# Components of Time Series

Traditional methods of time series analysis are concerned with decomposing 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).

## Components of Time Series

The components, by which a time series is composed, are called the components of time series data. A time series is not necessarily composed of all these four components of Time Series Data. The components of time series are (i) Seasonal Effect, (ii) Cyclic Variation, (iii) Secular Trend, and (iv) Irregular Variation. The four basic components of time series are described below.

Different Sources of Variation are:

### Seasonal effect (Seasonal Variation or Seasonal Fluctuations)

Many of the time series data exhibit a seasonal variation which is the annual period, e.g., sales and temperature readings. Seasonal variations are easy to understand and can be easily measured or removed from the data to give deseasonalized data. Seasonal Fluctuations describe any regular variation with a period of less than one year. For example, the cost of various types of fruits and vegetables, clothes, unemployment figures, average daily rainfall, increase in the sale of tea in winter, increase in the 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 the morning and evening hours, Sales at festivals like EID, etc., an increase in the number of passengers at the weekend, etc. Climate, social customs, religious activities, etc cause seasonal variations. The main causes of seasonal variations are seasons, religious festivals, and social customs.

### 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 that varies in a recognizable cycle. These variations are considered a more dangerous effect on business and economic activity. Sometimes series exhibits oscillation which does not have a fixed period but is somewhat predictable. For example, economic data is affected by business cycles with a period varying between about 5 and 7 years.

The cyclical component may describe any regular variation (fluctuations) in time series data in weekly or monthly data. The cyclical variation is periodic and repeats itself like a business cycle, which has four phases (i) Peak/Prosperity (ii) Recession (iii) Trough/Depression (iv) Expansion.

### 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. It represents a relatively smooth, steady, and gradual movement of a time series in the same direction. To understand the meaning of the long term, consider the climate variables. These variables sometimes exhibit cyclic variation over a very long time period such as 50 years.

If one just had 20 years of data, this long-term oscillation would appear to be a trend, but if several hundreds of years of data are available, then long-term oscillations would be visible. These movements are systematic where the movements are broad, steady, showing a slow rise or fall in the same direction. The trend may be linear or non-linear (curvilinear). Some examples of secular trends are:

• Increase in prices,
• Increase in pollution,
• an increase in the need for wheat,
• an increase in literacy rate,
• decrease in deaths due to advances in science.

Taking averages over a certain period is a simple way of detecting a trend in seasonal data. Change in averages with time is evidence of a trend in the given series. There are more formal tests for detecting a trend in time series.

### Other Irregular Variation (Irregular Fluctuations)

When trend and cyclical variations are removed from a set of time series data, the residual is 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 variations occur due to sudden causes are called residual variations (also called accidental or erratic fluctuations) and are unpredictable. For example, a rise in prices of steel due to strikes in the factory, accidents due to failure of the break, flood, earth quick, and war, etc.

The figure below further explains the components of time series data.

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