Autoregressive (AR) Models

本文介绍了自回归(AR)模型在时间序列分析中的应用。AR模型通过递归线性滤波来描述平稳时间序列,其中输出是由滤波器的前一时刻输出的加权和构成。文中还详细解释了AR模型的定义及其参数。

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The autoregressive (AR) models are used in time series analysis . to describe stationary time series . These models represent time series that are generated by passing the white noise through a recursive linear filter . The output of such a filter at the moment Math image is a weighted sum of Math image previous values of the filter output. The integer parameter Math image is called the order of the AR-model.

The AR-model of a random process Math image in discrete time Math image is defined by the following expression:

 

where

  • Math image are the coefficients of the recursive filter;

  • Math image is the order of the model;

  • Math image are output uncorrelated errors.

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