FPP 1. Getting started

Applied forecasting forbusiness and economics

1. Getting startedOTexts.com/fpp/1/

ETC2450

Outline

1 A brief history of forecasting

2 Types of data

3 Forecasting models

4 Some case studies

5 The statistical forecasting perspective

6 Introduction to R

1. Getting started A brief history of forecasting 2

Standard business practice today

“What-if scenarios” based on assumed andfixed future conditions.

Highly subjective.

Not replicable or testable.

No possible way of quantifying probabilisticuncertainty.

Lack of uncertainty statements leads to falsesense of accuracy.

Largely guesswork.

Is this any better than a sheep’s liver orhallucinogens?


The rise of stochastic models


1959 exponential smoothing (Brown)1970 ARIMA models (Box, Jenkins)1980 VAR models (Sims, Granger)1980 non-linear models (Granger, Tong, Hamilton,

Teräsvirta, . . . )1982 ARCH/GARCH (Engle, Bollerslev)1986 neural networks (Rumelhart)1989 state space models (Harvey, West, Harrison)1994 nonparametric forecasting (Tjøstheim,

Härdle, Tsay,. . . )2002 exponential smoothing state space models

(Snyder, Hyndman, Koehler, Ord)

Advantages of stochastic models

Based on empirical data

Computable

Replicable

Testable

Objective measure of uncertainty

Able to compute prediction intervals


Outline


2 Types of data


4 Some case studies


6 Introduction to R

1. Getting started Types of data 6

Types of data

Most forecasting problems use either

1 Time series data (collected at regular intervalsover time)

2 Cross-sectional data are for a single point intime.

Time series examples

Daily IBM stock pricesMonthly rainfallAnnual Google profitsQuarterly Australian beer production

Forecasting is estimating how the sequenceof observations will continue into the future.


Australian beer production


Year

meg

alite

rs

1995 2000 2005 2010

400

450

500

Types of data

Cross-sectional examples

House prices for all houses sold in 2009 inClayton. We are interested in predicting theprice of a house not in our data set using housecharacteristics: position, no. bedrooms, age,etc.

Fuel economy data for a range of 2009 modelcars. We are interested in predicting the carbonfootprint of a vehicle not in our data set usinginformation such as the size of the engine andthe fuel efficiency of the car.


Vehicle carbon footprints

Model Cyl. Litres City Highway CarbonMPG MPG footprint

Chevrolet Aveo 4 1.6 25.0 34 6.6Chrysler PT Cruiser 4 2.4 19.0 24 8.7Dodge Avenger 4 2.4 21.0 30 7.7Ford Escape FWD 4 2.5 20.0 28 8.0Ford Ranger Pickup 2WD 4 2.3 19.0 24 8.7GMC Canyon 2WD 4 2.9 18.0 24 9.2Honda Accord 4 2.4 21.0 30 7.7Honda Civic 4 1.8 25.0 36 6.3. . .

All vehicles with automatic transmission and usingregular fuel. How to predict carbon footprint (tonsof CO2 per year) for other vehicles?


Outline


2 Types of data


4 Some case studies


6 Introduction to R

1. Getting started Forecasting models 11

Time series models

Time series models use only information on thevariable to be forecast

EDt+1 = f(EDt,EDt−1,EDt−2,EDt−3, . . . , error),

where t is time and ED is electricity demand.

e.g., ARIMA models and exponential smoothing.

Useful when predictor variables not known or measured.

Useful if prediction of predictor variables difficult.

Doesn’t lead to much understanding of system


Cross-sectional models

Cross-sectional models assume that variable tobe forecast is affected by one or more otherpredictor variables.

ED = f(current temperature, GDP,

population, time of day, day of week,

error).

e.g., regression models.


Mixed models

Mixed model

EDt+1 = f(EDt, current temperature,

time of day, day of week, error).

e.g., dynamic regression models, panel datamodels, longitudinal models, transfer functionmodels


Outline


2 Types of data


4 Some case studies


6 Introduction to R

1. Getting started Some case studies 15

CASE STUDY 1: Paperware company

Client: large company manufacturing disposable tableware.Problem: They want forecasts of each of hundreds of items.Series can be stationary, trended or seasonal. They currentlyhave a large forecasting program written in-house but itdoesn’t seem to produce sensible forecasts. They want me totell them what is wrong and fix it.Additional information

The program is written in COBOL making numericalcalculations limited. It is not possible to do anyoptimisation.

Their programmer has little experience in numericalcomputing.

They employ no statisticians and want the program toproduce forecasts automatically.


CASE STUDY 1: Paperware company

Methods currently used

A 12 month average

C 6 month average

E straight line regression over last 12 months

G straight line regression over last 6 months

H average slope between last year’s and this year’svalues.(Equivalent to differencing at lag 12 and takingmean.)

I Same as H except over 6 months.

K I couldn’t understand the explanation.


CASE STUDY 2: PBS

Client: Federal governmentProblem: Develop methodology to forecast annualbudget for Pharmaceutical Benefit Scheme (around$7billion).

Additional informationAt the time, they used Excel to fit a trend linethrough three observations from about 10years earlier.All calculations must be done in Excel.They have under-estimated expenditure bynearly $1billion in last two years.


CASE STUDY 3: Car fleet company

Client: One of Australia’s largest car fleetcompaniesProblem: how to forecast resale value of vehicles?How should this affect leasing and sales policies?

Additional information

They can provide a large amount of data onprevious vehicles and their eventual resalevalues.

The resale values are currently estimated by agroup of specialists. They see me as a threatand do not cooperate.


CASE STUDY 4: Airline

Client: Ansett.Problem: how to forecast passenger traffic onmajor routes.

Additional information

They can provide a large amount of data onprevious routes.

Traffic is affected by school holidays, specialevents such as the Grand Prix, advertisingcampaigns, competition behaviour, etc.

They have a highly capable team of people whoare able to do most of the computing.


Outline


2 Types of data


4 Some case studies


6 Introduction to R

1. Getting started The statistical forecasting perspective 21

Statistical forecasting

Thing to be forecast: a random variable, yi.

Forecast distribution: If I is all observations,then yi|I means “the random variable yi givenwhat we know in I”.

The “point forecast” is the mean (or median) ofyi|IThe “forecast variance” is var[yi|I]A prediction interval or “interval forecast” is arange of values of yi with high probability.

With time series, yt|t−1 = yt|{y1, y2, . . . , yt−1}.yT+h|T = E[yT+h|y1, . . . , yT] (an h-step forecasttaking account of all observations up to time T).

1. Getting started The statistical forecasting perspective 22

Outline


2 Types of data


4 Some case studies


6 Introduction to R

1. Getting started Introduction to R 23

Australian GDPausgdp <- ts(scan("gdp.dat"),frequency=4,

start=1971+2/4)Class: tsPrint and plotting methods available.

> ausgdpQtr1 Qtr2 Qtr3 Qtr4

1971 4612 46511972 4645 4615 4645 47221973 4780 4830 4887 49331974 4921 4875 4867 49051975 4938 4934 4942 49791976 5028 5079 5112 51271977 5130 5101 5072 50691978 5100 5166 5244 53121979 5349 5370 5388 53961980 5388 5403 5442 5482


Australian GDP


Time

ausg

dp

1975 1980 1985 1990 19954500

5000

5500

6000

6500

7000

7500 > plot(ausgdp)

Residential electricity sales

> elecsalesTime Series:Start = 1989End = 2008Frequency = 1[1] 2354.34 2379.71 2318.52 2468.99 2386.09 2569.47[7] 2575.72 2762.72 2844.50 3000.70 3108.10 3357.50

[13] 3075.70 3180.60 3221.60 3176.20 3430.60 3527.48[19] 3637.89 3655.00


Credit scores

credit <- read.table("bankdata.csv",header=TRUE, sep=",")

Class: data.frame

Print and plotting methods available.> head(credit)

score savings income fte single time.address time.employed3282 39.39981 0.012 111.168 TRUE FALSE 27 85018 51.79090 0.654 56.400 TRUE FALSE 29 338317 32.81704 0.748 36.744 TRUE TRUE 2 1613766 57.30881 0.616 55.992 TRUE TRUE 14 72325 37.17328 4.132 62.040 TRUE TRUE 2 1413573 33.68829 0.000 43.752 TRUE TRUE 7 7


Credit scores


score

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0 40 80

040

80

time.employed

plot(credit)

Class package

> library(fpp)This loads:

some data for use in examples and exercisesforecast package (for forecasting functions)tseries package (for a few time seriesfunctions)fma package (for lots of time series data)expsmooth package (for more time seriesdata)lmtest package (for some regressionfunctions)


FPP 1. Getting started

Education

Transcript of FPP 1. Getting started