A Model of Vector Autoregression

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Vector autoregression (VAR) generalizes univariate autoregression (AR). A VAR process of order can be formulated as



where is an random vector, are fixed coefficient matrices, and is -dimensional white noise.

In econometrics, the VAR process is used to model linear interdependencies among multiple time series. This Demonstration serves as an analytical tool for modeling multiple time series data (mean adjusted) using the stable model . Outputs include model estimation, a residual check, and forecasts. You can also choose preferable estimation method (OLS or Yule–Walker estimator).

The functions are based on [1] and [2].


Contributed by: Matus Baniar (March 2014)
(Charles University, Prague)
Open content licensed under CC BY-NC-SA



Data samples:

1. generated by stationary process

2. generated by stationary process

3. generated by stationary process

4. first differences of logarithm of daily close prices of Apple, Google, and Microsoft in the time period from 2013/02/01 to 2013/11/15

5. generated by nonstationary process

For a selected model , the first data values are used as presampled values.


[1] T. Cipra, Finanční ekonometrie, Praha, Czech Republic: Ekopress, 2008.

[2] H. Lütkepohl, New Introduction to Multiple Time Series Analysis, Berlin: Springer, 2005.

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