Lecture 1: Introduction to Forecasting

Transcription

1 NATCOR: Forecasting & Predictive Analytics Lecture 1: Introduction to Forecasting Professor John Boylan Lancaster Centre for Forecasting Department of Management Science

2 Leading research centre in applied forecasting in Europe Training courses and tutorials Systems auditing and enhancement Consultancy and research proects Knowledge-transfer partnerships MSc summer proects PhD research partnerships Prof John Boylan Dr Sven Crone Prof Robert Fildes Dr Dr Nikolaos Kourentzes Dr Dr Nicos Nicos Pavlidis Pavlidis Ivan Svetunkov Slide 2

3 Academic Timetable Session Day Time Lecturer Lecture 1 Monday John Introduction 2 Monday John Exponential Smoothing 3 Tuesday Nikos ARIMA Models 4 Tuesday Nikos Model Evaluation 5 Tuesday Sven Data Mining 6 Tuesday Robert Guest Speaker and Discussion 7 Wednesday Sven Predictive Analytics 8 Wednesday Robert Regression Modelling (1) 9 Wednesday Robert Regression Modelling (2) 10 Wednesday John Assessment & Close Slide 3

4 Complementary Reading Principles of Business Forecasting (Ord & Fildes, 2013, Cengage) Forecasting: Principles and Practice (Hyndman & Athanasopoulos) Slide 4

5 What do Organisations need to Forecast? Internal Sales Revenue Sales Volume Effect of price Effect of promotion Costs Costs of materials Costs of labour Effect of volume External Total market Market share Interest rates Exchange rates New products & processes Diffusion rate Demographics Wealth profile Slide 5 and many more variables.

6 What is a forecast? A statement about what will happen in the future, based on information that is available now. Information may include: Historical observational data Information on events or actions that may affect the future. Slide 6

7 Why Forecast? In general, the purpose of forecasting is to inform the process of planning. The reason for planning is to develop a course of action so that things don t ust happen based on a nochange forecast. Planning models may be purely forecast-based, or may be based on other OR models (eg optimization or simulation) with forecasting inputs. Slide 7

8 PHIVE: A Forecasting Framework Purpose Horizon Information Value Evaluation Slide 8

9 Purpose What is the specific purpose of forecasting? What decisions will it support? What plans will it inform? The answers to these questions will help to determine: What is to be forecast and At what level of aggregation Slide 9

10 Supply Chain Forecasting at Different Levels of Aggregation Slide 10 Syntetos et al (2015)

11 Mini Exercise 1. What decisions do your own OR models support? (NB: models may be of any form) 2. What are the inputs to your models? 3. Which of your input variables need to be forecasted and at what level of aggregation? Slide 11

12 PHIVE: A Forecasting Framework Purpose Horizon Information Value Evaluation Slide 12

13 Horizon The forecast horizon is the length of time into the future for which forecasts are to be prepared. (The forecast frequency is how often the forecast is run). The answers relating to questions of forecast purpose will help to determine: The forecast horizon and The forecast frequency eg If a company makes and has a lead-time of three weeks, then Horizon= 4 weeks, Frequency = 1 week. Slide 13

14 Temporal Aggregation Suppose historical data is collected monthly and the Forecast Horizon is one quarter (or three months). Forecasts based on disaggregated data Inspect the monthly data Produce forecasts for one-, two- and three-months-ahead. Total these forecasts. Forecasts based on (temporally) aggregated data Aggregate the monthly data into quarterly data. Inspect the quarterly data. Produce a one-quarter-ahead forecast. Slide 14

15 Temporal Aggregation and Subsequent Disaggregation Slide 15 Nikolopoulos et al (2011)

16 PHIVE: A Forecasting Framework Purpose Horizon Information Value Evaluation Slide 16

17 Information Information may include: Historical observations of the variable to be forecasted. Observations and forecasts on associated variables that may influence the variable to be forecasted. Information on events or actions that may affect the future Slide 17

18 Matrix Plots for Associated Variables 1 2 Slide 18 In (1), y=p/e and x=roc In (2), y=roc and x=p/e

19 Information on Events and Associated Variables Product: Trend: 0 - Season 13: 0 - Season 52: 1 Events Demand Promocode Product: Adcode: 401 Adcode: 406 Adcode: 408 Adcode: 410 Adcode: Discount % Associated Variable (Discount %) Slide 19 Data visualisation can support analysis and client communication.

20 PHIVE: A Forecasting Framework Purpose Horizon Information Value Evaluation Slide 20

21 Value Forecast Value Added The change in a forecast performance metric that can be attributed to a particular step or participant. Performance Metric Accuracy Metric Accuracy-Implication Metric Slide 21

22 Accuracy-Implication Metric Should we view forecast accuracy as an end in itself or as a means to an end? An accuracy-implication metric is a measure of the effect of forecast accuracy on some aspect of organisational performance. Examples Financial metrics Service metrics Slide 22

23 Inventory Management Example Forecasting Method Stock-holding Costs Stock Management System Inventory Rule Stock Availability Slide 23 Boylan & Syntetos (2006)

24 PHIVE: A Forecasting Framework Purpose Horizon Information Value Evaluation Slide 24

25 Forecast Error Accuracy Evaluation Error = Actual Forecast Is an error of -100 good or bad? This depends on the size of the actual observations. If the actual is 15,000, the error may be considered good. If the actual is 150, it may be bad. PE = Percentage _ Error = 100 Actual Forecast Actual PE is a scale-independent measure. This is particularly useful when assessing accuracy across multiple series, varying in scale. Slide 25

26 Notation Actuals Historical data available, eg: y1, y2,..., y24 In general, if data is available up to time period t y y,..., 1, 2 y t Forecasts If forecast is made at the end of period t, using data up to (and including) period t, the forecast for h- periods ahead is denoted by: y ˆ t + h t or, more simply, by ˆ when the forecast origin (time t) is understood. y t + h Slide 26

27 Single and Rolling Origins Single Origin Error of forecast made at a single origin (time t) for h-periods-ahead: e t + h = yt + h yˆ t + h t Rolling Origins (More Robust) Look at h-ahead forecasts made at multiple origins: times t, t+1, t+2,, t+m-1. (NB: forecast is updated at each new origin). Then, we can calculate the Mean Error (ME): Slide 27 ME = 1 1 m m = 0 e 1 m 1 t+ h+ = ( yt+ h+ m = 0 yˆ t+ h+ t+ )

28 Example of Rolling Origins : Temperature Forecasts t t+1.,....., t+19 Slide 28 h=1, h=2, h=3, h=4, h=5

29 Error Measures (Continued) Slide 29 Mean Squared Error Penalises larger errors though squared-function. Also ignores sign of error, but penalises larger errors less strongly than MSE. Note: Both MSE and MAE are scale-dependent Mean Absolute Error = = = = ) ˆ ( 1 1 m m t h t h t h t y y m e m MSE = = = = ˆ 1 1 m m t h t h t h t y y m e m MAE

30 Mean Absolute Percentage Error MAPE = 100 m m 1 = 0 e y m 1 t+ h+ 100 yt+ h+ t+ h+ = m y yˆ = 0 t+ h+ t+ h+ t+ Intuitive to explain to practitioners (eg on average the forecast is out by 10% ). y Some organisations use (100% - MAPE) as a measure of forecast accuracy. MAPE is a scale-independent measure. So, may be used for comparisons across multiple series. MAPE puts a heavier penalty on negative errors than positive errors ( Slide 30

31 Evaluation of Accuracy Implications Monte Carlo Simulation Based on purpose of forecasting, identify what needs to be forecast and over what horizon, and suitable performance metrics (eg financial) Collect historical data. Generate forecasts, over appropriate horizon, using only data that would have been available at the time: Current method Alternative method(s) Simulate effect of methods on performance metrics Compare summary statistics Slide 31

32 Summary Consideration of purpose should inform choice of horizon and level of aggregation. Essential to gauge information available (numeric and qualitative) to select forecasting method. Assess value added of udgemental methods and of any recommended method. Take care in evaluating forecasts, recognising the strengths and weaknesses of error metrics available. Slide 32

33 References Armstrong JS (2001) Principles of Forecasting, Kluwer. Boylan JE & Syntetos AA (2006) Accuracy and accuracy-implication metrics for intermittent demand. Foresight: the International Journal of Applied Forecasting, 4, Goodwin P, Fildes R, Lawrence M & Nikolopoulos K (2007) The process of using a forecasting support system. International Journal of Forecasting, 23, Nikolopoulos K, Syntetos AA, Boylan JE, Petropoulos F & Assimakopoulos V (2011) An Aggregate-Disaggregate Intermittent Demand Approach (ADIDA) to forecasting. Journal of the Operational Research Society, 62, Sanders NR & Manrodt KB (2003) Forecasting software in practice: use, satisfaction and performance. Interfaces, 33, Syntetos AA, Babai MZ, Boylan JE, Kolassa S & Nikolopoulos K (2015) Supply chain forecasting: theory, practice, their gap and the future. European Journal of Operational Research. Slide 33