2. Trend forecasting
Trend forecasting is technique of time series
forecasting which uses statistical methods in
order to predict future patterns of time series
data.
Trend forecasting is used to predict future data
by relying on historical (past) data.
3. Trend is often shown graphically (as line graphs) with the
level of a dependent variable on the y-axis and the time
period on the x-axis
Trend forecasting may be used to determine a trend line (projection) for
future forecasts. The linear trend is any long-term increase or decrease
in a time series in which the rate of change is relatively constant.
4. For example, having statistics on company profit for 5 years (table 1)
you can find the profit forecast for the next period t = n +1=5+1=6
(for 2014, because 2014 is the sixth period).
5. Three steps in trend forecasting
• 1-st step: Select the equation.
• 2-d step: Calculate the
forecast based on trend
equation.
• 3-d step: Estimate the forecast.
6. 1-st step: Select the equation
Trend equation is used to determine the trend in the variable
y, which can be used to forecasting.
Linear equation describes the process when the economic
data increase or decrease by more or less constant
value. Linear equation looks like:
^
where a and b – are the linear coefficients;
t – is the independent variable (time – years, quarters,
months).
y а b t t = + ×
8. For example: statistical data on demand for products for 10 months are
given in the table 2. Calculate the demand forecast for January and
February using trend forecasting.
11. 2-d step: Calculate the forecast based on
trend equation
Demand forecast with trend forecasting
12. 3-d step: Estimate the forecast
• Coefficient of determination
• Correlation coefficient
• Absolute forecast error
• Mean forecast error
• Mean squared forecast error
• Root mean squared forecast error
• Mean percentage error
13. Coefficient of determination (R2) – is a measure used in
trend analysis to assess how well a linear equation
explains and predicts future outcomes
• values between 0 and 0,3 indicate a weak
positive linear relationship;
• values between 0,3 and 0,7 indicate a
moderate positive linear relationship;
• values between 0,7 and 1 indicate a
strong positive linear relationship.
14. Correlation coefficient is the square root
of the coefficient of determination
The following points are accepted guidelines for interpreting the
correlation coefficient:
• 1) 0 indicates no linear relationship;
• 2) +1 indicates a perfect positive linear relationship: as one variable
increases in its values, the other variable also increases in its values;
• 3) -1 indicates a perfect negative linear relationship: as one variable
increases in its values, the other variable decreases in its values;
• 4) values between 0 and 0,3 (0 and -0,3) indicate a weak positive
(negative) linear relationship;
• 5) values between 0,3 and 0,7 (-0,3 and -0,7) indicate a moderate positive
(negative) linear relationship;
• 6) values between 0,7 and 1 (-0,7 and -1) indicate a strong positive
(negative) linear relationship.
17. For example: statistical data on demand for products for 10 months
are given in the table 2. Calculate the absolute forecast error, mean
forecast error, mean squared forecast error, root mean squared
forecast error, mean percentage error, correlation coefficient and
coefficient of determination.
19. Calculation results
Correlation coefficient (r) is a square root of the
coefficient of determination
r = 0,614 = 0,78
approximately 78% (0,78*100%) of the variation in
the dependent variable (demand) can be explained
by the linear equation.
