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In the below:

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from top of Page 13: http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf

how do you interpret what x is an element of? It looks like the set of real numbers, transposed, power set with p?? :s

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1  
You draw the real number line, and then rotate it by 90 degrees :) –  nbubis Jul 13 '13 at 20:52
    
Seriously.....? It's just a vector of the real numbers? What about the "x p" part? –  user997112 Jul 13 '13 at 20:54
    
I think you'll need to specify what $T$ and $p$ are. –  Jack M Jul 13 '13 at 20:54
    
@JackM T is not defined, I believe it does mean transposed. I will link the paper if you want to see. p stands for a stock price. –  user997112 Jul 13 '13 at 20:55
    
What if $\mathbb R^p$ means column vectors and $\mathbb R^{T \times p}$ means row vectors? No: $p$ is a real number, a variable, isn't it? –  Francesco Genovese Jul 13 '13 at 20:55

1 Answer 1

up vote 2 down vote accepted

I still think it's a typo, and that there should be an $n$. If you look at other papers/sources on time-varying covariates (for example, this one), they say that $\mathbf{x_i}$ is column vector, and since we know $\beta$ is also a column vector, it has to be a dot product (implying T is the transpose operation). I think it's just errors and incorrect notation in the paper you're looking at. Based on what I've seen, it should say something like:

$$ \beta\in\mathbb{R}^p, \quad\mathbb{x_t}\in\mathbb{R}^{p\times n} $$

otherwise:

  • The summations being provided later in your paper do not have enough $\mathbb{x_i}$ vectors
  • The dot product between $\mathbb{x_i}$ and $\beta$ is undefined
  • If T were a variable, it is never clearly defined
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Oh sorry didn't realise this is what you pointed out in your other answer!!! It wasn't because I didn't trust your judgement :) –  user997112 Jul 13 '13 at 21:47
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No worries, I had to stop and look at it a bit myself, it's a pretty confusing (and awful) typo, to be honest. :) –  Kendra Lynne Jul 13 '13 at 21:50
    
Don't suppose you could glance at this one could you: math.stackexchange.com/questions/443022/… you'll know the answer in about 5 seconds! :) –  user997112 Jul 13 '13 at 22:03

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