XeTex - Times New Roman font for Romanian characters ș, ț, Ș and Ț

I have downloaded the Times New Roman font and put it into `.local/fonts` where it should be (my OS is Fedora 17 and I use TexLive 2012). It is recognized by LibreOffice and LyX. LibreOffice displays correctly the Romanian characters `ș,ț,Ș,Ț` and even converting the LibreOffice document to pdf keeps them visible and rightly displayed, but when I write a document in LyX using Times New Roman and XeTex compilation, even though I see them in the input document, the pdf output displays four squares instead of the desired characters. I expected that, since the command `fc-list :lang=ro | Times` does not display anything, so it's an incompatibility between Times New Roman and Romanian language (which I can't explain since LibreOffice correctly displays the four characters). How can I solve this? Do I need a special Times New Roman font? I haven't found one, it's almost 2013 and there's no Times New Roman for the Romanian language used in LyX with XeTex :)

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I'm not sure, but this might be relevant: lyx.org/trac/ticket/7348 – scottkosty Dec 13 '12 at 23:40
LibreOffice (and most GUI applications) can fallback to a different font for characters missing from the requested font, XeTeX does not do that. – Khaled Hosny Dec 14 '12 at 3:39
Is there a reason you are using an arbitrary Times New Roman font (of unknown quality) rather than TeX Gyre Termes, a free Times clone developed by the 'TeX community' (GUST plus money from others)? The TeX Gyre fonts are pretty good on accent coverage. – Joseph Wright Dec 14 '12 at 7:05
Can you add a minimal example of LaTeX code with which you get such a problem? – egreg Dec 14 '12 at 7:58
@Khaled Hosny - No, it is not the case. I didn't notice any difference between the four characters and the others when using Times New Roman. They are the same. – riderplus Dec 14 '12 at 14:00