9

4

To estimate 1-dimensional VAR process (which is AR process) you can easily use functions `EstimatedProcess`

or `FindProcessParameters`

like this:

```
sample = RandomFunction[ARProcess[{.2,-.4},.1], {1,300}];
EstimatedProcess[sample, ARProcess[{a,b},v]]
(*or*)
FindProcessParameters[sample, ARProcess[{a,b},v]]
```

Now lets say we have sample

```
alpha = {{.2,.1}, {-.3,.2}};
sigma = {{1.0,0}, {0,0.3}};
sample = RandomFunction[ARProcess[{alpha},sigma], {1,100}]
```

which is based on two dimensional VAR process (I took this definition from `ARProcess`

documentation).

Then neither of this two ways does work:

```
EstimatedProcess[sample,ARProcess[{{{a1,a2}, {a3,a4}}}, {{v1,v2}, {v3,v4}}]]
FindProcessParameters[sample,ARProcess[{{{a1,a2}, {a3,a4}}}, {{v1,v2}, {v3,v4}}]]
```

Is it possible to estimate vector autoregressive process in Mathematica?

The error message

"Estimation is not currently supported for the parameters in process ARProcess[{{{a1,a2},{a3,a4}}},{{v1,v2},{v3,v4}}]"says no. So, other than programming it yourself it looks like it's not possible. – Sjoerd C. de Vries – 2014-01-30T21:54:32.1101Thanks for asking, I've long wanted to ask the same question here. It seems that in time series and macroeconomic modeling mma lags far behind packages such as free IRIS Toolbox for Matlab or EViews. – iav – 2014-04-10T14:57:40.583

1

Look at this demo: http://demonstrations.wolfram.com/AModelOfVectorAutoregression/ If you download the source code you'll easily find functions for OLS and Yule-Walker estimation procedures.

– iav – 2014-04-10T17:21:10.1632Thanks for the answer and especially thanks for recommending my demo. :) At first, I was using EViews as well but its not that difficult to apply those methods using such a friendly language as Wolfram language. – matt525252 – 2014-04-11T19:04:47.900

@matt525252, it would be very nice of you if you would be able to share some of the tools you've developed. The demo is impressive. Have you ever tried to implement and estimate any of the state-space models in mma? – iav – 2014-04-23T15:36:21.497

1@iav, thank you. I focused only on VAR models. Every function I developed should be included in demo. I basically made this demo as a tool because of some calculations in my masters thesis. But maybe in the future I will have time to create some other functions for estimating different types of models. And what do you mean by mma? – matt525252 – 2014-04-28T12:22:49.740

@matt, it seems that mma is used here as a shorthand for Mathematica. – iav – 2014-04-29T16:46:53.723

@matt525252, both of your expressions work. – garej – 2017-08-15T07:10:38.280