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Unit 22: Time Series Analysis—Introduction and Components of Time Series

example of secular trend. From year to year, the cost of living varies a great deal; but, if we Notes
consider a long-term period, we see that the trend is towards steady increase. Other examples
of secular trend are steady increase of population over a period of time, steady growth of
agricultural food production in India over the last ten to fifteen years of time.
• Seasonal variation involves patterns of change within a year, that tend to be repeated from year
to year. For example, sale of umbrellas is on the increase during the months of June and July
every year because of the seasonal requirement. Since these are regular patterns, they are useful
in forecasting the future production runs.
• Secular trend represents the long-term variation of the time series. One way to describe the
trend component in a time series data is to fit a line to a set of points on a graph. An approach
to fit the trend line is by the method of least squares.
• In many situations, studying the secular trend of time series allows us to eliminate the trend
component from the series. This makes it easier for us to study the other components of the
time series. If we want to determine the seasonal variation in the sale of shoes, the elimination
of the trend component gives us more accurate idea of the seasonal component.
• The trend values are regarded as normal values. These normal values provide the basis for
determining the nature of fluctuations. In other words, it can be found whether the fluctuations
are regular or irregular. So general tendency of the data can be analysed with the help of secular
trend.
• The trend analysis facilitates the comparison of two or more time
• Cyclical variation is that component of a time series that tends to oscillate above and below the
secular trend line for periods longer than one year and that they do not ordinarily exhibit
regular periodicity. The periods and amplitudes may be quite irregular.
• Another method used to measure the cyclical variation is the relative cyclical residual method. In
this method, the percentage deviation from the trend is found for each value.
• The cyclical variations are very helpful in studying the characteristics of fluctuations of a business.
One can come to know how sensitive is the business to general cyclical influences ? The general
pattern of a particular firm’s production, profits, sales, raw material prices, etc. can also be
known.
• The study of cyclical variations is helpful in analysing and isolating the effects of irregular
fluctuations. One can come to know either the variations are unpredictable or are caused by
other isolated special occurrences like floods, earthquakes, strikes, wars, etc.
• Seasonal variations are those forces affecting time series that are the result of man made or
physical phenomena. The major characteristic of seasonal variations is that they are repetitive
and periodic, the period is less than one year, say a week, a month or a quarter. Seasonal
variations can affect a time during November is normal, it can examine the seasonal pattern in
the previous years and get the information it needs.
• Seasonal variations help us to project past patterns into the future. In the case of long range
decisions, secular trend analysis may be adequate. However, for short-run decisions, the ability
to predict seasonal fluctuations is essential. For example, consider the case of a wholesale food
dealer who wants to maintain a minimum adequate stock of all food items. The ability to predict
short-run patterns, such as the demand of food items during Diwali, or at Christmas, or during
the summer, is very useful to the management of the store.
• The method of the ratio-to-moving average for computing the indices of seasonal variation is a
procedure whereby the different components in the series are measured and are isolated or
eliminated. Subsequently, the seasonal effect is identified and expressed in percentage form.
We first take a series in which seasonal pattern is suspected and plot this series on a graph to
identify the recurrence of the pattern. To identify the seasonal component, the data could be in
quarters or months or any other time period less than a year.
• The seasonal indices are used to remove the seasonal effects from a time series. Before identifying
either the trend or cyclical components of a time series, one must eliminate the seasonal variation.

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