Automatic time series forecasting

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Transcript of Automatic time series forecasting

  • Rob J Hyndman

    Automatic time seriesforecasting

  • Outline

    1 Motivation

    2 Forecasting competitions

    3 Forecasting the PBS

    4 Exponential smoothing

    5 ARIMA modelling

    6 Automatic nonlinear forecasting?

    7 Time series with complex seasonality

    8 Recent developments

    Automatic time series forecasting Motivation 2

  • Motivation

    Automatic time series forecasting Motivation 3

  • Motivation

    Automatic time series forecasting Motivation 3

  • Motivation

    Automatic time series forecasting Motivation 3

  • Motivation

    Automatic time series forecasting Motivation 3

  • Motivation

    Automatic time series forecasting Motivation 3

  • Motivation

    1 Common in business to have over 1000products that need forecasting at least monthly.

    2 Forecasts are often required by people who areuntrained in time series analysis.

    Specifications

    Automatic forecasting algorithms must:

    determine an appropriate time series model;

    estimate the parameters;

    compute the forecasts with prediction intervals.

    Automatic time series forecasting Motivation 4

  • Motivation

    1 Common in business to have over 1000products that need forecasting at least monthly.

    2 Forecasts are often required by people who areuntrained in time series analysis.

    Specifications

    Automatic forecasting algorithms must:

    determine an appropriate time series model;

    estimate the parameters;

    compute the forecasts with prediction intervals.

    Automatic time series forecasting Motivation 4

  • Example: Asian sheep

    Automatic time series forecasting Motivation 5

    Numbers of sheep in Asia

    Year

    milli

    ons

    of s

    heep

    1960 1970 1980 1990 2000 2010

    250

    300

    350

    400

    450

    500

    550

  • Example: Asian sheep

    Automatic time series forecasting Motivation 5

    Automatic ETS forecasts

    Year

    milli

    ons

    of s

    heep

    1960 1970 1980 1990 2000 2010

    250

    300

    350

    400

    450

    500

    550

  • Example: Cortecosteroid sales

    Automatic time series forecasting Motivation 6

    Monthly cortecosteroid drug sales in Australia

    Year

    Tota

    l scr

    ipts

    (millio

    ns)

    1995 2000 2005 2010

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4

  • Example: Cortecosteroid sales

    Automatic time series forecasting Motivation 6

    Automatic ARIMA forecasts

    Year

    Tota

    l scr

    ipts

    (millio

    ns)

    1995 2000 2005 2010

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4

  • Outline

    1 Motivation

    2 Forecasting competitions

    3 Forecasting the PBS

    4 Exponential smoothing

    5 ARIMA modelling

    6 Automatic nonlinear forecasting?

    7 Time series with complex seasonality

    8 Recent developments

    Automatic time series forecasting Forecasting competitions 7

  • Makridakis and Hibon (1979)

    Automatic time series forecasting Forecasting competitions 8

  • Makridakis and Hibon (1979)

    Automatic time series forecasting Forecasting competitions 8

  • Makridakis and Hibon (1979)

    This was the first large-scale empirical evaluation oftime series forecasting methods.

    Highly controversial at the time.

    Difficulties:8 How to measure forecast accuracy?8 How to apply methods consistently and objectively?8 How to explain unexpected results?

    Common thinking was that the moresophisticated mathematical models (ARIMAmodels at the time) were necessarily better.If results showed ARIMA models not best, itmust be because analyst was unskilled.Automatic time series forecasting Forecasting competitions 9

  • Makridakis and Hibon (1979)

    I do not believe that it is very fruitful to attempt toclassify series according to which forecasting techniquesperform best. The performance of any particulartechnique when applied to a particular series dependsessentially on (a) the model which the series obeys;(b) our ability to identify and fit this model correctly and(c) the criterion chosen to measure the forecastingaccuracy. M.B. Priestley

    . . . the paper suggests the application of normal scientificexperimental design to forecasting, with measures ofunbiased testing of forecasts against subsequent reality,for success or failure. A long overdue reform.

    F.H. Hansford-Miller

    Automatic time series forecasting Forecasting competitions 10

  • Makridakis and Hibon (1979)

    I do not believe that it is very fruitful to attempt toclassify series according to which forecasting techniquesperform best. The performance of any particulartechnique when applied to a particular series dependsessentially on (a) the model which the series obeys;(b) our ability to identify and fit this model correctly and(c) the criterion chosen to measure the forecastingaccuracy. M.B. Priestley

    . . . the paper suggests the application of normal scientificexperimental design to forecasting, with measures ofunbiased testing of forecasts against subsequent reality,for success or failure. A long overdue reform.

    F.H. Hansford-Miller

    Automatic time series forecasting Forecasting competitions 10

  • Makridakis and Hibon (1979)

    Modern man is fascinated with the subject offorecasting W.G. Gilchrist

    It is amazing to me, however, that after all thisexercise in identifying models, transforming and soon, that the autoregressive moving averages comeout so badly. I wonder whether it might be partlydue to the authors not using the backwardsforecasting approach to obtain the initial errors.

    W.G. Gilchrist

    Automatic time series forecasting Forecasting competitions 11

  • Makridakis and Hibon (1979)

    Modern man is fascinated with the subject offorecasting W.G. Gilchrist

    It is amazing to me, however, that after all thisexercise in identifying models, transforming and soon, that the autoregressive moving averages comeout so badly. I wonder whether it might be partlydue to the authors not using the backwardsforecasting approach to obtain the initial errors.

    W.G. Gilchrist

    Automatic time series forecasting Forecasting competitions 11

  • Makridakis and Hibon (1979)

    I find it hard to believe that Box-Jenkins, if properlyapplied, can actually be worse than so many of thesimple methods C. Chatfield

    Why do empirical studies sometimes give differentanswers? It may depend on the selected sample oftime series, but I suspect it is more likely to dependon the skill of the analyst and on their individualinterpretations of what is meant by Method X.

    C. Chatfield

    . . . these authors are more at home with simpleprocedures than with Box-Jenkins. C. Chatfield

    Automatic time series forecasting Forecasting competitions 12

  • Makridakis and Hibon (1979)

    I find it hard to believe that Box-Jenkins, if properlyapplied, can actually be worse than so many of thesimple methods C. Chatfield

    Why do empirical studies sometimes give differentanswers? It may depend on the selected sample oftime series, but I suspect it is more likely to dependon the skill of the analyst and on their individualinterpretations of what is meant by Method X.

    C. Chatfield

    . . . these authors are more at home with simpleprocedures than with Box-Jenkins. C. Chatfield

    Automatic time series forecasting Forecasting competitions 12

  • Makridakis and Hibon (1979)

    I find it hard to believe that Box-Jenkins, if properlyapplied, can actually be worse than so many of thesimple methods C. Chatfield

    Why do empirical studies sometimes give differentanswers? It may depend on the selected sample oftime series, but I suspect it is more likely to dependon the skill of the analyst and on their individualinterpretations of what is meant by Method X.

    C. Chatfield

    . . . these authors are more at home with simpleprocedures than with Box-Jenkins. C. Chatfield

    Automatic time series forecasting Forecasting competitions 12

  • Makridakis and Hibon (1979)

    There is a fact that Professor Priestley must accept:empirical evidence is in disagreement with histheoretical arguments. S. Makridakis & M. Hibon

    Dr Chatfield expresses some personal views aboutthe first author . . . It might be useful for Dr Chatfieldto read some of the psychological literature quotedin the main paper, and he can then learn a littlemore about biases and how they affect priorprobabilities. S. Makridakis & M. Hibon

    Automatic time series forecasting Forecasting competitions 13

  • Makridakis and Hibon (1979)

    There is a fact that Professor Priestley must accept:empirical evidence is in disagreement with histheoretical arguments. S. Makridakis & M. Hibon

    Dr Chatfield expresses some personal views aboutthe first author . . . It might be useful for Dr Chatfieldto read some of the psychological literature quotedin the main paper, and he can then learn a littlemore about biases and how they affect priorprobabilities. S. Makridakis & M. Hibon

    Automatic time series forecasting Forecasting competitions 13

  • Consequences of M&H (1979)

    As a result of this paper, researchers started to:

    consider how to automate forecasting methods;

    study what methods give the best forecasts;

    be aware of the dangers of over-fitting;

    treat forecasting as a different problem fromtime series analysis.

    Makridakis & Hibon followed up with a newcompetition in 1982:

    1001 seri