How do ARMA and ARMA-GARCH models relate?
ARMA/GARCH estimation in sequence
Compact vs Mirrorless - why pick one over another? What would be a reason for one to pick the compact (whatever it'd be P&amp;S or something more advanced) over mirrorless compact system camera  ?  Right now market is quite confusing — we have huge market of tiny-sensor compacts, we have mirrorless that use sensors in a size of these from P&amp;S cameras (Nikon 1 being notable example), we have compacts with sensors bigger than most popular mirrorless system (Canon G1X vs m4/3), we have lot of APS-C sensor mirrorless which are matched by some of the compacts (Fuji X100 being most notable example, but even Leica has its X2),  and to make it even more confusing — Sony released RX1 with full frame sensor, beating crap out of every mirrorless on a market.  So what are your arguments to pick compact over a mirrorless?  Why are they better, what's the reason behind logic of companies like Fujifilm which at the same time offers P&amp;S and X-mount mirrorless using same sensor size? I have got hundreds images of products with clear white backgrounds. I would like to change the white background color to become transparent.   Is there a means of batch processing this particular process with Photoshop or any other applications? How do I embed an image from the web into a Trello card comment or description? So far I have been successful embedding Youtube videos into Trello card comments; simply by including the URL in the comment Trello picks it up and renders an embedded Youtube thumbnail.   What I would like to do is the same thing, but with a simple PNG image. I don't want to upload the image as it is a Balsamiq mockup permalink which will get updated periodically, and I want the latest version to be displayed on the Trello card.   However, pasting the image URL into the Trello card has no effect.  Am I missing somthing? I have an external HD which used to be my TimeMachine drive. I got a different drive for that, so I want the original drive back as an external on my Windows box, but it has this random 200 MB partition labeled as EFI System Partition. How do I get rid of this? I installed or upgraded to Ubuntu 16.04, but I'm having some problems with my graphics card.   The display is blank The display flickers Items on the screen do not display correctly Certain programs complain of graphics issues The computer boots to low-graphics mode Your specific issue may not be here, but try the solutions described in the answers anyway.   This question is very broad, but each one of these issues likely has one solution.    If you are experiencing a login loop, check the last part of my answer.    If you experience one of the listed issues and have your own solution (mine didn't work, or there's a faster way), feel free to post another POLITE answer, describing your problem and how you fixed it.    Those attempting to install Ubuntu, please refer to the section titled: If you are unable to enter a TTY or are trying to install Ubuntu. How can I use the "signature" function in Preview on Mac Mini with no camera? I have a Mac Mini with no attached camera. I would like to use the feature of Preview that allows you to insert a signature. This relies on taking an image of your signature using an isight/facetime/webcam. I do not have on.  I do have a MacBook pro on which I use the signature function. Is there a way to copy a file from the the MacBook Pro to the Mac Mini to enable this function on the Mini? Fantasy/scifi combo - band of travelers who must get from "sphere" or domain to domain - each geographic area is ruled by a magician - it turns out later these are people who are unwittingly tapping into the computer grid they all live on to alter their own reality? Let $x$ and $y$ be positive integers such that $xy \mid  x^2+y^2+1$. Show that $$ \frac{x^2+y^2+1}{xy}= 3 \;.$$ I have been solving this for a week and I do not know how to prove the statement. I saw this in a book and I am greatly challenged. Can anyone give me a hint on how to attack the problem? thanks Equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$ Find the equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$. will it also be an ellipse? In Trailhead we have the query to get the Contacts for the Account named "SFDC Computing", with an inner query.   SELECT Name, (SELECT LastName FROM Contacts) FROM Account WHERE Name = 'SFDC Computing'   It works fine for my purposes.  "Contacts" is the name of the relationship, per Trailhead. So, I went to Object Manager and examined the Account object's "Fields and Relationships". There is nothing named "Contacts"!   In general, how do I get the name of the relationship, for use in similar SOQL queries? I cannot make xmodmap run on login in Ubuntu 13.04. I have searched around, including in askubuntu and all answers I found do not work.  I have a file named .Xmodmap in my home folder which contains the desired mappings. If I run it manually it works fine, so there is no error there. In order to make it run on startup, I have tried:     Using various .xinitrc containing one of the following commands:      xmodmap .Xmodmap xmodmap ~/.Xmodmap   /usr/bin/xmodmap /home/NAME/.Xmodmap if [ -s ~/.Xmodmap ]; then xmodmap ~/.Xmodmap fi  Using .Xresources instead of .xinitrc with the same variations. Setting it as a startup application.   None of the above works in Ubuntu 13.04 (64-bit). I also saw a few ideas about globally changing the keyboard mappings, but most of them were not applicable in Ubuntu 13.04 (i.e. the corresponding files did not exist where specified) and I prefer not to touch the global settings anyway. "going to come down" vs "going to have to come down" What is the difference between the following sentences?        This fence is going to come down.   This fence is going to have to come down.      I have doubt that when you are saying fence is going to have to come down, that is enough to say it right? but why I hear in movies saying fence is going to have to come down, is there a difference between them? Minkowski Metric Signature When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}   $$ where $ x^0,x^1,x^2,x^3 $ come from $ x^{\mu} : \mu = 0,1,2,3 $, and $ c $ is the speed of light. The first resource I had access to--I have to do a bit of digging for the exact paper--of course addressed that this invariant takes the tensor form: $$ ds^2 = g_{\mu \nu}dx^{\mu}dx^{\nu} $$ as well. This two things I've seen in all of my texts and online resources regarding resources. The element in question that varies between authors, is the time coordinate, $ x^0 $. When it was first explained to me, it was using the standard Cartesian representation for the spatial portion of the coordinates, and the time coordinate was labeled as $ x^0 = ict $. Squaring gives $ (x^0)^2 = -c^2t^2 $, and applying differential calculus, we get $ (dx^0)^2 = -c^2dt^2 $. Sensible and expected to have the tensor formula spit out the Minkowski Metric. The author then later explicitly states the coordinates are $ x^0 = ict, x^1=x,x^2=y,$ and $x^3 = z$.  My questions is then, why is it most authors on the subject omit the imaginary unit on the time coordinate? For example, .   The only reason I can fathom omission is if the author is using metric signature $ [+,-,-,-] $, where I started off learning the theory with signature $ [-,+,+,+] $ which may be the reason seeing the time coord with no imaginary unit seems dissonant to me. All help appreciated!  Edit: After reading the other answers, my questions is now one of why and how (mathematically) do we obtain the Minkowski Metric Signature. More specifically the one element with a different sign. Stripped out bottom bracket I have the following recurrence that I've been pounding on:  $$ a(0)=1\\ a(1)=1\\ a(2)=2\\ a(2n)=a(n)+a(n+1)+n\ \ \ (\forall n&gt;1)\\ a(2n+1)=a(n)+a(n-1)+1\ \ \ (\forall n\ge 1) $$  I don't have much background in solving these things, so I've been googling around looking for different techniques. Unfortunately, I haven't been able to correctly apply them yet. So far I've tried:   Characteristic equations Generating functions Plugging it into Wolfram Alpha Telescoping Observation   I'm sure that one or more of these is the way to go, but my biggest problem right now is figuring out how to deal with the idea that there are different equations for odd and even values of $n$. I'm not necessarily looking for a solution (though it would be gratefully accepted), but any nudges in the right direction would be much appreciated.    To follow up, it turned out that the speed problem described in my comment, below was related to the Decimal implementation in Python 2.7. Switching to Python 3.3 (and Java) made everything many orders of magnitude better. How do you detect where two line segments intersect? How do I determine whether or not two lines intersect, and if they do, at what x,y point? This is the proof from the book:     Theorem. There are infinitely many primes of the form $4n+3$.    Lemma. If $a$ and $b$ are integers, both of the form $4n + 1$, then the product $ab$ is also in this form.  Proof of Theorem: Let assume that there are only a finite number of primes of the form $4n + 3$, say  $$p_0, p_1, p_2, \ldots, p_r.$$ Let $$Q = 4p_1p_2p_3\cdots p_r + 3.$$ Then there is at least one prime in the factorization of $Q$ of the form $4n + 3$. Otherwise, all of these primes would be of the form $4n + 1$, and by the Lemma above, this would imply that $Q$ would also be of this form, which is a contradiction. However, none of the prime $p_0, p_1,\ldots, p_n$ divides $Q$. The prime $3$ does not divide $Q$, for if $3|Q$  then $$3|(Q-3) = 4p_1p_2p_3\cdots p_r,$$ which is a contradiction. Likewise, none of the primes $p_j$ can divides $Q$, because $p_j | Q$ implies $p_j | ( Q - 4p_1p_2\cdots p_r ) = 3$, which is absurd. Hence, there are infinitely many primes of the form $4n +3$.   END  From "however, none of the prime ...." to the end, I totally lost!    My questions:   Is the author assuming $Q$ is prime or is not? Why none of the primes $p_0, p_1,\ldots, p_r$ divide $Q$? Based on what argument?     Can anyone share me a better proof?     Thanks. Do immigration checks exist between Northern Ireland and England/Scotland? (not just for flights but also ferry/bus/train) Do immigration checks exist between the Republic of Ireland and England/Scotland? How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer let $a_{i},i=1,2,\cdots,n$ be postive integer ,show that $$1^{n-1}2^{n-2}\cdots (n-2)^2(n-1)|\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$$  I know this $\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$ is  Vandermonde  determinants,and I found $$1^{n-1}2^{n-2}\cdots (n-2)^2\cdot (n-1)=1!2!3!\cdots (n-1)!=\prod_{1\le i&lt;j\le n}(j-i)$$ we only prove $$\prod_{1\le i&lt;j\le n}\dfrac{a_{j}-a_{i}}{j-i}$$ is integer  maybe consider Vandermonde determinants ? But I can't prove this Flag abusive users I think the community does a great job policing questions/answers, etc. and the community has some good tools available to do this.  Between flagging questions with some reasons behind it and editing posts, closing them, and deleting them, the only thing that seems to be missing to me is the ability to flag a user.  Reasons to flag a user as abusive:   Duplicate User Abusive Behavior Offensive user name or profile User profile consists of spam Others?