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Unit 11: Analysis of Time Series

11.1 Time Series Notes

A series of observations, on a variable, recorded after successive intervals of time is called a time
series.

It should be noted here that the time series data are bivariate data in which one of the variables
is time. This variable will be denoted by t. The symbol Y will be used to denote the observed
t
value, at point of time t, of the other variable. If the data pertains to n periods, it can be written
as (t, Y ), t = 1, 2, .... n.
t
11.1.1 Objectives of Time Series Analysis

The analysis of time series implies its decomposition into various factors that affect the value of
its variable in a given period. It is a quantitative and objective evaluation of the effects of
various factors on the activity under consideration.

There are two main objectives of the analysis of any time series data:
1. To study the past behaviour of data.
2. To make forecasts for future.
The study of past behaviour is essential because it provides us the knowledge of the effects of
various forces. This can facilitate the process of anticipation of future course of events and, thus,
forecasting the value of the variable as well as planning for future.

11.1.2 Components of a Time Series

An observed value of a time series, Y , is the net effect of many types of influences such as
t
changes in population, techniques of production, seasons, level of business activity, tastes and
habits, incidence of fire floods, etc. It may be noted here that different types of variables may be
affected by different types of factors, e.g., factors affecting the agricultural output may be entirely
different from the factors affecting industrial output. However, for the purpose of time series
analysis, various factors are classified into the following three general categories applicable to
any type of variable.
1. Secular Trend or simply Trend
2. Periodic or Oscillatory Variations

(a) Seasonal Variations
(b) Cyclical Variations
3. Random or Irregular Variations
1. Secular Trend: Secular trend or simply trend is the general tendency of the data to increase
or decrease or stagnate over a long period of time. Most of the business and economic time
series would reveal a tendency to increase or to decrease over a number of years. For
example, data regarding industrial production, agricultural production, population, bank
deposits, deficit financing, etc., show that, in general, these magnitudes have been rising
over a fairly long period. As opposed to this, a time series may also reveal a declining
trend, e.g., in the case of substitution of one commodity by another, the demand of the
substituted commodity would reveal a declining trend such as the demand for cotton
clothes, demand for coarse grains like bajra, jowar, etc. With the improved medical facilities,
the death rate is likely to show a declining trend, etc. The change in trend, in either case, is
attributable to the fundamental forces such as changes in population, technology,
composition of production, etc.

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