1. Forecasting using trend analysis
Part 1. Theory
Part 2. Using Excel: a demonstration.
Assignment 1, 2

2. 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

3. 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”

4. Prerequisites: 1. Data pattern: Trend

5. Prerequisites: 2. Correlation
There should be a sufficient correlation between the time parameter and the values of the time-series data

6. 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

7. 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.

8. The general equation for a trend line
F=a+bt
Where:
F – forecast,
t – time value,
a – y intercept,
b – slope of the line.

9. 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.

10. The trend line is the “best-fit” line: an example

11. Statistical measures of goodness of fit
In trend analysis the following measures will be used:
The Correlation Coefficient
The Determination Coefficient

12. 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.

13. Goodness of fitt: Determination Coefficient RSQ
Range: [0, 1].
RSQ=1 means best fitting;
RSQ=0 means worse fitting;

14. 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.

15. Open a Workbook trend.xls, save it to your computer
Part 2. Switch to Excel
Open a Workbook trend.xls, save it to your computer

16. 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

17. 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)

18. Part 3. Non-linear trends

19. Non-linear trends Logarythmic Polynomial Power Exponential
Excel provides easy calculation of the following trends
Logarythmic
Polynomial
Power
Exponential

24. 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

25. End