Time Series Analysis

Under development

This lesson is part of the course scaffold and is being actively written. The learning objectives and outline below define its final scope.

Learning objectives

By the end of this lesson you will be able to:

• Test price and return series for stationarity using ADF and KPSS tests and interpret cases where the two disagree.
• Compute and interpret ACF and PACF of returns, absolute returns, and squared returns, including rolling autocorrelation over time.
• Fit ARIMA and GARCH-family models to return series, run residual diagnostics, and produce out-of-sample volatility forecasts.
• Test asset pairs and baskets for cointegration using the Engle-Granger and Johansen procedures and extract the cointegrating relationship.

Outline

1. Stationarity — definitions, why it matters for every downstream model
2. Unit-root tests — ADF, KPSS, and how to read their disagreement
3. ACF and PACF — estimation, significance bands, returns vs absolute returns
4. ARIMA models — identification, fitting, residual diagnostics
5. The GARCH family — GARCH, EGARCH, GJR; volatility forecasting and evaluation
6. Cointegration with Engle-Granger — the two-step procedure on real pairs
7. The Johansen framework — multivariate cointegration and rank tests

Prerequisites

• Statistical Models
• Markov Chains