ANALYSIS OF TIME SERIES
• Time Series
An arrangement of data by successive time period is called time series. For example, the total
monthly sales receipts in a departmental store, the annual yield of a crop in a country for a no
of years, hourly temperature recorded at a locality for a period of years, the weekly prices of
wheat in Lahore, the monthly consumption of electricity in a certain town, the monthly total of
passengers carried by rail, the quarterly sales of a certain fertilizer, the annual rainfall at
Karachi for a number of years, the enrolment of students in a college or university over a
number of years and so forth.
• Signal and Noise
Signal: The systematic component of variation in time series is called signal.
Noise: An irregular or random component of variation in the time series is called noise.
• Analysis of Time Series
The analysis of time series consists of the description, measurement, and isolation of the
various components present in the series, this analysis helps the economists, businessmen and
The value of the time series (Y) is the product effects of four components trend (T) , Cyclical
(C), Seasonal (S) and Irregular (I) Movements. Y T C S I
= × × ×
But some statistical; consider the components of a time series fallow and additive law.
Y T C S I
= + + +
• Components (Movements) of a Time Series
A typical time series has four types of movements usually called components for a time series.
a. Secular Trend (T)
b. Seasonal Movements or Seasonal Variation (S)
c. Cyclical Movements or Cyclical Variation or Cyclical Fluctuation (C)
d. Irregular, Accidental or Random Movements (I)
a. Secular Trend
These movements refer to long term variation which shows any tendencies of growth or
decline over a long period approximately 30 to 40 years. These are smooth, steady and
regular in nature for example, a continually increasing for more food due to population
increase, a decline in death rate due to advance in science.
b. Seasonal Moveme