Time Series

Objectives

The main objective of this course is to present multivariate time series analysis techniques commonly used in applications. Two cases are distinguished: stationary series and non-stationary series. In the stationary case, the main focus is on VAR (vector autoregressive) models. In the non-stationary case, the course concentrates on inference in the presence of unit roots and the estimation of cointegration relationships. The course begins with a review of the ARMA approach and (G)ARCH models for univariate series.

The aim of the workshop is to implement the estimation and testing methods presented in the parallel course. Theoretical concepts will be illustrated with real data processed using SAS software.

Course outline

1. Stationary processes (reminders/extensions):
1.1 Modeling conditional expectation – ARMA processes and SARIMA extensions.
1.2 Modeling conditional variance – (G)ARCH processes and their extensions.

2. Univariate non-stationary processes:
2.1. Different forms of non-stationarity: deterministic trend and unit root.
2.2. Unit root tests.

3. Stationary processes: VAR models
3.1 Stationarity.
3.2 Estimation and tests.
3.3 Causality and non-causality tests.

4. Non-stationary processes: unit root and cointegration processes.
4.1. Cointegration – Granger’s theorem and error-correction model.
4.2 Cointegration – vector error-correction model.

Prerequisites

Not indicated