, or state-space matrix.
Execute: run a small base-R example whose numerical result checks the derivation.
Interpret: write one sentence separating description, prediction, and identification.

The examples are deliberately small. A short simulation can expose a failed assumption more clearly than a large opaque download.

A ten-week route

Week	Preparation	Seminar or laboratory evidence
1	classical ARMA and projection review	classify six questions as statistical, financial, economic, or structural
2	log changes and aggregation	build a transformation matrix and audit units
3	persistent regressors and overlapping horizons	derive OLS and HAC covariance
4	conditional heteroskedasticity	estimate a GARCH model and explain persistence
5	unit roots	diagnose a spurious level regression
6	cointegration and error correction	separate long-run relation from short-run adjustment
7	reduced-form VAR	compute forecasts and impulse propagation
8	structural identification	compare two defensible shock definitions
9	state space and real-time data	produce a ragged-edge nowcast
10	forecast evaluation and synthesis	defend one decision using an honest pseudo-out-of-sample design

Suggested assessment map

This is a teaching design, not an institutional grading policy.

Evidence	Suggested share	Observable standard
transformation and information-set audit	20%	units, timing, releases, and revisions are explicit
matrix derivations and R checks	30%	dimensions, assumptions, and numerical identities agree
comparative forecast exercise	20%	benchmark, loss, horizon, and evaluation window are justified
finance or economics capstone	30%	claim is bounded; uncertainty and failure modes are reported

Expected independent work is about 4–6 hours per module: 1 hour preparation, 1.5 hours guided reading, 1.5 hours code, and 1–2 hours interpretation. All core R cells run in the browser. A learner who cannot use the interactive runtime may copy the same base-R code into a local R session and submit text tables instead of plots.

Start

Begin with Three Versions of Time Series. Do not choose a model until you can name the observation clock, the forecast horizon, the available information, and the loss attached to a wrong decision.

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Capstone — The Evening Delivery Promise

An integrated HarborMart case from decision contract to monitored rollout

Three Versions of Time Series

A decision guide to classical statistical, financial, and economic time series, with matched examples and method-selection rules.