Page 300 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 23 : Time Series Methods—Graphic, Method of Semi-averages
Dilfraz Singh, Lovely Professional University

Unit 23 : Time Series Methods—Graphic, Notes

Method of Semi-averages

CONTENTS
Objectives
Introduction
23.1 Graphic
23.2 Semi-averages Method
23.3 Summary
23.4 Key-Words
23.5 Review Questions
23.6 Further Readings

Objectives

After reading this unit students will be able to:
• Describe Graphic Method.
• Explain Semi-average Method.
Introduction

Fitting a trend curve involves assuming that a given time series exhibits a certain trend movement
which, were it not for cyclical, irregular and seasonal fluctuations would have been a linear or non-
linear form. Therefore, we first assume that the data to be plotted on a graph exhibit a certain trend
form (linear, parabolic or exponential) and then an attempt is made to measure this trend. Measuring
a trend actually means computing the constants of the equation that we have chosen to be
representative of the trend in the data. However, it should be remembered that if we choose a wrong
curve for the data, then the constants of the equation computed would be wrong, and any forecasting
made on the basis of this equation would be wrong.
23.1 Graphic

Freehand method is also called the graphic method in the sense that the trend line is determined by
inspecting the graph of the series. According to this method, the trend values are determined by
drawing freehand straight line through the time series data that is judged by the analyst to represent
adequately the long-term movement in the series. Once the freehand trend line is drawn, a trend
equation for the line can be approximated. This is done by first reading off the trend values of the
first and the last period from the chart with reference to the freehand line. For this purpose, the first
period is usually considered the origin. Thus, the trend value for the first period is the value of a for
the equation. Then the difference between the trend values of the first and the last period is obtained.
This difference represents the total change in variable Y throughout the whole duration of the series.
Therefore, when this difference is divided by the number of periods in the series, the result represents
the average change in Y per unit time period. This is the value of b in the equation. The trend line for
many series may be satisfactorily drawn provided the fluctuations around the general drift are so
small that the path of the trend is clearly defined. The main trouble with this method is that it is too
subjective. Even an expert in this subject may draw different lines at different times for the same
series. There is no formal statistical criterion whereby the adequacy of such a line can be judged.

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