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### MGTSC 352

Reminders

- HW 3 Posted
- HW 1 Graded and Posted
- Grading appeal process

Lecture 6: Forecasting

Wrap-up of ForecastingHoldout strategyDebugging Forecasting Models

Monte Carlo SimulationPlaying Roulette with ExcelBard Outside example

95% Prediction Interval

- Technically correct formula;
- Forecast + Bias + 2 x Std Error
- Heuristic for use in this class;
- Forecast 2 SE

Steps in a Forecasting Project

-1: Collect data

0: Plot the data (helps detect patterns)

1: Decide which models to use

- level – SA, SMA, WMA, ES
- level + trend – SLR, DES
- level + trend + seas. – TES, SLR w SI, ...

2: Use models

3: Compare and select (one or more)

4: Generate forecast and range (prediction interval)

More on selection

Checking for (Yearly) Seasonality

Number of calls / month

Weekly or Hourly Seasonality

Avg. # of calls / hr., 2004

How to select a model?

- Look at performance measures
- BIAS, MAD, MAPE, MSE
- Use holdout strategy
- Example: 4 years of data
- Use first 3 years to fit model(s)
- Forecast for Year 4 and check the fit(s)
- Select model(s)
- Refit model(s) adding Year 4 data
- If you have more than one good model...

COMBINE FORECASTS

TES vs. SLR w SI(Both optimized to minimize SE)

Which method would you choose?

One possibility: Combining Forecasts

TES

SLR w SI

weight

+ (1 - weight)

Minimize SE of the combined forecast to find the best weight

Holdout Strategy

- Ignore part of the data (the “holdout data”)
- Build models using the rest of the data
- Optimize parameters
- Forecast for the holdout data
- Calculate perf. measures for holdout data
- Choose model that performs best on holdout data
- Refit parameters of best model, using all data

TES vs. SLR w SI …… in holdout period

Now which method would you choose?

Holdout Strategy Recap

- Performance during holdout period: a.k.a. “out of sample” performance
- In other words: how well does the method perform when forecasting data it hasn’t “seen” yet?
- Question: Why is SE during holdout period worse than SE during “training period”?

Do we have to implement these models from scratch?

- Forecasting software survey
- http://lionhrtpub.com/orms/surveys/FSS/FSS.html
- General statistics program
- Minitab, NCSS, SAS, Systat
- Dedicated forecast software
- AutoBox, Forecast Pro (MGTSC 405)

Do Spreadsheet Models Have Errors?

- Field audits of real-world spreadsheets: 94% had errorshttp://panko.cba.hawaii.edu/ssr/Mypapers/whatknow.htm
- What are the consequences of spreadsheet errors?
- Incorrect financial statements
- Bad publicity, loss of investor confidence
- Lawsuits
- Loss of election
- See http://www.eusprig.org/stories.htm for more

Debugging – Finding Your Mistakes

- Before entering a formula:
- Pause and predict the result
- After entering a formula:
- Double-click to see where numbers are coming from
- Try simple test values: 0, 1
- Graph your results
- ctrl+~ – use to look for breaks in patterns

To Excel

Playing roulette with Excel

To Excel …

Game 1

- Spin the spinner once
- Payoff = (spinner outcome) ($1 Million)
- Q1: What would you pay to play this game?
- Q2: Suppose the game were played 10,000 times. What do you think the payoff distribution will look like?

Game 2

- Spin the spinner twice
- Payoff = ($1 Million) x (spinner outcome 1 + spinner outcome 2)/2 Q1: What would you pay to play this game?
- Q2: Suppose the game were played 10,000 times. What do you think the payoff distribution will look like?

Using Excel to get the right answer

- Simulate one spin: =RAND()
- Repeat 10,000 times
- Plot histogram
- To Excel

Excel Details

- Using Data tables to replicate a simulation
- Enter replication numbers (1, …, n) in leftmost column
- Enter formulas for outputs in top row
- Highlight table
- Data Table …
- Column input cell: any empty cell

“Freezing” simulated values:

Copy the values

Paste special … values

Frequency distributions:(see also pg. 134)

Generate sample

Enter “bins” values

Highlight range where frequencies should be calculated

=FREQUENCY(sample, bins)

“Ctrl + shift + enter” instead of just “enter.”

More Excel DetailsBard Outside

- The Bard Outside theatre group puts on plays by Shakespeare 20 times every summer in a 200-seat outdoor theatre.
- Data:
- Attendance and weather (rain / no rain) for last five seasons (5 x 20 = 100 shows)
- Revenue = $10 per customer
- Cost = $1,600 per show
- Question: how much would profit increase if the number of seats were increased?

Data Analysis

- What’s the probability of rain?
- What is the mean and standard deviation of demand when it rains?
- How about when it doesn’t rain?
- How can we simulate demand?

To Excel …

Simulating Profit per show

- Simulate weather
- Simulate demand
- Make sure 0 ≤ demand ≤ capacity
- Calculate revenue
- Subtract cost
- Replicate!
- Remember: freeze tables of simulation results

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