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Filter

Filter

Filter:

A filter is an algorithm for processing a time series or random process . There are two major classes of problems solved by filters:

1. To estimate the current value of a time series (X(t), t = 1,2, ...) , which is not directly observable, from observed values of another time series (Y(t), t=1,2,...) , related to the time series X(t).


2. To predict the next value Y(t+1) of the observed time series Y from the current value Y(t) and previous values Y(t-1),Y(t-2), ... .


Consider a simple example - a time series x(i) observed in the presence of additive noise


y(i) = x(i) + n(i);   i = 1,2, ...


where y(i) are observed values, x(i) are non-observable values, and ni are values of additive random noise. the goal is to estimate x(i) from y(i) . A filter of order N can be specified, for example, by function FN() of N+1 arguments:


^
xi
 
= FN(y(i), y(i-1), ..., y(i-N) )


Filters are also used for processing random process es. In this case filters are specified by integral operators or differential equations.

Browse Other Glossary Entries

Courses Using This Term

Forecasting Analytics
This course will teach you how to choose an appropriate time series model: fit the model, conduct diagnostics, and use the model for forecasting.
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