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Archive for the ‘Series’ Category

What is time series?

Time series is a series of observations taken sequentially over time. Time series can be equally spaced.

What are time series used for?

The applications of time series are:

1. forecasting to give a view of an uncertain future
2. analysis to give description of what happened.

Applications and uses of time series

Forecasting

To use time series in forecasting, first construct a suitable model taking into account:

• the analysis of historical development of the series
• utilization of relevant information likely to affect future development.

When the quantity being forecast is known, incorporate the new information into the model.

Time series procedure

The procedure of time series analysis is to produce future forecast. There are two main steps to time series analysis for forecasting. The first is to forecast observation and the second is the analysis of data. Then the process is repeated incorporating new data.

Basic models of time series analysis

There are three basic models of time series analysis:

1. models for simple time trends using linear regression
2. systematic cyclical variation model of time series
3. influential or causal variable (regressions)

Laurent series of Laurent expansion is the expression applied to a function that is analytic in a punctured disk or annulus. Laurent series or Laurent expression is the expression of the given function as a doubly infinite power series.

Laurent Series Formula

Example of Laurent series in use

The Laurent series or Laurent expansion of: in { z:0 <

Taylor Series Expansion

Taylor series is the expansion of a function f into a power series about the point a. Taylor series expansion is as follows: 

 

represents the nth derivative of f at point a. 

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Maclaurin Series

Maclaurin series is the special case of Taylor Series expansion when a = 0. 

 

Maclaurin series expansions of sin x and cos x are given by: 

sin x =  

cos x =