# Introduction

**Topics:**Regression analysis, Trend estimation, Time series

**Pages:**10 (461 words)

**Published:**February 25, 2013

Forecasting

Reza

Ramezan

Introduction

Examples

STAT 443: Forecasting

Fall 2012

Reza Ramezan

rramezan@uwaterloo.ca

M3 3144

STAT 443:

Forecasting

Timetable

Reza

Ramezan

Introduction

Examples

The following is a tentative schedule:

Week

Jan. 07

Jan. 14

Jan. 21

Jan. 28

Feb. 04

Feb. 11

Feb. 18

Feb. 25

Mar. 04

Mar. 11

Mar. 18

Mar. 25

Apr. 01

Course Material

Introduction

Regression

Regression

Smoothing / linear processes

linear processes

Case study

Reading Week

Box-Jenkins Models

Box-Jenkins / Case study

Algorithms

Algorithms / Forecasting

Forecasting / Case study

ARCH / GARCH models

Deadlines

Assignment 1 (4th Feb.)

Midterm (15th Feb.)

Assignment 2 (15th Mar.)

Assignment 3 (8th Apr.)

STAT 443:

Forecasting

R

Reza

Ramezan

Introduction

Examples

• One of the aims of the course is to become ﬂuent in the

computation associated with forecasting

• In this course R will be the language used for

computation

• Assignments will need coding in R

• In Exams you will be expected to interpret R output

STAT 443:

Forecasting

The Candy Rule

Reza

Ramezan

Introduction

Examples

The candy rule states that:

• If you answer questions about the course material I ask

during lectures, or ask good questions, you get candy.

• If I forget to give you one, you STAND UP FOR IT.

There are no stupid questions to ask. This is a class to

learn. If you don’t know it, ask it.

STAT 443:

Forecasting

Forecasting

Reza

Ramezan

Introduction

Examples

• Why forecast?

• Why understand uncertainty of forecast?

• What information to use in forecast?

STAT 443:

Forecasting

Example: Accidental deaths

Reza

Ramezan

Introduction

Examples

• Many examples are time series– forecast what

happens in future

• Example: monthly number of accidental deaths in USA-

1973-79

• Look at structure of data

STAT 443:

Forecasting

Example: Accidental deaths

Reza

Ramezan

Introduction

Examples

9000 10000

8000

7000

USAccDeaths

Accidental deaths

1973

1974

1975

1976

Time

1977

1978

1979

STAT 443:

Forecasting

Example: Accidental deaths

Reza

Ramezan

Decomposition of additive time series

observed

9000

8400 8800 9200 9600

7000

trend

seasonal

1000

0

−400

random

400

−1500

0

Examples

11000

Introduction

1973

1974

1975

1976

Time

1977

1978

1979

STAT 443:

Forecasting

Example: Denmark births

Reza

Ramezan

Introduction

Examples

7000

6000

5000

4000

birth

8000

9000

Monthly Births in Denmark

1900

1920

1940

1960

Time

1980

STAT 443:

Forecasting

Example: Denmark births

Reza

Ramezan

Introduction

Decomposition of additive time series

8000

6000

7000

0 200

500

0

−500

random

−400

seasonal

600

5000

trend

4000

observed

Examples

1900

1920

1940

1960

Time

1980

STAT 443:

Forecasting

Reza

Ramezan

General approach to modelling

Introduction

Examples

• Plot series and look for trend, seasonality, sharp

change in behaviour, and outlying observations

• remove trend and seasonal components to get

stationary residuals

• choose a model for residuals

• forecasting achieved by forecasting residuals then

adding back trend and seasonal parts.

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