Famous forecasting quotes

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Famous forecasting quotes

• --Winston Churchill
• "I always avoid prophesying beforehand because it
  is much better to prophesy after the event has
  already taken place. "

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Forecasting using trend analysis

• 1. Theory
• 2. Using Excel a demonstration.
• 3. 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

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Main idea of the trend analysis forecasting
method

• a forecast is calculated by inserting a time
  value into the regression equation. The
  regression equation is determined from the
  time-series data using the least squares method
  

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• Prerequisites Trend data pattern. Example
  linear trendNot long time-series

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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 linear trend line

• Fabt

• Where
• F forecast,
• t time value,
• a y intercept,
• b slope of the line.

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Least Square Method

• Least square method determines the values for
  parameters a and b of the regression equation 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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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 R2

• The coefficient of determination, R2, measures
  the percentage of variation 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 fit Determination Coefficient R2

• Range 0, 1
• R21 means best fitting
• R20 means worse fitting
• In Excel R2 is denoted as RSQ (R squared)

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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 trends in such cases) 2) not applicable
  for seasonal and cyclic data patterns.

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Switch to Excel

• Open a Workbook trend.xls, save it to your
  computer

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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 (left click on the
  line) ?
• Right click and select Add Trend line ?
• 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

• Logarithmic
• Polynomial
• Power
• Exponential

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Examples of the non-linear trends
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Choosing the trend that fits best

• 1) Roughly Visually, comparing the data pattern
  to the one of the 5 trends (linear, logarithmic,
  polynomial, power, exponential)
• 2) In a detailed way By means of the
  determination coefficient

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End