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I am a econometrics student, and I've to understand what type of process the one in the image below is. I am not able to go back to the main classic stochastic processes (AR, MA, ARMA, ARCH/GARCH). In particular, the fact that epsilon is multiplied and not added generated confusion in me. Epsilon is a Gaussian white noise Thanks!

enter image description here

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closed as unclear what you're asking by whuber Nov 25 '18 at 21:01

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    $\begingroup$ So $\{X_t\}$ is a complex valued? Are you sure $\epsilon_t$ is Gaussian (rather than something else like lognormal)? $\endgroup$ – Matthew Gunn Nov 25 '18 at 20:14
  • $\begingroup$ Yes, epsilon is the disturbance distribuited as a Normal. {Xt} is simply the value of the process at time t. But for example in an Autoregressive process I expect that the disturbance is added not multiplied. $\endgroup$ – White Noise Nov 25 '18 at 20:26
  • $\begingroup$ For $X_t$ to be well-defined, you need to specify which square root you are taking, especially (but not only) for negative or complex values. If this isn't perfectly clear, write a (simple) program to simulate a realization of this process: it will run into trouble the first time $X_{t-1}$ is negative, which will happen quickly. $\endgroup$ – whuber Nov 25 '18 at 21:01
  • $\begingroup$ @whuber thanks for the answer. The exercise must be done without any simulation, it's a written test. I have to tell which type of process is it among the ones studied during the course, and then obtain the autocorrelation function. I think we'are dealing only with real numbers. $\endgroup$ – White Noise Nov 25 '18 at 21:08
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    $\begingroup$ @whuber really thanks for all the answers. There was a typo in the original source. Thanks a lot $\endgroup$ – White Noise Nov 26 '18 at 22:02