Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Component of Time Series Data

Traditional methods of time series analysis are concerned with decomposing of a series into a trend, a seasonal variation and other irregular fluctuations. Although this approach is not always the best but still useful (Kendall and Stuart, 1996).

The components, by which time series is composed of, are called component of time series data. There are four basic Component of time series data described below.

Different Sources of Variation are:

  1. Seasonal effect (Seasonal Variation or Seasonal Fluctuations)
    Many of the time series data exhibits a seasonal variation which is annual period, such as sales and temperature readings.  This type of variation is easy to understand and can be easily measured or removed from the data to give de-seasonalized data.Seasonal Fluctuations describes any regular variation (fluctuation) with a period of less than one year for example cost of variation types of fruits and vegetables, cloths, unemployment figures, average daily rainfall, increase in sale of tea in winter, increase in sale of ice cream in summer etc., all show seasonal variations.The changes which repeat themselves within a fixed period, are also called seasonal variations, for example, traffic on roads in morning and evening hours, Sales at festivals like EID etc., increase in the number of passengers at weekend etc. Seasonal variations are caused by climate, social customs, religious activities etc.
  2. Other Cyclic Changes (Cyclical Variation or Cyclic Fluctuations)
    Time series exhibits Cyclical Variations at a fixed period due to some other physical cause, such as daily variation in temperature. Cyclical variation is a non-seasonal component which varies in recognizable cycle. sometime series exhibits oscillation which do not have a fixed period but are predictable to some extent. For example, economic data affected by business cycles with a period varying between about 5 and 7 years.In weekly or monthly data, the cyclical component may describes any regular variation (fluctuations) in time series data. The cyclical variation are periodic in nature and repeat themselves like business cycle, which has four phases (i) Peak (ii) Recession (iii) Trough/Depression (iv) Expansion.
  3. Trend (Secular Trend or Long Term Variation)
    It is a longer term change. Here we take into account the number of observations available and make a subjective assessment of what is long term. To understand the meaning of long term, let for example climate variables sometimes exhibit cyclic variation over a very long time period such as 50 years. If one just had 20 years data, this long term oscillation would appear to be a trend, but if several hundreds years of data is available, then long term oscillations would be visible.These movements are systematic in nature where the movements are broad, steady, showing slow rise or fall in the same direction. The trend may be linear or non-linear (curvilinear). Some examples of secular trend are: Increase in prices, Increase in pollution, increase in the need of wheat, increase in literacy rate, decrease in deaths due to advances in science.Taking averages over a certain period is a simple way of detecting trend in seasonal data. Change in averages with time is evidence of a trend in the given series, though there are more formal tests for detecting trend in time series.
  4. Other Irregular Variation (Irregular Fluctuations)
    When trend and cyclical variations are removed from a set of time series data, the residual left, which may or may not be random. Various techniques for analyzing series of this type examine to see “if irregular variation may be explained in terms of probability models such as moving average or autoregressive  models, i.e. we can see if any cyclical variation is still left in the residuals.These variation occur due to sudden causes are called residual variation (irregular variation or accidental or erratic fluctuations) and are unpredictable, for example rise in prices of steel due to strike in the factory, accident due to failure of break, flood, earth quick, war etc.
Component of Time Series Data

Component of Time Series Data



The Author

Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.


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  1. hi, i like u for what u re. Am a versity student from kyambogo uganda persuing a bechelors degree in economics and statistic how would i get help directly from u?

  2. Salam sir, I am Ramzan assistant professor of statistics, government college karachi, PhD student at sindh university jamshoro.
    sir my topic is time series modeling
    please help in this regard
    pl rply

    1. It is better to read relevant articles.

      1. sir can you help me in analyzing data

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