If you check Bayes` Theorem the denominator is just used as a normalizing constant that ensures that in the continuous case the posterior density integrates to 1. And it is easy to show that the ...

Here my thoughts. Hope you already found the solution as I am sort of at the same point. Changing the Likelihood of y for GLM changes the full conditional of your betas and likely the variance. So I ...

I think you have two options with option one using a SAR(IMA) model. If you have a reoccurring effect every weekday (dummy), then you can already improve the model. Option 2: As you stated - I would ...

To capture the relative effect i would go for x_t - x_t-1 / x_t-1 If you want the same result in your example x_t-1 = 13 x_t = 23 & z_t-1 = 3 z_t = 13 you could just go for the difference x_t - ...

Using Fourier series is machine learning. Machine/Statistical learning is just a general term for all kinds of tasks where learning from data is required.

1) The factor map indicates that my two first principal components explain 48% of the variance in the data. I've read that this might be due to that the correlation among variables... PCA does only ...

You might want to check the definition of "supervised" & "unsupervised" statistical (machine) learning. And most importantly check & understand the methods you want to apply. I wouldn't ...