ISS (Statistical Services) Statistics Paper III: Questions 1 of 96
Appeared in Year: 2015
Describe in Detail
List the main components of a times series. Explain the method of link relative for measurement of seasonal fluctuations of a times series.
The main components of a times series are the following:
(i) Secular Trend (T) : Long term movements in the mean
This measures smooth and regular long-term movements of a times series delineating the increasing, decreasing or stagnant trend over a long span of time.
(ii) Seasonal Variation (S) : Cyclical fluctuations related to the calendar
Short-term fluctuations observed in a time series data, particularly in a specified period usually within a year. Seasonal variations are more akin to climatic and weather conditions.
(iii) Cyclical Variation (C) : Relates to periodic changes
A cycle consists of more than a year period. The cycles in a time series depict the prosperity and recession, ups and downs, booms and slumps of a business. A complete cycle usually consist four elements: prosperity, recession, depression and recovery.
(iv) Irregular Variation (I) : other random and systematic fluctuations
These variations usually occur due to epidemics, earthquakes, floods, war etc. Another name is residual variations.
Link-relative method: Various step for measuring seasonal fluctuations by link-relative
method are given below: Step-1. The link relative formula is
Calculation of link relatives eliminates the influence of the trend.
Step-2. Find the mean or median for each season whichever is considered appropriate.
Step-3. Convert link relatives into chain relatives. The formula for chain relative can be given as
where I varies over all periods.
Step-4. The chain relative for the first season is calculated on the basis of the last season by the formula
For the above two formula, the adjustment factor c is worked out by
The corrections for chain relatives for I, II, … periods are 0×c, 1×c, … etc. To add these quantities, we obtain the adjusted chain relatives.
Seasonal index by the link-relative method is