Marking Philosophy
• Feasibility: could the plan you proposed
be used in reality
• Consistency: are your numbers internally
consistent?
• Optimality: is your plan the best possible,
or close to it?
Example: Marking of HW1, Q5
• You submitted:
– The plan: # to catch in years 0 – 30
– The consequence: NPV
• We plug your plan into a correct model and
check:
– Feasibility: is fish population always non-negative?
– Consistency: does your plan result in the NPV you
reported?
– Optimality: how does your NPV compare to the best
possible NPV?
From the Grading Manager
• Put only numbers in cells for numerical
answers
– 1234
– $1,234
– 1 234  Excel interprets this as text, not a
number (because of the space)
– 1234 fish  ditto
Reminders
• HW 2 due Wednesday at 11:59 pm
MGTSC 352
Lecture 4: Forecasting
Methods that capture Level, Trend, and Seasonality:
TES = Triple Exponential Smoothing
Intro to SLR w SI = Simple Linear Regression
with Seasonality Indices
Forecasting: Common Mistakes
• Computing forecast error when either the
data or the forecast is missing
• MSE: dividing with “n” instead of “n-1”
• MSE: SSE/n – 1 instead of SSE/(n – 1)
• Simple methods: forgetting that the
forecasts are the same for all future time
periods
Recap: How Different Models
Predict
• Simple models:
– Ft+k = Ft+1, k = 2, 3, …
• DES:
– Ft+k = Lt + (k  Tt ), k = 1, 2, 3, …
– Linear trend
• TES and SLR w SI (cover today):
– Ft+k = (Lt + k  Tt)  (Seasonality Index)
What’s a Seasonality Index (SI)?
• Informal definition: SI = actual / level
• Example:
– Average monthly sales = $100M
– July sales = $150M
– July SI = 150/100 = 1.5
• SI = actual / level means:
– Actual = level  SI
– Level = actual / SI
TES tamed
Works in three phases
• Initialization
• Learning
• Prediction
Tracks three components
• Level
• Trend
• Seasonality
Actual data
Level
Prediction
Prediction
Initialization
Learning
Actual data
Level
Forecast = (predicted level)  SI
Prediction
predicted level
k periods
into future
k  trend
Time to try it out – Excel
Pg. 29
TES - Calibration (p = # of seasons)
L t  LS
Dt
 (1  LS)(L t 1  Tt 1)
S t p
Tt  TS(Lt  Lt 1)  (1  TS)Tt 1
St  SS
Dt
 (1  SS)S t p
Lt
Always: UPDATED = (S) NEW + (1-S) OLD
One-step Forecast: Ft+1 = (Lt + Tt) St+1-p
Level: learning phase
L(t) = LS * D(t) / S(t-p) + ( 1 - LS )*( L(t-1) + T(t-1) )
•
NEW: D(t) / S(t-p) = de-seasonalize data for period t using
seasonality of corresponding previous season  level = actual / SI
•
OLD: L(t-1) + T(t-1) = best previous estimate of level for period t
Trend: learning phase
T(t) = TS * ( L(t) - L(t-1) ) + ( 1 - TS ) * T(t-1)
•
NEW: L(t) - L(t-1) = growth from period t-1 to period t
•
OLD: T(t-1) = best previous estimate for trend for period t
Seasonality: learning phase
S(t) = SS * D(t) / L(t) + ( 1 - SS ) * S(t-p)
•
NEW: D(t) / L(t) = actual / level  SI = actual / level
•
OLD: S(t-p) = previous SI estimate for corresponding season
25
One-step forecasting: the past
F(t+1) = [L(t) + T(t)] * S(t+1-p)
"To forecast one step into the future, take the previous period’s level,
add the previous period’s trend, and multiply the sum with the
seasonality index from one cycle ago."
Pg. 30
k-step forecasting: the future
(“real” forecast)
F(t+1) = [L(t) + k*T(t)] * S(t+1-p)
Active learning: translate the formula into English
• One minute, in pairs
TES vs SLRwSI
• TES
Ft+k = (Lt + k  Tt)  St+k-p
• SLRwSI
additive trend
multiplicative
seasonality
Ft+k = (intercept + (t + k)  slope)  SI
TES vs SLRwSI
• Both estimate Level, Trend, Seasonality
• Data points are weighted differently
– TES: weights decline as data age
– SLRwSI: same weight for all points
• Hence, TES adapts, SLRwSI does not
Which Method Would Work Well for This Data?
500
450
400
350
Data
300
250
200
150
100
50
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Patterns in the Data?
• Trend:
– Yes, but it is not constant
– Zero, then positive, then zero again
• Seasonality?
– Yes, cycle of length four
Comparison
• TES:
SE = 24.7
• SLRwSI:
500
450
400
350
300
250
200
150
100
50
0
Data
TES
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
• TES trend is adaptive
500
450
400
350
300
250
200
150
100
50
0
SE = 32.6
Data
SLR w SI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
• SLR uses constant trend
One-minute paper
• Don’t put on your coat put your books away or
whatnot, pull out a piece of paper instead.
• Review today’s lecture in your mind
– What were the two main things you learned?
– What did you find most confusing?
– Who is going to win the Superbowl?
• Don’t put your name on the paper.
• Stay in your seats for 1 minute.
• Hand in on your way out