I'm currently struggling with different Model like AR or MA.

If AR(1) is expressed as: $y_t = \beta + \beta_t \times y_{t-1} + \epsilon_t $

How do I know what the $\beta$ 's would be? What are the dependencies?

I think a simple example would help a lot.


1 Answer 1


You have a slight typo in the notation of a AR(1) model. The correct signature is,

$y_t = \beta_0 + \beta_1 \times y_{t-1}+\epsilon_t$ or $y(t) = \beta_0 + \beta_1 \times y(t-1) + \epsilon(t)$,

where $y(t)$ and $\epsilon(t)$ are random variables. If $y(t)$ is standard Gaussian you can estimate $\beta_{0,1}$ with a maximum likelihood estimator (MLE). If not you will need a more complex method. You can read more about it in this article on estimating at ARMA Process.

  • $\begingroup$ thank you very much for now. I will have a look at this. I'm currently participating in an EMC course for Big Data and need to present the chapter for Time Series Analysis on thursday, so I welcome any tips for beginners ;-) $\endgroup$
    – easysaesch
    Commented Nov 15, 2016 at 16:59
  • $\begingroup$ Welcome on Data science SE. Time series is a big... big... big... topic :). For a beginner I can highly recommend Rob Hyndman's book. This will take you through the preparatory steps that you need to take before you can use AR(I)(MA) such as making time series stationary, statistical tests, etc. Don't forget to accept and up vote my answer if it helped you :). $\endgroup$
    – Stereo
    Commented Nov 15, 2016 at 17:07
  • $\begingroup$ I would but 15 reputation points are required $\endgroup$
    – easysaesch
    Commented Nov 16, 2016 at 9:30

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