Time series analysis least square method solved examples

Time series analysis least square method solved examples In statistics or mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems by minimizing the sum of the squares of the residuals made in the results of each individual equation. The most important application is in data fitting.

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Time series definition of terms

Time series; A collection of observation of well defined data items obtained through repeated measurement over time. the components of time series are: secular trend, seasonal variations, cyclical fluctuations and irregular variations.
seasonal variations: is variation in a time series within one year that is repeated more or less regularly. Seasonal variation may be caused by the temperature, rainfall, public holidays, cycles of seasons or holidays.
cyclical fluctuations; refers to regular periodic fluctuations around the trend, excluding the irregular component, revealing a succession of phases of expansion and contraction.
secular trend; describes the movement over the long term of a time series that globally can be increasing, decreasing, or stable. The secular trend can be linear or not.
irregular variations; Irregular variations or random variations are not predictable constitute one of four components of a time series. They correspond to the movements that appear irregularly and generally during short periods.

Importance of time series analysis

Helps in cleaning the data
Understanding the data
For predicting the future