# Wroclaw Lecture

### Sylabus:

**Lecture given at Wroclaw University of Technology**

1. Stationary Linear and Nonlinear Time Series

1.1 Introduction

1.2 Notions and Examples of Stationary Time Series

1.3 Linear Processes

1.4 ARMA Processes

1.5 The CLT for Linear Processes

1.6 GARCH Processes

1.7 Optimal Prediction

2. Limit Theorems for Dependent Time Series

2.1 Introduction

2.2 Law of Large Numbers

2.3 A General Central Limit Theorem

2.4 Mixing Processes

2.5 The Central Limit Theorem for Mixing Processes

2.6 Asymptotics for the Autocovariance Function

3. Change-Points and Detection

3.1 Introduction

3.2 The Shewhart Chart

3.3 Off-Line Methods

3.4 Asymptotics of (Weighted) CUSUMS

3.5 On-Line Methods

3.6 Kernel Control Charts Under Local Alternatives

Participants can download the handwritten Lecture Notes. Please contact me for the link.

A. Steland