Trend, Seasonal, Cyclical And Irregular Variations In Time Series

Variations In Time Series - Trend, Seasonal, Cyclical And Irregular


In Nature, Time Series without variations are very hard to come by, there always exist some kind of variation either some kind of trend (either upward or downward trend) , Seasonal, Cyclical and Irregular Variations or even contain two or more of those variations, which will have to be eliminated before modeling commences on the series.

Identifying this variations in the series could be done easily by looking at the series plots or Auto-Correlation Plots and partial Auto-Correlation Plots. I will take you through the identification using series plots.

1. Trend In Time Series

Secular Trend Or Long Term Trend : This refers to the general direction that Characterizes a Time Series over Long periods of time. This variation in time series shows the actual direction of the series over long periods.

In statistics , trend analysis often refers to techniques for extracting an underlying pattern of behavior in a time series which would otherwise be partly or nearly completely hidden by noise.

Trend analysis is the rampant practice of collecting data and attempting to spot a pattern, which is either trend (either upward or downward trend)

Upward trend 


2.  Seasonal Variations In Time Series : These are periodic occurrence in the trend that complete their cycle in one year, reoccurring in the next year in the same pattern.

This means that there is a regularly repeating pattern of highs and lows related to calendar time such as seasons, quarters, months, days of the week, take for example, traffic on roads in morning and evening hours, Sales during festivals like New Yam, increase in the number of passengers at weekends etc.

Seasonal variations are caused by climate, unemployment figures, average daily rainfall, increase in sale of tea in winter, increase in sale of ice cream in summer, social customs, religious activities e.t.c and this type of variation should be removed from the data to give De - seasonalized data

Seasonal Trend 


3. Cyclical Variations
Cyclical variations refer to those  recurring Up's and Down movements around trend level in the series, they are basically a long-run cycle or period unrelated to seasonality factors.

They are non-seasonal component which varies in recognizable cycle. At-times the series exhibits oscillation having no fixed period but are predictable to some extent.

Unlike seasonal Variations, The cyclical variation do not repeat themselves, they are characterized with phases, Peak,  Recession, Trough/Depression, Expansion.

4. Random And Irregular Variations : They are abrupt or sudden changes to either the level of the series or the variance. They are accidental or erratic fluctuations, very unpredictable
These sudden changes occur due to hardly predictable occurrences like stricks, Famines, Drought, War, failure of break, flood, earthquakes e.t.c

Irregular Variations 


It is always difficult to get a series with just one trend, so we have brought together some images to show how this trend will combine in a real life situation.




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