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Quantitative forecasting methods in library management Prof. Dr. Algirdas Budrevicius Vilnius University, Faculty of Communication Course website: http://www.kf.vu.lt/~albud/progn/Engl
Quantitative forecasting methods in library
management
Prof. Dr. Algirdas Budrevicius
Vilnius University, Faculty of Communication
Course website: http://www.kf.vu.lt/~albud/progn/Engl
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"If you can look into the seeds of time, and say which grain will grow and which will not, speak then unto me. "
--William Shakespeare
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• "It is far better to foresee even without certainty than not to foresee at all. "
• --Henri Poincare in The Foundations of Science, page 129.
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Course plan
• Lecture 1. Forecasting: history and current situation. Forecasting in management. Qualitative and quantitative forecasting. Time series forecasting. Visual data pattern analysis. Forecasting in library management. Naive forecasting methods.
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Course plan (continued)
• Lecture 2. Part 1: Moving average forecasting method. Errors of forecast. Part 2: Practical work with Excel
• Lecture 3. Part 1: Forecasting using linear regression. Trend analysis. Part 2: Practical work with Excel
• Lecture 4-5. Forecasting project: analysis of forecasting situations in libraries; examples. Practical work with Excel
• Lecture 6. Discussions
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Course materials
• Course description: Website http://www.kf.vu.lt/~albud/progn/Engl
• Lectures: PowerPoint presentations
• Data, demonstrations, task solutions: Excel workbooks
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Development of the forecasting technique
• Non scientiffic forecasting: e.g. Astrology, Book of Changes.
• 19-20 century. Demographic forecasts
• Development of the quantitative methods: middle-to-second part of the 20th century.
• New developments: Neural network based methods
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Current situation in forecasting
• Forecasting is widely used in management now• There exist a well defined set of quantitative
forecasting methods that changes very little during last fiew decades
• There exists computer software that may be quite simply applied in forecasting
• Excel program allows to solve simple forecasting tasks
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Forecasting in management
• Personnel management
• Resource management
• Finance management
• Organizational management
Forecasting is usedin various domains of management, such as:
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Taxonomy of forecasting methods
• Methods: quantitative and qualitative• Qualitative: judgmental (based on expert
opinions) and technological (used for long term forecasts)
• Quantitative: time series methods and reasoning
• Note: only time series methods will be considered in this course.
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Definition of a forecasting situation
• Data (time series, or historical data)
• Forecasting method (e.g. Moving average, Trend analysis)
• Forecast
• Error of forecast
Quantitative time series based forecasting
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Naive forecasts NF1 and NF2
• Naive forecasts: (a “folk forecasting technique”) • NF1. (“The value tomorow will be the same as
today”). Example: Number of library visitors today was 120. Forecast NF1 for tomorow: 120.
• NF2. (“The value tomorow will be less (greater) by …10% ”). Example: Average temperature this month is 20 degrees. Forecast NF2 for the next month: Temperature will be 25 degrees (increase of 25%).
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Time-series methods of forecasting
• Time series analysis relies on historical data and attempts to project historical patterns into the future
• Note: only time series methods will further be considered
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Time-series example
Number of visitors in a library (in th.)
Year 1998 1999 2000 2001 2002 2003
Number
420 450 440 460 470 465
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Recomended form to present data and forecasts: an example
Year Number of readers Forecast Error
1995
1996
...
2005 (forecast)
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Example of real time series data concerning libraries
• Number of libraries (network)• Document stocks• Loan of documents• Number of users• Number of visitors, etc. (also see examples in
Excell worksheets)
Conclusion: good possibilities to apply forecasting methods, based on time series analysis
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Example of dataNework of Municipal Public Libraries in Lithuania in 1991-2002
Year Number of libraries 1991 16621992 15691993 15211994 15141995 15061996 14841997 14731998 14591999 14472000 14482001 14272002 1400
Source: Statistics of Lithuanian Libraries.
Municipal public libraries in Lithuania in 1991-2002
13001400150016001700
19901991199219931994199519961997199819992000200120022003
Year
Nu
mb
er
of
lib
rari
es
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Example of forecastingForecasting using linear trend. Demonstration
1. Calculating correlation: 0,995741Week Number of library visitors Signifficant correlation
1 1063 2. Plotting a chart (XY scatter)2 2369 3. Adding a linear trend line3 3159 Options: display equation4 3964 4. Calculating the forecast 5 5001 (by inserting number of the week x=6 into the equation)
6 5. Evaluation (using RSQ) 0,99Very good fitting
Forecasted number of visitors: 5953
Number of library visitors
y = 947,1x + 269,9
R2 = 0,9915
0
2000
4000
6000
8000
0 1 2 3 4 5
Week
Vis
ito
rs
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Patterns of the time-series data
• Horizontal (random, irregular variation)
• Trend (linear)
• Periodical (cyclical, seasonal)
• Complex (a combination of part or all listed above)
A forecasting method should comply with the data pattern. There are 4 basic data patterns:
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Horizontal pattern
Horizontal (irregular variations)
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Trend
Trend (close to the linear growth)
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Periodical pattern
Periodical seasonal
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Complex pattern
Complex data pattern including random, trend and periodical variations
Measuring forecast accuracy
What is the accuracy of a particular forecast?
How to measure the suitability of a particular forecasting method for a
given data set?
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Definition of the forecast error
• Error (e) of a forecast is measured as a difference between the actual (A) and forecasted values (F), that is,
• e=A-F,
• or, in a relative form: e=100% (A-F)/A.
• The error can be determined only when actual (future) data are available.
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Standard statistical measures to estimate errors (1)
• Mean (average) error (ME)
• Mean absolute error (MAE)
• Mean squared error (MSE)
•To preliminary evaluate a forecast and suitability of a method, various statistical measures may be used. In evaluating forecasts obtained by means of the moving average method, the following measures may be used:
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Standard statistical measures to estimate errors (2 - relative)
• Mean percentage error (MPE)
• Mean absolute percentage error (MAPE)
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Statistical measures of goodness of fit
• The Correlation Coefficient
• The Determination Coefficient
In trend analysis the following measures will be used:
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The Correlation Coefficient
• The correlation coefficient, R, measure the strength and direction of linear relationships between two variables. It has a value between –1 and +1
• A correlation near zero indicates little linear relationship, and a correlation near one indicates a strong linear relationship between the two variables
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The Coefficient of Determination
• The coefficient of determination, R2, measures the percentage of variaion in the dependent variable that is explained by the regression or trend line. It has a value between zero and one, with a high value indicating a good fit.
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