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Main idea of the trend analysis forecasting method:

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a forecast is calculated by inserting a time value into the regression equation. ... 1) not always applicable for the long-term time-series (because there exist ... – PowerPoint PPT presentation

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Title: Main idea of the trend analysis forecasting method:


1
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

2
Prerequisite Correlation
There should be a sufficient correlation between
the time parameter and the values of the
time-series data
3
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

4
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.

5
The trend line is the best-fit line an example
6
Statistical measures of goodness of fit
In trend analysis the following measures will be
used
  • The Correlation Coefficient
  • The Determination Coefficient

7
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.

8
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)

9
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.

10
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)

11
Non-linear trends
Excel provides easy calculation of the following
trends
  • Logarithmic
  • Polynomial
  • Power
  • Exponential

12
Examples of the non-linear trends
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17
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

18
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