Basic Concepts in Time Series Analysis (Part-1)

This post will be the first of a series of posts discussing about time sereis concepts. Here, we will briefly discuss on the definition of time series.

Definition

Time series is a sequence of numerical data points in successive order (time). Their mathematical formulation is a vector x(t), t=1,2,3,…,n where x(t) is random variable which gets some numerical values over t which is the time that has elapsed from the beginning of the observation.

A time series concerning only one variable is called univariate time series. When multiple variables are observed, the time series are termed as multivariate. There is also classification of the time series based on the time intervals for which observations are available. If we have observations in every instance of time, then we have continuous time series. Stock exchange rates or river flows may be observations recorded continuously. On the other hand, if the intervals are discrete, then the time series are termed as discrete time series. Usually, in discrete time series, observations are recorded sequentially in equally-spaced time intervals. For example, monthly/annual observations of water demand, is an example of equally-spaced discrete time series. Of course, time series could be un-equal spaced and in that case have to be transformed to equally-spaced time series in order to apply regular modeling techniques. The literature so far is mostly focused on evenly-spaced data though.

In the next part of the series, we will discuss about time series components.

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