In which languages/environments are there tools to estimate a VMA model of a given order? That is, given $q\in\mathbb{N}$ and a multivariate time series $y_t\in\mathbb{R}^d$, $t=1,\dots,T$, a function that returns best-fitting (in some sense, ML for instance) matrices $\Theta_i\in\mathbb{R}^{d\times d}$ such that $y_t$ is generated by the process

$$y_t=u_t+\Theta_1 u_{t-1} + \dots + \Theta_q u_{t-q},$$

where $u_i\in\mathbb{R}^d$ are iid random variables (for instance, multivariate Gaussians)?

I'd be especially interested in open-source languages such as Python or Julia.

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    $\begingroup$ "MTS" package in R, see functions VMA, VMACpp, VMAe, VMAoder, VMAs. $\endgroup$ – Richard Hardy Aug 21 '15 at 12:51
  • $\begingroup$ Thanks! Are there other alternatives? I know Mathematica had a time series package, which has now been discontinued, for instance. $\endgroup$ – Federico Poloni Aug 21 '15 at 12:54
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    $\begingroup$ I am only using R, so I cannot comment on other statistical packages. In R there are also a few other packages that can do VARMA models, I'd recommend to take a look around. "dse" may be one of them, if I remember correctly. $\endgroup$ – Richard Hardy Aug 21 '15 at 13:12

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