Method of estimating Secular Trend

The chief characteristics of a secular trend may be analysed as under.

(i)  It is either upward or downward.

The secular trend of a series is generally either upward or downward in nature. For example, the data relating to population, production etc. have a general tendency to move upward, and the data relating to birth rate and death rate due to the advancement in medical technology, improved medical facilities, better sanitation, diet etc. have a general tendency to move downward. However, such a trend may not always hold good. It is quite possible that in certain part of a time period it may move upward, in certain part it may move downward, and in certain other part of the time it may remain stable.

(ii) It occurs as result of such forces which are more, or less stable.

The secular trend of a series usually takes place on account of some forces which are more or less stable over a long time or which change very slowly or gradually. The Examples of such forces are: changes in technology, discovery of new natural sources, or their depletion etc. the effects of which are very gradual, slow, smooth, and move generally in one direction. They operate in an evolutionary process and do not reflect any sudden change.

(iii) It relates to a long period of time.

The secular trend, always, refers to the general tendency of the data to rise, or fall over a long period of time, an evolution of trend for a short period is not proper because there is likelihood of cyclical movement contained therein to be taken as a long period trend. Regarding the spam of the period, there is no such hard and fast rule. It all depends of on the nature of the date under study. In case of data relating in every 15 seconds over a period of 10 hours may be considered a long one to study the general tendency. But in case of data relating to the national income, growth in population, imports and exports of a country etc. a period of 3 to 4 years may not be even sufficient to reveal the general tendency of the data. However, the longer, the time period of a series the better would be the result and as a matter of safe-guard, the time period should cover a minimum of two to three complete cycles.

(iv) It is likely to fluctuate round a constant.

The secular trend of a phenomenon does not necessarily show always a rising or falling tendency. It is quite likely to fluctuate within a particular range. For example, the temperature of human body, or that of a locality always fluctuates between some constant limits at various times.

Broadly speaking there are three types of methods for measuring the trend values in a time series. They are: (i) Free hand graphic method, (ii) Average method and (iii) Least square method. The average method, again, consists of three different methods viz: (i) Arbitrary average method, (ii) Semi average method and (iii) Moving average method. Similarly, the method of least square consists of five different types of methods. They are: (i) Straight line method, (ii) parabolic method, (iii) Geometric or logarithmic method, (iv) Exponential method, and (v) Growth curve method. Thus, in all, we have nine different methods of measuring the trend values of a time series. They are:

• Free hand graphic method
• Arbitrary average method
• Semi average method
• Moving average method
• Straight line method of least square
• Parabolic method of least square
• Geometric method of least square
• Exponential method of least square
• Growth curve method of least square

The secular trend of a time series has many uses for a statistician. Some such uses are outlined here as under:

• It is used for getting a general idea about the pattern of behaviour of a phenomenon under study. This very much helps the business men in forecasting and planning their future course of action relating to inventary and production etc. This, also, helps an economist in formulating his economic policies, and planning for a country.
• It is used in making comparisons between two or more time series and in drawing meaningful conclusions therefrom.
• It is used in the further study of the short time fluctuations of a time series viz: season, cyclic, and irregular ones. This is done by determining the trend values first and then isolation such trend values from the observed values of the time series either by the process of subtraction or division.
• It is used in the extra-polation of the future values of a phenomenon. With reference to the trend values we can very well forecast the future behaviour of a variable on the assumption that its past behaviour will be repeated in future.