# Introduction

Topics: Regression analysis, Trend estimation, Time series Pages: 10 (461 words) Published: February 25, 2013
STAT 443:
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
Box-Jenkins Models
Box-Jenkins / Case study
Algorithms
Algorithms / Forecasting
Forecasting / Case study
ARCH / GARCH models

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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