Main idea of the trend analysis forecasting method:

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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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Prerequisite 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 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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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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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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