# How to calculate ARMA model manually without R or Python

I kindly ask if someone at this forum knows how to manually calculate the arma model using time series data. I know how to do this using Python and R but im in need to do this manually. The data would be volatile. For example: 3.375, 3.200, 3.160, 3.110, 3.105, 3.230, 3.295, 3.375, 3.445, 3.315, 3.675. So it would both increase and decrease.

How would I, by using the example data, build an ARMA forecast model?

edit: Im new to this forum and if the question is not relevant, I apologize! Thanks in advance!

• What counts as "manually"? On your fingers? Pencil and paper? – The Laconic Feb 3 at 0:10
• Sorry for being unclear but yeah, pretty much. It would be ''easy'' doing this in R and/or python. However, im trying to incorporate the ARMA model into a programme where I can not use any advanced functions and have to do this manually. Im asking for someone to give an example of how to practically/manually calculate the model. I've found many examples of this online but I found them too theoretical without any pracitcal examples on how to apply data to the function – Vichtor Feb 3 at 0:25
• Can you please edit that new info into the Q? Some wants to close as 7nclear, with this incorporated it can stand – kjetil b halvorsen Feb 3 at 1:40
• Which is what I tried to do here stats.stackexchange.com/questions/77663/… – forecaster Feb 3 at 1:49
• Tack Kjetil, will do! – Vichtor Feb 3 at 2:46

$$\ell_{x}(\mu,\boldsymbol{\phi},\boldsymbol{\theta}) = - \frac{1}{2} \ln | \boldsymbol{\Sigma}(\boldsymbol{\phi},\boldsymbol{\theta})| + (\mathbf{x} - \mu \boldsymbol{1})^\text{T} \boldsymbol{\Sigma}(\boldsymbol{\phi},\boldsymbol{\theta})^{-1} (\mathbf{x} - \mu \boldsymbol{1}),$$
where the covariance matrix $$\boldsymbol{\Sigma}(\boldsymbol{\phi},\boldsymbol{\theta})$$ depends on the parameters $$\boldsymbol{\phi}$$ and $$\boldsymbol{\theta}$$ according to the auto-covariance function for the ARMA model. This function has two terms. The second is a standard sum-of-squares term, but the first is a more complicated term involving the logarithm of the determinant of the covariance matrix.