HW1 Q5: One Possible Approach

• First, let the population grow

• At some point, start harvesting the growth– Annual catch = annual growth

• In year 30, catch all but 1,000 fish– Maybe not be a good idea in reality

• Remaining question: how far should we let the population grow?

MGTSC 352Lecture 3: Forecasting

“Simple” time series forecasting methodsIncluding SES = Simple Exponential Smoothing

Performance measures

“Tuning” a forecasting method to optimize a performance measure

Components of a time series

DES = Double Exponential Smoothing

Today’s active learning

• Groups of two again

• Recorder: person who got up earlier this morning

SES is really a WMA (pg. 19)

Ft+1 = LS Dt + (1–LS) Ft

t = 6: F7 = LS D6 + (1–LS) F6

t = 5: F6 = LS D5 + (1–LS) F5

t = 4: F5 = LS D4 + (1–LS) F4

t = 3: F4 = LS D3 + (1–LS) F3

t = 2: F3 = LS D2 + (1–LS) F2

t = 1: F2 = D1

Plug t = 5 equation into t = 6 equation:

F7 = LS D6 + (1–LS) (LS D5 + (1–LS) F5)

Active learning: Multiply out

F7 = LS D6 + LS (1–LS) D5 + (1–LS)2 F5

Repeat for t = 4, 3, 2, 1

Final result:

F7 = [LS D6] + [LS (1–LS) D5] + [LS (1–LS)2 D4]

+ [LS (1–LS)3 D3] + LS (1–LS)4 D2] + (1–LS)5 D1

The Weights

-

0.20

0.40

0.60

D6 D5 D4 D3 D2 D1

Weight

LS = 0.5

-

0.10

0.20

0.30

0.40

D6 D5 D4 D3 D2 D1

Weight

LS = 0.3

-

0.20

0.40

0.60

0.80

D6 D5 D4 D3 D2 D1

Weight

LS = 0.1

• Weights get smaller and smaller for demand that is further and further in the past – except:– Oldest data point may have more weight than

second oldest data point.– Only matters for small data sets and small LS

Simple Models Recap

• LP, AVG, SMA, WMA, SES• Three phases:

– Initialization– Learning– Prediction

• Prediction: so far, we’ve only done one-period-into-the-future

• k periods-into-the-future: Ft+k = Ft+1, k = 2, 3, …

• Active learning: translate formula into English

Performance Measures

• BIAS = Bias• MAD = Mean Absolute Deviation• SE = Standard Error• MSE = Mean Squared Error• MAPE = Mean Absolute Percent Error

(formulas in course pack, p. 21)

Excel

Components of a Time Series– level– trend– seasonality– cyclic (we will ignore this)– random (unpredictable by definition)

• (Simple) Exponential Smoothing incorporates...– Level only– Will lag trend– Miss seasonality

Pg. 23

Level, Trend, Seasonality

Level + random

Level + trend + random

Level + trend + seasonality + random

Level, Trend, Seasonality

• Additive trend, multiplicative seasonality• (Level + Trend)

seasonality index• Example:

– Level: 1000 – Trend: 10– Seasonality index: 1.1– Forecast: (1000 + 10) 1.1 = 1111

Models

• Double Exponential Smoothing– Level, Trend– Today

• Triple Exponential Smoothing– Next week

• Simple Linear Regression with Seas. Indices– Next week

Double Exponential Smoothing

• Initialization– Level, Trend

• Learning

• Prediction

• Formulas in course pack

• Work on an example

Excel

Pg. 25

Learning

In general: UPDATED = S NEW + (1 – S) OLD

− −= × + − × +t t t 1 t 1L LS D (1 LS) (L T )

− −= × − + − ×t t t 1 t 1T TS (L L ) (1 TS) T