Time Series Forecasting Tools e.g. Simple / Holt / Winters Exponential Smoothing

1. Text: Chapter 12 Time Series Forecasting Tools e.g. Simple / Holt / Winters Exponential Smoothing

2. Motivation: Job Interview Assignment by Fortune10 company

3. Motivation: Demand Forecast • Think of a Business Plan, product or service you provide • Discussion: • Why is there a need to forecast future demand? • How would you forecast future demand? • Does the type & availability of information / data matter? • e.g. past sales data • “Forward” sales intelligence e.g. market research ; Buyers’ intentions • Novel product / service: Gut feeling? ; Experts’ opinions? • Does forecast horizon matter i.e. short, medium, long term?

4. Evidence indicates: A “good” demand forecast • Defines the success of the Supply Chain • Operational Efficiency: Sourcing, staffing, capital investment, logistics, … • Is a Collaborative process internally & externally • Internally: R & D, Marketing, Finance etc. forecast “together” • Externally: Forecasts from agents ; feedback from customers etc. • i.e. concensus-driven and a shared ownership ; needs regular update • Defined by its degree of usefulness / adoption rather than accuracy (“6 Rules for Effective Forecasting” HBR article)

5. Approach Qualitative Non-numerical / Subjective Short / Long Range Planning Quantitative Numerical / Objective i.e. “Look BACK twice as far you look forward“ Intermediate Range Planning Forecasting Methods Empirical Evidence: No one method is superior. Hybrid method (quantitative+qualitative) enhances accuracy / mitigates bias e.g. HBR Reading “6 Rules for Effective Forecasting”

6. Analytical Forecasting Tools • Regression Forecasting: • Demand = f(Price, Competitor’s Price, Business Cycle, Life Cycle, …) • Profit = f(time) e.g. uniform or straight line relationship over time • Time Series Forecasting: Extrapolation of past patterns • Focus on non-uniform / varying relationship over time

8. Statistically Speaking • Time Series : Collection of data recorded over time • Daily #Breakdowns; Monthly downtimes ; Quarterly Productivity ; Annual Profit. • Data variability : Data is dynamic i.e. fluctuate with time • Forecast : Prediction of future using current & past data • Backcast: What should “present” be given “future” ? • Eg. Intakes of personnel / Engineering/ Science students determined by backcasting specified future R&D personnel. • Backcasting = Forecasting on “reverse” time scale.

9. Coverage • Regression Models using Time as a predictor • Time Series Forecasting Tools • Naïve Forecast (i.e. Random Walk): • Forecast of next lag,F(t+1)=Current Data, Y(t) • Moving Average: • F(t+1) = Average [Y(t), Y(t-1), Y(t-2),…] egAvg(Today, Yesterday, …] • Exponential Smoothing: • For data w/o trend F(t+1) = Weighted Average [Y(t), Y(t-1), Y(t-2),…] • For data with Trend : Holt Method • For data with Trend & Seasonality : Winters Method • Benchmarking / Monitoring Forecasting Accuracy • Forecast error metrics: MAD ; MSE ; MAPE Parsimony: Select low p

10. Trend Models • P-order model:Data is a function of time • Autoregressive model:Data is a function of its past * * * * * * * * * * * *

11. Growth Models • Constant Growth Model: e.g. Moore’s Law: Computer chip “power” doubles every 18 months Applications (1) Annual growth in China’s Foreign Reserves (2) Microsoft Profit CAGR t

12. New Product Forecasting: A Life-Cycle Model i.e. S-Curve Saturation Level, S (eg market research) Discuss: How is S-curve Connected to Bell Curve? Half Life: Demand = ½ S Demand Delay Factor, F Inflection Point, I Time, t

13. Time Series Forecasting via Smoothing Methods • Data smoothing = Data “massaging” Averaging “zeroes out” variability to reveal trend. • Two smoothing techniques: • Moving Average • Exponential Smoothing

14. Moving Average • Average of moving window of data eg 3 period MA: Forecast F(t+1)= [Y(t-2) + Y(t-1) + Y(t)] / 3 • Shortcomings • Window length: Why not MA(4), MA(5) etc. • Valid for flat / non-trending TS • Why use equal weights in averaging past data ? v/s say F(t+1) = 0.2 Y(t-2) + 0.3 Y(t-1) + 0.5 Y(t) • Application: Demand Intensity or Competition for COE 1 2 3 F(4) 2 3 4 F(5) 3 4 5 F(6)

15. L(t-1) F(t+1) Y(t) Simple Exponential Smoothing for “flat” Time Series • Define L(t-1)= WeightedAvg of Y1, Y2, …,Y(t-1) L(t-1) = “past level” • => New Level L(t) = Weighted Average of Y(t) and L(t-1) = a Y(t) + (1-a) L(t-1), = Forecast (t+1) i.e. Forecast of Y(t+1) • a = 1 => Naïve Forecast ; a = 0 => Y(t) “not credible” & ignored by forecast • Start with F(2) = L(1) = Y(1) • F(3) = L(2) = a Y(2) + (1-a) Y(1) • F(4) = L(3) = • = • Concept:Forecast = exponentially weighted average of Present & Past! • Problem: Which exponential weight a to use? • Case Study: Demand Intensity for COE Exponential Weights .7 .21 .09

16. Benchmarking Forecasting Accuracy • Good Forecasts small forecasting errors. • 3 commonly-used benchmarks: • Mean Absolute Deviation, MAD = • Mean Squared Error, MSE = • Mean Absolute Percentage Error, MAPE = • Minimize (any) forecasting error metrics above to obtain “optimal” forecasting model

17. Holt Smoothing for Trending TS • Generalization of simple exponential smoothing • Updates Level and Trend i.e. weighted average of PRESENT and PAST • = weighted average of • = weighted average of slopes • Applications: Oil Prices & Australian Wine Grape Production Current Observation Past Level Current Slope Past Trend

18. Seasonal Indices: Application • Application: Calendar Sales Plan for Major Oil Company Country Yearly Sales Target = 838 mbbl • Target: Better Delivery Planning using Seasonal Indices Jan Feb Mar Apr May Jun Jul Aug Sep …. Actual Sales 57 45 73 72 71 73 63 62 78 …. Delivery Plan 70 70 70 70 70 70 70 70 70 …. % Sales / Plan 81 64 104 103 101 104 90 89 112 …. Calendar Plan 63 46 74 78 75 70 63 61 76 …. (= 70 x monthly seasonal index) % Sales / CP 90 98 99 92 95 104 100102 103

19. Winters Exponential Smoothing Model for Trend & Seasonality • Generalization of simple exponential smoothing & Holt • Updates (deseasonalized) level, trend and seasonality components • Produces “seasonal” forecast • Applications: Singapore GDP S = 1 =>Holt Winters

20. Hallmarks of Good Forecasting • Forecasting Horizon • Long: Expert ; Medium: Regression ; Short: Time Series Methods • Inspect time series • “Constant Level”: Simple Exponential Smoothing • Trends & Seasons: Holt / Winters Exponential Smoothing • Forecasts should be • Based on good-quality data o/w GIGO (Garbage-in-garbage-out) • Timely to allow planning. It is in fact critical to every business plan! • Monitored for reliability / quality • Simple and easy to obtain via software. You can’t go wrong if you always use Winters vs Holt vs Simple ES: WHY?