Tuesday, February 4, 2014

Time series introductory notes

What is Time Series?

"A time series is a sequence of data points, measured typically at uniform time intervals."[1]


Trend : "A systematic change in a time series that does not appear to be periodic is called trend." [2] We can see either upward trend or downward trend in a Time Series.

Upward trend:

Downward trend:

Another characteristics of Time Series is Shift.

Downwards shift:

Upward shift:

Seasonal patterns 

These are fluctuations which occurs for short duration at a fixed time of year or month. A good example can be spikes in sales during thanksgiving every year. Another example is sales of woolen clothes over the period of several years will form seasonal pattern due to change in season.



These are recurrent upward and downward variations in Time series which generally happens over significant amount of time. These are not regular as Seasonal patterns. Recession cycles are good examples of it. [3]

Decomposition of Time Series 

It is a statistical process which deconstruct a Time Series into different components. The decomposition can be done based on rate of change or predictability. 

The rate of change is widely used method for decomposition which gives us [4]
  • Trend Component T_t
  • Cyclical Component C_t
  • Seasonal Component S_t
  • Irregular Component I_t (also called noise or random component)


[1] Time series wiki
[2] Introduction to time series by Cowpertwait and Metcalfe
[3] Time series presentation
[4] Decomposition of Time Series

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