Paper 4: Fundamentals of Business Mathematics & Statistic

Time series is statistical data that are arranged and presented in a chronological order i.e., over a period of
time.

8.1 DEFINITION

According to Spiegel, “A time series is a set of observations taken at specified times, usually at equal
intervals.”
According to Ya-Lun-Chou, “A time series may be defined as a collection of reading belonging to different
time period of same economic variable or composite of variables.”

8.2 COMPONENTS OF TIME SERIES

There are various forces that affect the values of a phenomenon in a time series; these may be broadly
divided into the following four categories, commonly known as the components of a time series.
(1) Long term movement or Secular Trend
(2) Seasonal variations
(3) Cyclical variations
(4) Random or irregular variations
(1) Secular Trend or Simple trend - The general tendency of a data to increase or decrease or stagnate
over a long period of time is called secular trend or simple trend.
Most of the time series relating to Economic, Business and Commerce might show an upward tendency
in case of population, production & sales of products, incomes, prices; or downward tendency might
be noticed in time series relating to share prices, death, birth rate etc. due to global melt down, or
improvement in medical facilities etc. All these indicate trend.
(2) Seasonal variations - Over a span of one year, seasonal variation takes place due to the rhythmic
forces which operate in a regular and periodic manner. These forces have the same or almost similar
pattern year after year.
Seasonal variations could be seen and calculated if the data are recorded quarterly, monthly, weekly,
daily or hourly basis. So if in a time series data only annual figures are given, there will be no seasonal
variations.

Study Note - 8

TIME SERIES ANALYSIS

This Study Note includes

8.1 Definition

8.2 Components of Time Series

8.3 Models of Time Series Analysis

8.4 Measurement of Secular Trend

8.5 Method of Semi Averages

8.6 Moving Average Method

8.7 Method of Least Squares

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 8.1