econ2209 week 1

Business Forecasting ECON2209

Slides 01

Lecturer: Minxian Yang

BF-01 1 my, School of Economics, UNSW

About BF

• Staff – Lecturer: Dr Minxian Yang, ASB452, 93853353, Fri 10-1 – Tutors: see Tutorial Contacts

• Prerequisite, required textbook & software – Requires ECON1203, required by ECON3206 – Elements of Forecasting, 4th Edition, by F. X. Diebold – Software: Eviews in Labs: Mon 9-11 (QG021) & Tue 10-12 (MAT211)

• Assessment – Class participation = 3% – 2 Class-tests = 20 % (10% each) – 1 Project = 17% (due week 12) – Final exam = 60%

BF-01 my, School of Economics, UNSW 2

Submit the Project to Your tutor before or at the beginning of your tutorial!

No one else will accept your submission.

Tutorials in Weeks 3 will be held in labs.

About BF

• Objective of BF – Foster skills for analysing time series data and capabilities of applying models, principles, techniques

in a business environment • Coverage

– Focus mainly on uni-variate time series models, which is the foundation for complex models.

– Will touch upon multi-variate time series models. • Your knowledge in BF is a big plus in job market

– Banks, financial institutions, government agencies, consultancy firms: forecasters are valuable!


About BF

• Course resources – Course website: announcements, course outline, lecture slides, tutorial

questions/answers, assignment, data, Eviews code – Library open (close) reserve – Discuss course material in consultation (not by email)

• Read Course Outline carefully – Submission of project: your tutor, in time – Assessment: work, travel, wedding, … cannot be excuses – Class participation: 80% attendance expected, be active

• Make up your mind before the census day


Ch.1 Introduction

Introduction • Forecast

A statement about the future values of a variable, based on current knowledge

• Purpose of business forecasting To assist decision making e.g. – Forecast sales/revenue for investment decisions – Forecast GNP/inflation/population for policy decisions – Forecast the risks of assets for risk management – Analyse what forecasts inflation


Ch.1 Introduction

• Essence of forecasting e.g. Try to predict the next number a) 2, 4, ?. b) 2, 4, 8, ?. c) 2, 4, 8, 14, ?.

– How did we predict?

• Inspect data; (gather information) • Find a pattern; (fit a model) • Predict according to the pattern. (extrapolate model)


Ch.1 Introduction

• Essence of forecasting Predict by exploiting the pattern in data


data Pattern & model prediction

Economists are better at predicting the past than the future.

- Joseph E. Stiglitz

Better data → More info about pattern → Better model → Better prediction.

Ch.1 Introduction

• Uncertainty – Consider USD/AUD exchange rate.

No hope to perfectly predict the rate at 5pm, 1/April. – Similarly, it is impossible to perfectly predict

• the sales/revenue of David Jones, or • the Australian inflation/GDP-growth.

– Because there are more than one possible outcome! BF-01 my, School of Economics, UNSW 8

Ch.1 Introduction

• Uncertainty – Forecasting under uncertainty is challenging:

• Many possible outcomes (randomness): Perfect prediction is impossible. Forecast errors must be allowed.

– Sources of uncertainty: • Outcomes are affected by human (re)actions, • Also by many small factors that are hard to pin down.

– Distributional regularities exist. • Central tendency: Extreme values are rare. • Dependence on the past: Tomorrow depends on today.

Regularities can be exploited to construct forecasts.

– Major task: find distributional regularities (patterns).


Ch.1 Introduction

• Uncertainty – BF is about finding patters in data and using patters to

extrapolate: • If these patters persist, then the variables will behave with these patters in the future.

– We do not have a “magic crystal ball”. Forecasting is not “fortune telling”! Forecasting carries errors. We try to minimise errors by exploiting available information.


Ch.1 Introduction

• Forecasting Model A good model captures major patterns in data.

eg. Sales = Regular Sales + Disturbance


forecast object, with past observations

pattern, which is summarised by a model

“unpredictable”, with distributional regularities

Ch.1 Introduction

• Topics to be covered – Framework of business forecasting

• Forecast environment, loss function, info set, horizon, parsimony principle

– Statistical techniques • Time series description, classical decomposition, trend and

seasonality, ARMA models, estimation/testing, VAR models

– Application emphasised • Data description (statistical/graphical), model selection,

interpretation of results, forecast statement • Implementation of models, EViews

– End of Ch.1


Ch.3 Basics of Forecasting

Basic Concepts of Forecasting • Contents

– Decision environment – Forecast objects – Forecast horizon – Information set – Loss function – Forecast statement – Parsimony principle – Conditioning on information set



Basic Concepts of Forecasting • Decision environment (know the role of forecasting)

– Forecasts are used to support decision making. – Important to know the decision making process and

where forecasts fit in. eg1. To decide the rate, Reserve Bank needs to know the

expected future inflation, employment, and GDP when the rate does not change and when the rate changes.

eg2. To decide investments in human resource and infrastructure,

businesses need to know the expected future demand for their products.



• Forecast object This is usually a future event of interest.

– Forecast outcome: quantitative/qualitative

eg. Winner of the next election (qualitative) Next quarter’s GDP growth rate (quantitative)

– Forecast timing

eg. When will the next election be held? When will GDP growth rate become negative?



• Forecast horizon This is the number of periods to the target date.

– h-Step ahead forecast eg. 4-quarter-ahead forecast of GDP growth rate: 0.6% (quarterly)

– h-Step ahead extrapolation (a sequence of forecasts) eg. 4-quarter-ahead extrapolation of GDP growth rate: 0.7%, 0.9%, 0.8%, 0.6% (quarterly)


f.o. q1 q2 q3 q4

0.6 0.7 0.9 0.8


• Information set This includes historical data relevant to forecast objects.

– The quality of forecasts depends on • The quality and quantity of data • The skills and experience in exploiting data

– Notation


.explain touseful covariate a is where

,...,,;,...,,

is at set info The interest. of variable thebe Let

2121t

yx

xxxyyy

ty

tt=ΩEverything

useful & observed at Date t


• Loss function It measures the “badness” of forecasts.

– Notation


).()ˆ(usually function, loss :)ˆ,(error;forecast :ˆ

; for forecast :ˆforecast; be toe variabl :

eLyyLLyyLyye

yyy

=−=−=


• Loss function – Required properties of L(e)

• L(0) = 0; (no loss with perfect prediction)

• L(e) is increasing in |e|; (further away from zero the error, larger the loss)

• L(e) is continuous; (small change in error leads to small change in loss)

BF-01 my, School of Economics, UNSW 19 e0

L(e)

Asymmetry under-forecast may incur more costs.


• Loss function – Symmetric loss functions e.g.

• Quadratic: L(e) = e2 (most commonly used)

• Absolute: L(e) = |e|

– Asymmetric/discrete loss functions e.g.

– Loss L is random (as y is random). How do we measure the quality of forecasts?


= otherwise ,1

direction same in the move ˆ and if ,0)ˆ,(

yyyyL


• Loss function – Expected loss We average L using the distribution of y:

It measures the badness of forecasts on average.

e.g. Assume y = 0 or 1 with probability 0.5. The loss function is quadratic. For predictor = 0, the expected loss is 0.5. For predictor = 0.5, the expected loss is 0.25.

– Optimal forecast Choose to minimise expected L for a given info set.


L(e) = (y-.5)2

EL(e) = (1-.5)2(.5) + (0-.5)2(.5)

Expectation: average weighted

by probability

).ˆ,(E loss expected yyL=

y

2y1y


• Loss function – Mean squared forecast error (quadratic loss)

where

– Optimal forecast under MSFE MSFE is minimised by choosing e.g. In previous example: is optimal under MSFE.


)ˆ(E)(E

)ˆ(EMSFE

22

2

yyyy

yy

−+−=

−=

.Eˆ* yyy ==

.E yy =

2y

We can only choose y-hat.

‘E’ should be evaluated relative to given info set, ie, conditional expectation.


• Forecast statement This is the presentation of forecasts, which depends on the decision environment. – Point forecast (simplest) It is a single-value prediction. eg. 4th quarter GNP growth “point forecast” = 0.6%

– Interval forecast It is an interval with a coverage probability. eg. 4th quarter GDP growth “90%-interval-forecast” = [0.4%, 0.8%]

– Distribution forecast (most sophisticated) It is a distribution about the future y. eg. 4th quarter GDP growth “distribution forecast” is N[0.6%, (0.2%)2].


Prob(future y is in the interval) = 0.9


• Parsimony principle – A model is a simplified description of reality. It should capture the major features of data. eg. Data y = Australian annual GDP Model-1: y = a + b∙Year + error Model-2: y = a + b∙Year + c∙Year2 + error


1970 1980 1990 2000 2010

400

600

800

1000

1200

Year

GD

P ($

billi

on)


• Parsimony principle – Simple model

• It emphasises important features and ignores many unimportant details.

• Easy to implement • Experience: simple models often do well in forecasting.

– Complex model • It captures more details of data. But details may blur

important features. • More details could contain more noises. • Harder to implement, carries more estimation errors.


forecast error estimation error

description error


• Parsimony principle – Parsimony principle Other things being equal, simpler models are preferred.

eg.

Unless Model (ii) has proven better, we will use Model (i)


USD/AUD exchange rate:

(i)

(ii)

;ˆ 1 TT yy =+

.ˆ ˆ 1 TTT xyy θ+=+


• Conditioning on information set eg. Predict at Feb/82 Predict at Feb/88 Predict at Feb/94

– Different info set lead to different forecasts.


Unemployment

0

200

400

600

800

1000

1200

Feb-78

Feb-80

Feb-82

Feb-84

Feb-86

Feb-88

Feb-90

Feb-92

Feb-94

Feb-96

Feb-98

'000


• Summary – Forecasts are made to support decision making – Essence of forecasting – Future uncertainty – Concepts:

• forecast object • forecast horizon • information set • loss function • forecast statement

– Parsimony principle – Forecasts are based on available information set


Know your purpose Know your data know your tools

econ2209 week 1

Documents

data bf

model bf

school of economics

introduction introduction

minxian yang bf

bf staff lecturer

forecasts inflation

census day bf