# Vector autoregressive models

**URL:** <https://discourse.julialang.org/t/vector-autoregressive-models/136333>\
**Category:** General Usage\
**Created:** [March 22, 2026, 3:07pm UTC](https://discourse.julialang.org/t/vector-autoregressive-models/136333 "2026-03-22T15:07:55Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![freeman](https://avatars.discourse-cdn.com/v4/letter/f/ec9cab/32.png) [@freeman](https://discourse.julialang.org/u/freeman)\
**Post date:** [March 22, 2026, 3:07pm UTC](https://discourse.julialang.org/t/vector-autoregressive-models/136333/1 "2026-03-22T15:07:55Z")

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Hello!

What’s currently the situation on fitting and making predictions from vector autoregressive models?

Here’s the related packages I’ve found, but they either are not vector models, or look like scratch code:

> **[GitHub - lucabrugnolini/VectorAutoregressions.jl: Vector autoregressive model in Julia](https://github.com/lucabrugnolini/VectorAutoregressions.jl)**
>
> Vector autoregressive model in Julia

> **[GitHub - s-broda/ARCHModels.jl: A Julia package for estimating ARMA-GARCH models.](https://github.com/s-broda/ARCHModels.jl)**
>
> A Julia package for estimating ARMA-GARCH models.

> **[GitHub - AndreyKolev/GARCH.jl: Julia GARCH package](https://github.com/AndreyKolev/GARCH.jl)**
>
> Julia GARCH package

> **[GitHub - junyuan-chen/AutoregressiveModels.jl: Essential toolkits for working with autoregressive...](https://github.com/junyuan-chen/AutoregressiveModels.jl)**
>
> Essential toolkits for working with autoregressive models

I think the last one is the closest, but seems geared to predicting variance, not means.

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**Author:** ![Paul\_Soderlind](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/paul_soderlind/32/1753_2.png) [@Paul\_Soderlind](https://discourse.julialang.org/u/Paul_Soderlind)\
**Post date:** [March 22, 2026, 3:30pm UTC](https://discourse.julialang.org/t/vector-autoregressive-models/136333/2 "2026-03-22T15:30:23Z")

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This file (which is used in some lecture style notebooks in the same repository) contains some useful stuff:

> <https://github.com/PaulSoderlind/FinancialEconometrics/blob/master/src/TimeSeries_VAR.jl>

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**Author:** ![freeman](https://avatars.discourse-cdn.com/v4/letter/f/ec9cab/32.png) [@freeman](https://discourse.julialang.org/u/freeman)\
**Post date:** [March 22, 2026, 4:51pm UTC](https://discourse.julialang.org/t/vector-autoregressive-models/136333/3 "2026-03-22T16:51:37Z")

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> [@Paul\_Soderlind](#):
>
> `CompanionFormAR`

Thank you!

Just to be sure, on that file function `VAR1Forecast` returns `(Ex, Varx)`.

> <https://github.com/PaulSoderlind/FinancialEconometrics/blob/338955f9da5b2d47b9a7d4406a228d056d8c275a/src/TimeSeries_VAR.jl#L199-L222>

Does this stand for forecast of expected mean and expected variance?

As a separate comment, it seems a shame that this isn’t in a package.

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**Author:** ![Paul\_Soderlind](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/paul_soderlind/32/1753_2.png) [@Paul\_Soderlind](https://discourse.julialang.org/u/Paul_Soderlind)\
**Post date:** [March 22, 2026, 5:19pm UTC](https://discourse.julialang.org/t/vector-autoregressive-models/136333/4 "2026-03-22T17:19:26Z")

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Ex is the forecast, and Varx the variance of the forecast error.