Page 248 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 11: Analysis of Time Series

Notes

Case Study Production Estimate

uppose that there is a series of quarterly production figures (in thousand tonnes) in
an industry for the years 2004 to 2010 and the equation of linear trend fitted to the
Sannual data is Xt = 107.2 + 2.93t , where t = year 2007 and Xt the annual production in
time period t. Use this equation to estimate the annual production for the year 2005 and
2011.
Suppose now the quarterly indices of seasonal variations are: January-March 125, April-
June 105, July-September 87, October-December 88. (The multiplicative model for the
time series is assumed.) Use these indices to estimate the production during the first
quarter of 1987.

11.3 Summary

A series of observations, on a variable, recorded after successive intervals of time is called
a time series.
The data on the population of India is a time series data where time interval between
two successive figures is 10 years. Similarly figures of national income, agricultural and
industrial production, etc., are available on yearly basis.
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.
Secular trend or simply trend is the general tendency of the data to increase or decrease or
stagnate over a long period of time.
Trend values of two or more time series can be used for their comparison
Oscillatory movements, repeat themselves after a regular interval of time. This time
interval is known as the period of oscillation.
The main objective of measuring seasonal variations is to eliminate the effect of seasonal
variations from the data.
Random variations are usually short-term variations but sometimes their effect may be so
intense that the value of trend may get permanently affected.
The main objectives of measuring seasonal variations is to understand their pattern.
The measurement of seasonal variation is done by isolating them from other components
of a time series.
There are four methods commonly used for the measurement of seasonal variations.
These methods are:

Method of Simple Averages
Ratio to Trend Method
Ratio to Moving Average Method
Method of Link Relatives

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