Forecasting using

12. Advanced methods

OTexts.com/fpp/2/5/

Forecasting using R 1

Rob J Hyndman

Outline

1 Cross-validation

2 Time series with complex seasonality

3 Forecasting proportions

4 Some case studies

5 Forecasting resources

Forecasting using R Cross-validation 2

Cross-validation

Standard cross-validationA more sophisticated version of training/test sets.

Select one observation for test set, and useremaining observations in training set.Compute error on test observation.

Repeat using each possible observation as thetest set.

Compute accuracy measure over all errors.

Does not work normally for time series becausewe cannot use future observations to build amodel.

Forecasting using R Cross-validation 3

Cross-validation

Standard cross-validationA more sophisticated version of training/test sets.

Select one observation for test set, and useremaining observations in training set.Compute error on test observation.

Repeat using each possible observation as thetest set.

Compute accuracy measure over all errors.

Does not work normally for time series becausewe cannot use future observations to build amodel.

Forecasting using R Cross-validation 3

Cross-validation

Standard cross-validationA more sophisticated version of training/test sets.

Select one observation for test set, and useremaining observations in training set.Compute error on test observation.

Repeat using each possible observation as thetest set.

Compute accuracy measure over all errors.

Does not work normally for time series becausewe cannot use future observations to build amodel.

Forecasting using R Cross-validation 3

Cross-validation

Standard cross-validationA more sophisticated version of training/test sets.

Select one observation for test set, and useremaining observations in training set.Compute error on test observation.

Repeat using each possible observation as thetest set.

Compute accuracy measure over all errors.

Does not work normally for time series becausewe cannot use future observations to build amodel.

Forecasting using R Cross-validation 3

Time series cross-validationAssume k is the minimum number of observationsfor a training set.

Select observation k + i for test set, and useobservations at times 1,2, . . . , k + i 1 toestimate model. Compute error on forecast fortime k + i.

Repeat for i = 0,1, . . . , T k where T is totalnumber of observations.

Compute accuracy measure over all errors.

Also called rolling forecasting origin because theorigin (k + i 1) at which forecast is based rollsforward in time.

Forecasting using R Cross-validation 4

Time series cross-validationAssume k is the minimum number of observationsfor a training set.

Select observation k + i for test set, and useobservations at times 1,2, . . . , k + i 1 toestimate model. Compute error on forecast fortime k + i.

Repeat for i = 0,1, . . . , T k where T is totalnumber of observations.

Compute accuracy measure over all errors.

Also called rolling forecasting origin because theorigin (k + i 1) at which forecast is based rollsforward in time.

Forecasting using R Cross-validation 4

Time series cross-validationAssume k is the minimum number of observationsfor a training set.

Select observation k + i for test set, and useobservations at times 1,2, . . . , k + i 1 toestimate model. Compute error on forecast fortime k + i.

Repeat for i = 0,1, . . . , T k where T is totalnumber of observations.

Compute accuracy measure over all errors.

Also called rolling forecasting origin because theorigin (k + i 1) at which forecast is based rollsforward in time.

Forecasting using R Cross-validation 4

Time series cross-validationAssume k is the minimum number of observationsfor a training set.

Select observation k + i for test set, and useobservations at times 1,2, . . . , k + i 1 toestimate model. Compute error on forecast fortime k + i.

Repeat for i = 0,1, . . . , T k where T is totalnumber of observations.

Compute accuracy measure over all errors.

Also called rolling forecasting origin because theorigin (k + i 1) at which forecast is based rollsforward in time.

Forecasting using R Cross-validation 4

Time series cross-validationAssume k is the minimum number of observationsfor a training set.

Select observation k + i for test set, and useobservations at times 1,2, . . . , k + i 1 toestimate model. Compute error on forecast fortime k + i.

Repeat for i = 0,1, . . . , T k where T is totalnumber of observations.

Compute accuracy measure over all errors.

Also called rolling forecasting origin because theorigin (k + i 1) at which forecast is based rollsforward in time.

Forecasting using R Cross-validation 4

Example: Pharmaceutical sales

Forecasting using R Cross-validation 5

Antidiabetic drug sales

Year

$ m

illio

n

1995 2000 2005

510

1520

2530

Example: Pharmaceutical sales

Forecasting using R Cross-validation 5

Log Antidiabetic drug sales

Year

1995 2000 2005

1.0

1.5

2.0

2.5

3.0

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Which of these models is best?1 Linear model with trend and seasonal dummies

applied to log data.

2 ARIMA model applied to log data

3 ETS model applied to original data

Set k = 48 as minimum training set.

Forecast 12 steps ahead based on data to timek + i 1 for i = 1,2, . . . ,156.Compare MAE values for each forecast horizon.

Forecasting using R Cross-validation 6

Example: Pharmaceutical sales

Forecasting using R Cross-validation 7

2 4 6 8 10 12

9010

011

012

013

014

0

horizon

MA

E

LMARIMAETS

Example: Pharmaceutical sales

Forecasting using R Cross-validation 7

2 4 6 8 10 12

9095

100

105

110

115

120

Onestep forecasts

horizon

MA

E

LMARIMAETS

Example: Pharmaceutical salesk

Variations on time series cross validation

Forecasting using R Cross-validation 9

Keep training window of fixed length.xshort

Outline

1 Cross-validation

2 Time series with complex seasonality

3 Forecasting proportions

4 Some case studies

5 Forecasting resources

Forecasting using R Time series with complex seasonality 10

Examples

Forecasting using R Time series with complex seasonality 11

US finished motor gasoline products

Weeks

Tho

usan

ds o

f bar

rels

per

day

1992 1994 1996 1998 2000 2002 2004

6500

7000

7500

8000

8500

9000

9500

Examples

Forecasting using R Time series with complex seasonality 11

Number of calls to large American bank (7am9pm)

5 minute intervals

Num

ber

of c

all a

rriv

als

100

200

300

400

3 March 17 March 31 March 14 April 28 April 12 May

Examples

Forecasting using R Time series with complex seasonality 11

Turkish electricity demand

Days

Ele

ctric

ity d

eman

d (G

W)

2000 2002 2004 2006 2008

1015

2025

TBATS model

TBATSTrigonometric terms for seasonalityBox-Cox transformations for heterogeneityARMA errors for short-term dynamicsTrend (possibly damped)Seasonal (including multiple and

non-integer periods)

Forecasting using R Time series with complex seasonality 12

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

Box-Cox transformation

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

Box-Cox transformation

M seasonal periods

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

Box-Cox transformation

M seasonal periods

global and local trend

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

Box-Cox transformation

M seasonal periods

global and local trend

ARMA error

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

Box-Cox transformation

M seasonal periods

global and local trend

ARMA error

Fourier-like seasonalterms

TBATS model

yt = observation at time t

y()t =

{(yt 1)/ if 6= 0;log yt if = 0.

y()t = `t1 + bt1 +Mi=1

s(i)tmi + dt

`t = `t1 + bt1 + dt

bt = (1 )b+ bt1 + dt

dt =pi=1

idti +qj=1

jtj + t

s(i)t =kij=1

s(i)j,t

Forecasting using R Time series with complex seasonality 13

s(i)j,t = s(i)j,t1 cos

(i)j + s

(i)j,t1 sin

(i)j +

(i)1 dt

s(i)j,t = s(i)j,t1 sin

(i)j + s

(i)j,t1 cos

(i)j +

(i)2 dt

Box-Cox transformation

M seasonal periods

global and local trend

ARMA error

Fourier-like seasonalterms

TBATSTrigonometric

Box-Cox

ARMA

Trend

Seasonal

Examples

fit

Examples

fit

Examples

fit

Outline

1 Cross-validation

2 Time series with complex seasonality

3 Forecasting proportions

4 Some case studies

5 Forecasting resources

Forecasting using R Forecasting proportions 17

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Forecasting proportions

Simple approachUse a logit transformation on proportions:f (u) = log

(u

1u)

Then build model and back-transform the forecasts.More complicated:

Let yt be a binary variable (e.g., water quality abovesome threshold value on day t).Use a generalized linear model with a latentautocorrelated process. e.g., Pr(yt) = f1( + xt + ut)where xt is a vector of predictors and ut is a correlatedprocess.Theory and methodology not well developed and verylittle software available.bild and gee packages allows some simple correlationstructures.

Forecasting using R Forecasting proportions 18

Outline

1 Cross-validation

2 Time series with complex seasonality

3 Forecasting proportions

4 Some case studies

5 Forecasting resources

Forecasting using R Some case studies 19

CASE STUDY 1: Paperware company

Forecasting using R Some case studies 20

Problem: Want forecasts of each ofhundreds of items. Series can bestationary, trended or seasonal. Theycurrently have a large forecastingprogram written in-house but it doesntseem to produce sensible forecasts.They want me to tell them what iswrong and fix it.

CASE STUDY 1: Paperware company

Forecasting using R Some case studies 20

Problem: Want forecasts of each ofhundreds of items. Series can bestationary, trended or seasonal. Theycurrently have a large forecastingprogram written in-house but it doesntseem to produce sensible forecasts.They want me to tell them what iswrong and fix it.

Additional informationProgram written in COBOL making numerical calculationslimited. It is not possible to do any optimisation.

CASE STUDY 1: Paperware company

Forecasting using R Some case studies 20

Problem: Want forecasts of each ofhundreds of items. Series can bestationary, trended or seasonal. Theycurrently have a large forecastingprogram written in-house but it doesntseem to produce sensible forecasts.They want me to tell them what iswrong and fix it.

Additional informationProgram written in COBOL making numerical calculationslimited. It is not possible to do any optimisation.Their programmer has little experience in numericalcomputing.

CASE STUDY 1: Paperware company

Forecasting using R Some case studies 20

Problem: Want forecasts of each ofhundreds of items. Series can bestationary, trended or seasonal. Theycurrently have a large forecastingprogram written in-house but it doesntseem to produce sensible forecasts.They want me to tell them what iswrong and fix it.

Additional informationProgram written in COBOL making numerical calculationslimited. It is not possible to do any optimisation.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 years and thisyears values.(Equivalent to differencing at lag 12 andtaking mean.)

I Same as H except over 6 months.

K I couldnt understand the explanation.

Forecasting using R Some case studies 21

CASE STUDY 2: PBS

Forecasting using R Some case studies 22

CASE STUDY 2: PBS

The Pharmaceutical Benefits Scheme (PBS) isthe Australian government drugs subsidy scheme.

Many drugs bought from pharmacies aresubsidised to allow more equitable access tomodern drugs.

The cost to government is determined by thenumber and types of drugs purchased.Currently nearly 1% of GDP.

The total cost is budgeted based on forecastsof drug usage.

Forecasting using R Some case studies 23

CASE STUDY 2: PBS

The Pharmaceutical Benefits Scheme (PBS) isthe Australian government drugs subsidy scheme.

Many drugs bought from pharmacies aresubsidised to allow more equitable access tomodern drugs.

The cost to government is determined by thenumber and types of drugs purchased.Currently nearly 1% of GDP.

The total cost is budgeted based on forecastsof drug usage.

Forecasting using R Some case studies 23

CASE STUDY 2: PBS

The Pharmaceutical Benefits Scheme (PBS) isthe Australian government drugs subsidy scheme.

Many drugs bought from pharmacies aresubsidised to allow more equitable access tomodern drugs.

The cost to government is determined by thenumber and types of drugs purchased.Currently nearly 1% of GDP.

The total cost is budgeted based on forecastsof drug usage.

Forecasting using R Some case studies 23

CASE STUDY 2: PBS

The Pharmaceutical Benefits Scheme (PBS) isthe Australian government drugs subsidy scheme.

Many drugs bought from pharmacies aresubsidised to allow more equitable access tomodern drugs.

The cost to government is determined by thenumber and types of drugs purchased.Currently nearly 1% of GDP.

The total cost is budgeted based on forecastsof drug usage.

Forecasting using R Some case studies 23

CASE STUDY 2: PBS

Forecasting using R Some case studies 24

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecastedby $800 million.Thousands of products. Seasonal demand.Subject to covert marketing, volatile products,uncontrollable expenditure.Although monthly data available for 10 years,data are aggregated to annual values, and onlythe first three years are used in estimating theforecasts.All forecasts being done with the FORECASTfunction in MS-Excel!

Problem: How to do the forecasting better?

Forecasting using R Some case studies 25

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecastedby $800 million.Thousands of products. Seasonal demand.Subject to covert marketing, volatile products,uncontrollable expenditure.Although monthly data available for 10 years,data are aggregated to annual values, and onlythe first three years are used in estimating theforecasts.All forecasts being done with the FORECASTfunction in MS-Excel!

Problem: How to do the forecasting better?

Forecasting using R Some case studies 25

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecastedby $800 million.Thousands of products. Seasonal demand.Subject to covert marketing, volatile products,uncontrollable expenditure.Although monthly data available for 10 years,data are aggregated to annual values, and onlythe first three years are used in estimating theforecasts.All forecasts being done with the FORECASTfunction in MS-Excel!

Problem: How to do the forecasting better?

Forecasting using R Some case studies 25

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecastedby $800 million.Thousands of products. Seasonal demand.Subject to covert marketing, volatile products,uncontrollable expenditure.Although monthly data available for 10 years,data are aggregated to annual values, and onlythe first three years are used in estimating theforecasts.All forecasts being done with the FORECASTfunction in MS-Excel!

Problem: How to do the forecasting better?

Forecasting using R Some case studies 25

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecastedby $800 million.Thousands of products. Seasonal demand.Subject to covert marketing, volatile products,uncontrollable expenditure.Although monthly data available for 10 years,data are aggregated to annual values, and onlythe first three years are used in estimating theforecasts.All forecasts being done with the FORECASTfunction in MS-Excel!

Problem: How to do the forecasting better?

Forecasting using R Some case studies 25

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecastedby $800 million.Thousands of products. Seasonal demand.Subject to covert marketing, volatile products,uncontrollable expenditure.Although monthly data available for 10 years,data are aggregated to annual values, and onlythe first three years are used in estimating theforecasts.All forecasts being done with the FORECASTfunction in MS-Excel!

Problem: How to do the forecasting better?

Forecasting using R Some case studies 25

CASE STUDY 3: Airline

Forecasting using R Some case studies 26

CASE STUDY 3: Airline

Forecasting using R Some case studies 27

First class passengers: MelbourneSydney

Year

1988 1989 1990 1991 1992 1993

0.0

1.0

2.0

Business class passengers: MelbourneSydney

Year

1988 1989 1990 1991 1992 1993

02

46

8

Economy class passengers: MelbourneSydney

Year

1988 1989 1990 1991 1992 1993

010

2030

CASE STUDY 3: Airline

Forecasting using R Some case studies 27

First class passengers: MelbourneSydney

Year

1988 1989 1990 1991 1992 1993

0.0

1.0

2.0

Business class passengers: MelbourneSydney

Year

1988 1989 1990 1991 1992 1993

02

46

8

Economy class passengers: MelbourneSydney

Year

1988 1989 1990 1991 1992 1993

010

2030

Not the real data!Or is it?

CASE STUDY 3: Airline

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.

Forecasting using R Some case studies 28

CASE STUDY 3: Airline

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.

Forecasting using R Some case studies 28

CASE STUDY 3: Airline

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.

Forecasting using R Some case studies 28

CASE STUDY 3: Airline

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.

Forecasting using R Some case studies 28

Outline

1 Cross-validation

2 Time series with complex seasonality

3 Forecasting proportions

4 Some case studies

5 Forecasting resources

Forecasting using R Forecasting resources 29

Useful resources

Forecasting using R Forecasting resources 30

Organization: International Institute

of Forecasters.

Conferences: International

Symposium onForecasting. June2014, Rotterdam.

Journals: International Journal

of Forecasting Foresight

Useful resources

Forecasting using R Forecasting resources 30

Organization: International Institute

of Forecasters.

Conferences: International

Symposium onForecasting. June2014, Rotterdam.

Journals: International Journal

of Forecasting Foresight

Useful resources

Forecasting using R Forecasting resources 30

Organization: International Institute

of Forecasters.

Conferences: International

Symposium onForecasting. June2014, Rotterdam.

Journals: International Journal

of Forecasting Foresight

THE INTERNATIONAL JOURNAL OF APPLIED FORECASTINGSpring 2013 Issue 29

THE INTERNATIONAL JOURNAL OF APPLIED FORECASTING

5 Forecasting revenue in Professional Service Companies

14 Forecast value added: A Reality Check on Forecasting Practices

19 s&oP and Financial Planning

26 cPFr: Collaboration Beyond S&OP

39 Progress in Forecasting rare events

50 Review of "global trends 2030: alternative Worlds"

Useful resources

Forecasting using R Forecasting resources 30

Organization: International Institute

of Forecasters.

Conferences: International

Symposium onForecasting. June2014, Rotterdam.

Journals: International Journal

of Forecasting Foresight

THE INTERNATIONAL JOURNAL OF APPLIED FORECASTINGSpring 2013 Issue 29

THE INTERNATIONAL JOURNAL OF APPLIED FORECASTING

5 Forecasting revenue in Professional Service Companies

14 Forecast value added: A Reality Check on Forecasting Practices

19 s&oP and Financial Planning

26 cPFr: Collaboration Beyond S&OP

39 Progress in Forecasting rare events

50 Review of "global trends 2030: alternative Worlds"

Links to all of the above atwww.forecasters.org.

Final comments

Revolution Analytics will send you coursecompletion certificates.Please vote on the students who have mademost contribution to class. You will receive avoting form by email. I will announce theresults on Piazza.I will continue to answer questions on Piazzauntil Christmas.A discussion forum for forecasting planned forOTexts. Should be launched in early 2014.The FPP book will be available in print onAmazon by February 2014. Maybe a kindleversion will follow.

Forecasting using R Forecasting resources 31

Final comments

Revolution Analytics will send you coursecompletion certificates.Please vote on the students who have mademost contribution to class. You will receive avoting form by email. I will announce theresults on Piazza.I will continue to answer questions on Piazzauntil Christmas.A discussion forum for forecasting planned forOTexts. Should be launched in early 2014.The FPP book will be available in print onAmazon by February 2014. Maybe a kindleversion will follow.

Forecasting using R Forecasting resources 31

Final comments

Revolution Analytics will send you coursecompletion certificates.Please vote on the students who have mademost contribution to class. You will receive avoting form by email. I will announce theresults on Piazza.I will continue to answer questions on Piazzauntil Christmas.A discussion forum for forecasting planned forOTexts. Should be launched in early 2014.The FPP book will be available in print onAmazon by February 2014. Maybe a kindleversion will follow.

Forecasting using R Forecasting resources 31

Final comments

Revolution Analytics will send you coursecompletion certificates.Please vote on the students who have mademost contribution to class. You will receive avoting form by email. I will announce theresults on Piazza.I will continue to answer questions on Piazzauntil Christmas.A discussion forum for forecasting planned forOTexts. Should be launched in early 2014.The FPP book will be available in print onAmazon by February 2014. Maybe a kindleversion will follow.

Forecasting using R Forecasting resources 31

Final comments

Revolution Analytics will send you coursecompletion certificates.Please vote on the students who have mademost contribution to class. You will receive avoting form by email. I will announce theresults on Piazza.I will continue to answer questions on Piazzauntil Christmas.A discussion forum for forecasting planned forOTexts. Should be launched in early 2014.The FPP book will be available in print onAmazon by February 2014. Maybe a kindleversion will follow.

Forecasting using R Forecasting resources 31

Cross-validationTime series with complex seasonalityForecasting proportionsSome case studiesForecasting resources