Forecasting using trend analysis
 Part 1. Theory
 Part 2. Using Excel: a demonstration.
 Assignment 1, 2
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Learning objectives
To learn how:
 To compute a trend for a given time-series data using Excel
 To choose a best fitting trend line for a given time-series
 To calculate a forecast using regression equation
2
Main idea of the trend analysis
forecasting method
 Main idea of the method: a forecast is calculated by
inserting a time value into the regression equation. The
regression equation is determined from the time-serieas
data using the “least squares method”
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Prerequisites: 1. Data pattern: Trend
Trend (close to the linear growth)
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Prerequisites: 2. Correlation
There should be a sufficient correlation
between the time parameter and the
values of the time-series data
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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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Main idea of the trend analysis method
 Trend analysis uses a technique called least squares to fit a trend
line to a set of time series data and then project the line into the
future for a forecast.
 Trend analysis is a special case of regression analysis where the
dependent variable is the variable to be forecasted and the
independent variable is time.
 While moving average model limits the forecast to one period in
the future, trend analysis is a technique for making forecasts
further than one period into the future.
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The general equation for a trend line
F=a+bt
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Where:
 F – forecast,
 t – time value,
 a – y intercept,
 b – slope of the line.
Least Square Method
 Least square method determines the values for a and b
so that the resulting line is the best-fit line through a set
of the historical data.
 After a and b have been determined, the equation can be
used to forecast future values.
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The trend line is the “best-fit” line: an
example
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1999
Year
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Number of libraries
Municipal public libraries in Lithuania in 1991-2002
Statistical measures of goodness of fit
In trend analysis the following
measures will be used:
 The Correlation Coefficient
 The Determination Coefficient
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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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Goodness of fitt: Determination
Coefficient RSQ
 Range: [0, 1].
 RSQ=1 means best fitting;
 RSQ=0 means worse fitting;
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Evaluation of the trend analysis
forecasting method
 Advantages: Simple to use (if using appropriate software)
 Disadvantages: 1) not always applicable for the long-term
time series (because there exist several ternds in such cases);
2) not applicable for seasonal and cyclic datta patterns.
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Part 2. Switch to Excel
Open a Workbook trend.xls, save it to your
computer
Working with Excel
 Demonstration of the forecasting procedure using trend
analysis method
 Assignment 1. Repeating of the forecasting procedure with
the same data
 Assignment 2. Forecasting of the expenditure
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Using Excel to calculate linear trend
 Select a line on the diagram 
 Right click and select Add Trendline 
 Select a type of the trend (Linear)
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Part 3. Non-linear trends
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Non-linear trends
Excel provides easy calculation of the following trends
 Logarythmic
 Polynomial
 Power
 Exponential
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Logarithmic trend
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2
0
y = 4,6613Ln(x) + 1,0724
R2 = 0,9963
0
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Trend (power)
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2
0
y = 0,4826x1,5097
R2 = 0,9919
0
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2
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Trend (exponential)
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y = 0,0509e1,0055x
R2 = 0,9808
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0
0
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Trend (polynomial)
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y = -0,1142x3 + 1,6316x2 - 5,9775x + 7,7564
R2 = 0,9975
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2
0
0
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Choosing the trend that fitts best
 1) Roughly: Visually, comparing the data pattern to the one
of the 5 trends (linear, logarythmic, polynomial, power,
exponential)
 2) In a detailed way: By means of the determination
coefficient
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End