# ISS (Statistical Services) Statistics Paper III: Questions 1 of 109

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

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.

## Explanation

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