Session 4: Data and short run forecasting

Session 4: Data and short run forecasting

Demand Forecasting and

Planning in Crisis

30-31 July, Shanghai

Joseph Ogrodowczyk, Ph.D.

Session 4 Joseph Ogrodowczyk, Ph.D.

Demand Forecasting and Planning in Crisis 30-31 July, Shanghai 2

Data and short run forecasting

Session agenda Outlier detection and correction Naïve one-step, moving average, and confidence interval

forecasts

Activity: Produce short run forecasts with different historical data




Outlier detection and correction In the previous session, the data set contained data in

every month of the year

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec2000 102.3 105.7 108.0 109.1 106.7 109.2 101.6 105.0 105.4 103.7 97.7 90.22001 90.1 92.2 96.2 97.0 98.5 103.5 95.9 102.3 102.7 100.1 95.3 91.72002 94.1 96.4 100.2 102.1 101.2 106.4 99.3 104.3 103.1 103.8 97.0 92.02003 94.4 97.5 98.1 99.9 99.5 104.4 100.2 104.3 104.4 106.4 103.6 96.42004 99.0 102.5 103.3 105.6 105.5 108.1 104.8 108.2 105.2 109.6 103.0 97.72005 104.2 105.2 105.7 109.0 107.9 112.4 108.2 111.1 114.3 121.2 116.1 109.92006 111.9 113.2 114.8 114.5 113.9 116.4 111.7 112.7 109.8 105.0 98.8 97.12007 95.6 97.8 101.3 101.2 102.0 107.0 101.4 103.0 100.6 99.5 91.8 88.92008 88.2 88.5 90.1 91.6 90.4 93.0 88.6 89.8 85.9 81.4 75.6 67.42009 64.6 63.9




Outlier detection and correction Definition: Outliers are data points that are outside of (greater

or less than) the “normal” range for the data set Sometimes outliers can be identified with visual inspection Note: Outliers may also indicate seasonality, advertising jump,

or other vital variable




Outlier detection and correction Visual inspection in table format Historical data now include years 2000 – 2009

Data in bold below were the data set from previous example. Red values were the missing data points




Outlier detection and correction Visual inspection in graphical format

0

50

100

150

200

250

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

2004

2005

2006

2007

2008




Outlier detection and correction Mathematical detection

Calculate the mean and standard deviation Based on chronological or time buckets

Mean ±3*(standard deviation) With limited data, omit the suspected outlier Also called statistical control




Outlier detection and correction Mathematical detection

Chronological series

Time bucket series




Outlier detection and correction Means of correction

Two suggested methods Missing data method (average of preceding and following data points) Statistical control limit

Data series Average (99.0+103.3)/2 = 101.1

Statistical control 104.5 + (3*3.7) = 115.6




Outlier detection and correction Means of correction

Bucket series Average (97.5+105.2)/2 = 101.3 Note that we are using 2000-2008 not 2004-2008

Statistical control 99.6 + (3*8.0) = 123.6




Short run forecasting An executive has asked for a forecast of demand for the next

month Three suggested methods to use:

Naïve: Using the most recent data point as a forecast Moving average: Using an average of several most recent data

points as a forecast Confidence intervals: Using historical data to calculate areas of

demand probabilities




Short run forecasting Returning to the original full data set

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec2000 102.3 105.7 108.0 109.1 106.7 109.2 101.6 105.0 105.4 103.7 97.7 90.22001 90.1 92.2 96.2 97.0 98.5 103.5 95.9 102.3 102.7 100.1 95.3 91.72002 94.1 96.4 100.2 102.1 101.2 106.4 99.3 104.3 103.1 103.8 97.0 92.02003 94.4 97.5 98.1 99.9 99.5 104.4 100.2 104.3 104.4 106.4 103.6 96.42004 99.0 102.5 103.3 105.6 105.5 108.1 104.8 108.2 105.2 109.6 103.0 97.72005 104.2 105.2 105.7 109.0 107.9 112.4 108.2 111.1 114.3 121.2 116.1 109.92006 111.9 113.2 114.8 114.5 113.9 116.4 111.7 112.7 109.8 105.0 98.8 97.12007 95.6 97.8 101.3 101.2 102.0 107.0 101.4 103.0 100.6 99.5 91.8 88.92008 88.2 88.5 90.1 91.6 90.4 93.0 88.6 89.8 85.9 81.4 75.6 67.42009 64.6 63.9




Short run forecasting Suppose we wish to forecast January 2008 and we have just

completed December 2007 Naïve

Using the most recent

data point (88.9 in December 2007)

to forecast January 2008 Graph is shown on following

slide Each forecast is produced for

the next month

Month Forecast ActualJan 88.9 88.2Feb 88.2 88.5Mar 88.5 90.1Apr 90.1 91.6May 91.6 90.4Jun 90.4 93.0Jul 93.0 88.6Aug 88.6 89.8Sep 89.8 85.9Oct 85.9 81.4Nov 81.4 75.6Dec 75.6 67.4




Short run forecasting Forecasting one month ahead using naïve model

65

70

75

80

85

90

95


Forecast

Actual




Short run forecasting Now suppose we wish to forecast February 2008 and we have

just completed December 2007 Naïve

Using the most recent

data point (December 2007)

to forecast February 2008 Graph is shown on following

slide Note that the first forecast

quantity is the same as the

previous example

Month Forecast ActualJan 88.2Feb 88.9 88.5Mar 88.2 90.1Apr 88.5 91.6May 90.1 90.4Jun 91.6 93.0Jul 90.4 88.6Aug 93.0 89.8Sep 88.6 85.9Oct 89.8 81.4Nov 85.9 75.6Dec 81.4 67.4




Short run forecasting Forecasting two months ahead using naïve model

Looks similar to forecasting one month ahead Longer delay to recognize the decline (Nov. and Dec)

65

70

75

80

85

90

95


Forecast

Actual




Short run forecasting Forecasting January 2008 Moving average model: Calculate an average based on a set

of previous values Three-period moving average would use December, November

and October 2007 data

January 2008 forecast = 93.4 This forecast is made for the next month

Month SalesOct 99.5Nov 91.8Dec 88.9

Average 93.4




Short run forecasting Three-period moving average model

Month Forecast ActualJan 93.4 88.2Feb 89.6 88.5Mar 88.6 90.1Apr 89.0 91.6May 90.1 90.4Jun 90.7 93.0Jul 91.6 88.6Aug 90.7 89.8Sep 90.5 85.9Oct 88.1 81.4Nov 85.7 75.6Dec 81.0 67.4

65

70

75

80

85

90

95


Forecast

Actual




Short run forecasting Forecasting February 2008 Moving average model: Calculate an average based on a set

of previous values 3 period moving average would use December, November and

October of 2007 data

February 2008 forecast = 93.4 This forecast is made for two months ahead

Month SalesOct 99.5Nov 91.8Dec 88.9

Average 93.4




Short run forecasting 3 period moving average model two months ahead

Again, forecasts take longer to respond to declines in demand

Month Forecast ActualJan 88.2Feb 93.4 88.5Mar 89.6 90.1Apr 88.6 91.6May 89.0 90.4Jun 90.1 93.0Jul 90.7 88.6Aug 91.6 89.8Sep 90.7 85.9Oct 90.5 81.4Nov 88.1 75.6Dec 85.7 67.4 65

70

75

80

85

90

95


Forecast

Actual




Short run forecasting Forecasting January 2008 Confidence interval model

Based on the moving average model Constructing forecasting ranges with associated confidence levels

What is the likely level of demand in the future? The higher the confidence level, the greater the range of estimated

demand




Short run forecasting Confidence intervals

Calculations can be done according to the month being forecasted Use all previous January data (2000-2007) to construct the confidence

interval for January 2008 More statistically involved and uses probabilities taken from the

standard normal curve (bell curve) MAF ±(std normal statistic)*Std deviation

MAF: moving average forecast




Short run forecasting Standard normal statistic

A 95% confidence level

corresponds to a value of 1.64

A 99% confidence level

corresponds to a value of 2.33

Standard normal statistic

Confidence level

0.67 75%0.84 80%1.04 85%1.28 90%1.34 91%1.41 92%1.48 93%1.55 94%1.64 95%1.75 96%1.88 97%2.05 98%2.33 99%3.09 99.9%




Short run forecasting Confidence intervals

MAF ±(std normal statistic)*Std deviation Moving average forecast for January = 93.4 Std dev for January = 6.99, 95% confidence = 1.64

Lower limit: 93.4-(1.64)*6.99= 81.93

Upper limit: 93.4+(1.64)*6.99= 104.87 We are 95% confident (there is a 95% probability) that demand

for January 2008 will range from 81.93 to 104.87




Short run forecasting Confidence intervals for one month ahead 95% confidence level

Month Forecast Actual Std dev Lower UpperJan 93.4 88.2 6.99 81.93 104.87Feb 89.6 88.5 6.67 78.72 100.58Mar 88.6 90.1 5.99 78.73 98.38Apr 89.0 91.6 5.82 79.42 98.51May 90.1 90.4 5.15 81.65 98.53Jun 90.7 93.0 4.26 83.71 97.69Jul 91.6 88.6 5.11 83.27 100.03Aug 90.7 89.8 3.84 84.36 96.97Sep 90.5 85.9 4.38 83.29 97.67Oct 88.1 81.4 6.89 76.82 99.43Nov 85.7 75.6 7.41 73.57 97.86Dec 81.0 67.4 6.69 69.99 91.95

95% confidence

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85

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95

100

105

110


Forecast

Actual

Lower

Upper




Short run forecasting Confidence intervals for one month ahead 99% confidence level

Month Forecast Actual Std dev Lower UpperJan 93.4 88.2 6.99 77.11 109.69Feb 89.6 88.5 6.67 74.12 105.18Mar 88.6 90.1 5.99 74.60 102.52Apr 89.0 91.6 5.82 75.41 102.53May 90.1 90.4 5.15 78.09 102.08Jun 90.7 93.0 4.26 80.77 100.63Jul 91.6 88.6 5.11 79.74 103.55Aug 90.7 89.8 3.84 81.71 99.62Sep 90.5 85.9 4.38 80.26 100.69Oct 88.1 81.4 6.89 72.07 104.18Nov 85.7 75.6 7.41 68.46 102.97Dec 81.0 67.4 6.69 65.37 96.57

99% confidence




Short run forecasting Comparison of forecasts for one and two months ahead

Forecast type Forecast January ActualNaïve 88.9 88.2Moving average 93.4 88.2Confidence interval (95%) 81.93 - 104.87 88.2Confidence interval (99%) 77.11 - 109.69 88.2

Forecast type Forecast February ActualNaïve 88.9 89.6Moving average 93.4 89.6Confidence interval (95%) 82.47 - 104.33 89.6Confidence interval (99%) 77.87 - 108.93 89.6



Data and short run forecasting Short run forecasting

Note how each of the models responds to the sudden decrease in demand Naïve one-step responds quickest, moving average shows a

slight delay Trend needs to change before the calculations are affected Actual demand dropped in Sept and Oct. Forecasts responded in

Nov and Dec. This can be problematic in time of steep decline Confidence intervals assist by suggesting probabilities of demand

Higher confidence leads to greater intervals Upper range is the optimistic scenario while lower range is the risk

scenario All three models are better suited for short run forecasting

For longer run forecasting, we need to use models that produce dynamic forecast quantities



Data and short run forecasting For further reading

Armstrong J. Scott, ed. 2001. Principles of Forecasting: A handbook for researchers and practitioners. Norwell, Mass.: Kluwer Academic Publishers.

Jain, Chaman L. and Jack Malehorn. 2005. Practical Guide to Business Forecasting (2nd Ed.). Flushing, New York: Graceway Publishing Inc.

Newbold, Paul and Theodore Bos. 1994. Introductory Business & Economic Forecasting (2nd Ed.). Cincinnati, Ohio: South-Western Publishing Co.

Session 4: Data and short run forecasting

Documents

Transcript of Session 4: Data and short run forecasting