Forecasting using trend analysis

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Part 1. TheoryPart 2. Using Excel: a demonstration. Assignment 1, 2

Learning objectives

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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

To learn how:

Main idea of the trend analysis forecasting method

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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”

Prerequisites: 1. Data pattern: Trend

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Trend (close to the linear growth)

Prerequisites: 2. Correlation

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

The Correlation Coefficient

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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

Main idea of the trend analysis method

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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.

The general equation for a trend line

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F=a+bt Where:F – forecast,t – time value,a – y intercept,b – slope of the line.

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.

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

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Statistical measures of goodness of fit

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The Correlation CoefficientThe Determination Coefficient

In trend analysis the following measures will be used:

The Coefficient of Determination

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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.

Goodness of fitt: Determination Coefficient RSQ

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Range: [0, 1]. RSQ=1 means best fitting; RSQ=0 means worse fitting;

Evaluation of the trend analysis forecasting method

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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.

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

Part 2. Switch to Excel

Working with Excel

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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

Using Excel to calculate linear trend

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Select a line on the diagram Right click and select Add Trendline Select a type of the trend (Linear)

Part 3. Non-linear trends

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Non-linear trends

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LogarythmicPolynomialPowerExponential

Excel provides easy calculation of the following trends

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Logarithmic trend

y = 4,6613Ln(x) + 1,0724

R2 = 0,9963

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0 2 4 6 8

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Trend (power)

y = 0,4826x1,5097

R2 = 0,9919

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0 2 4 6 8

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Trend (exponential)

y = 0,0509e1,0055x

R2 = 0,9808

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Trend (polynomial)

y = -0,1142x3 + 1,6316x2 - 5,9775x + 7,7564

R2 = 0,9975

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Choosing the trend that fitts best

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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

End