I have two questions related to VAR and AR.  First question: What exactly is the difference between a VAR and AR?  Second question: Is the application of a two-variable VAR not the same as an AR with two variables?
What is the exact difference between an autoregressive (AR) and vector autoregressive model (VAR)?  I always thought that VAR would just be for more than two variables, until I learned that AR can also have more than two variables. I.e. I had a misunderstanding(?) that AR models are not always bivariate.  Before I write too much potentially false assumptions about the difference between AR and VAR, it would rather be interested to see if anyone can make provide a quick and good summary.
Fighting a black hole: Could a strong spherical shell inside an event horizon resist falling in to the singularity? As a thought experiment imagine an incredibly strong spherical shell with a diameter a bit smaller than the event horizon of a particular large black hole.  The shell is split into two hemispheres, and the two hemispheres are released from either side of the black hole such that they will meet and join inside the event horizon, forming a stationary uniform shell around the singularity. Of course, we consider that the shell is flawless, and exactly centred around a stationary singularity - clearly this is an unstable equilibrium but we imagine it is possible.  Is is possible that the structural forces provided by such a shell could be strong enough to resist the extreme gravity conditions inside the event horizon, and hence avoid being sucked into the singularity?      (For the purposes of this question we can consider taking the shell to extreme levels of strength, e.g. consider that the shell is made from a theoretical maximally densely packed neutronium-like material that is strongly resistant to any further compression due to the Pauli exclusion principle). Flow On Schedule I"ve created a flow that I'd like to run monthly on the 7th day of each month. How can I do this with scheduled apex. I have no experience writing apex from scratch. Any suggestions or starting off points appreciated.  Thanks,  Kris Can we use curved spacetime to measure the one-way speed of light? This is related to  and  The idea is to shine a beam of light from a clock towards a heavy mass, like a black hole, in some manner such that the curvature of spacetime around the mass is sufficient to &quot;bend&quot; the light directly back to the clock. That is, to send the light along a self-intersecting geodesic using a sufficiently curved spacetime. Note that in this case the source and the detector are the same object, so no clock synchronization is required. Hypothetically, this should measure the one-way speed of light. None of the given refutations from the similar posts on this site are convincing. Here are some of the main refutations, as I understand them, and my counter to them: (1) In being curved by spacetime, the light is actually changing direction, hence this is not the one-way speed. To my understanding of General Relativity, the light travels along a geodesic; that is, a curve such that, ignoring technicalities of Differential Geometry, its tangent direction is constant. There is no reflection or acceleration. So in this sense, how can the light with a constant tangent direction be said to change direction? One might say that the path deviates from a straight line in Euclidean space, but given that spacetime is not Euclidean, has no , and has no global notion of direction, this is the only definition of straight or &quot;one direction&quot; that makes sense. Thus, either the light does not change direction and is &quot;one-way,&quot; or we need to be clearer about what exactly we mean by &quot;one-way&quot; in the context of General Relativity. (2) Such an experiment would be impossible or impractical. I think some posters were saying this because the original questions implied that the clock would have to be at the event horizon of a black hole, which is of course impossible or impractical; however, I don't think such an extreme closeness to the black hole is required. Given that the  of a black hole, where light orbits in a circle, is outside of the event horizon, shining the light at some distance outside of the photon sphere should be sufficient to curve the light back to the clock, regardless of the distance of the clock from the black hole (see my rough illustration). At the extreme, we could place the clock directly on the photon sphere, which should be theoretically possible. Regardless, the question is not about practicality, but whether the one-way speed is theoretically measurable.  Update: Essentially what this argument boils down to, I think, is that the average speed of light along a single self-intersecting geodesic may differ from the average speed of light along a non-geodesic self-intersecting path, which is always c. Put that way, however, it does seem a little ridiculous. It is hard to see how the anisotropy of the speed could be defined in such a way as to be consistent with this pathological case. Presumably, we could approximate a single self-intersecting geodesic with a non-geodesic path arbitrarily closely, so, logically, the average speeds over each path should be approximately the same, i.e., c. Furthermore, how would the &quot;preferred direction&quot; of the speed of light behave around a black hole, for instance? Regardless, I still think this experiment does actually solve the problem for the given notion of &quot;direction&quot;. Though the problem is usually posed in the flat spacetime of Special Relativity, with a global notion of direction, so the apparent unanswerability of this question should be seen as a limitation of Special Relativity only, which is then solved by General Relativity. I want to know, if this bug is fixed, because all previous versions of Ubuntu didn't work for me. So I just want to know, should i leave Windows 10 and go for Ubuntu 17.10. Thanks! I'm not sure how password hashing works (will be implementing it later), but need to create database schema now.  I'm thinking of limiting passwords to 4-20 characters, but as I understand after encrypting hash string will be of different length.  So, how to store these passwords in the database? SharePoint 2013 Jan 2016 Updates Is anyone here experience problems in SharePoint after installing the latest JAN 2016 on 13th Jan 2016 (Western Australian Time) updates for SharePoint 2013. I am guessing it could be KB3114503 update giving me problems.  I am getting the same problem on other machines after running the same updates too.  The problem I am receiving is, on every list view I get this error message below:  TypeError: Unable to get property 'replace' of undefined or null reference   TypeError: Unable to get property 'replace' of undefined or null referenceSys.ArgumentNullException: Sys.ArgumentNullException: Value cannot be null. Parameter name: element Why is Ubuntu 14.04 so slow on my laptop? I just installed Ubuntu 14.04 on a Dell laptop with 1.7Ghz Pentium M and 1Gbyte memory.  Graphics are Intel® 852GM/855GM x86/MMX/SSE2, OS type is 32bit.  The whole system is VERY slow. When I launch the applications manager, for example, I need to wait in order to see the letters I typed appear!  It is as if the CPU was overloaded and no memory available, but I only have Firefox running.  How can I make the system run smoother? It used to have Windows XP installed and it worked fine. Prevent direct access to a php include file I have a php file which I will be using as exclusively as an include. Therefore I would like to throw an error instead of executing it when it's accessed directly by typing in the URL instead of being included.  Basically I need to do a check as follows in the php file:  if ( $REQUEST_URL == $URL_OF_CURRENT_PAGE ) die ("Direct access not premitted");   Is there an easy way to do this? Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$ I just need to know if this integral converges.  If it does, what is the value?  If not can anyone tell me what is the value of the $$ \int_{-\infty}^\infty 2\,\frac{\cos(w)\sin(w)}{w}\ dw ? $$ In Java, you can qualify local variables and method parameters with the final keyword.  public static void foo(final int x) {   final String qwerty = "bar";  }   Doing so results in not being able to reassign x and qwerty in the body of the method.  This practice nudges your code in the direction of immutability which is generally considered a plus. But, it also tends to clutter up code with "final" showing up everywhere. What is your opinion of the final keyword for local variables and method parameters in Java? Can I have multiple DHCP servers on one network? This is a  about Redundant DHCP Servers.   Is it possible to have more than one DHCP server on the same LAN? What are the implications of doing this?    What happens if there is more than one DHCP server available? How do my clients know which one to use?  How can I have DHCP servers supplying addresses to more than one subnet\network segment? How can I configure multiple DHCP servers to supply addresses for the same subnet. SQL JOIN - WHERE clause vs. ON clause After reading it, this is not a duplicate of . The answer may be related (or even the same) but the question is different.    What is the difference and what should go in each?  If I understand the theory correctly, the query optimizer should be able to use both interchangeably. How do you override page.tpl.php in Omega 4? I am using the  base theme, and am trying to override page.tpl.php.    This file is in the base theme in sites/all/themes/omega/templates/system.  When I copy it into my theme, edit it, clear caches, I don't see my changes?  Why can't I override this template? Why is mathematical induction a valid proof technique? terminal won't launch after install python 3.5 After I installed Python 3.5 and ran the commands below, my terminal and many other programs won't launch any more.  cd /usr/bin sudo rm python3 sudo ln -s python3.5 python3    How can I restore the default Python version again to fix these problems? Can I install any iOS version I wish by picking and choosing which firmware to restore? I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this? Safety of installing Ubuntu alongside Windows Is it really safe to choose the "Install Ubuntu alongside Windows" option from the Ubuntu installation program?  I never used that option, instead I used other tools such as partition magic or windows 7's disk tool to resize my partitions.  Since I'm going to install Ubuntu across a lot windows (XP, Vista and 7) machines. It would not be nice to damage those Windows partitions.  What is your experience? Can I use this feature without concerns? How can I disable animation when switching desktops in Lion? I would very much like to disable the sliding animation that occurs when switching desktops via ctrl+&#x2192;/&#x2190; or ctrl+[number] in Lion.   This was previously accomplished in previous versions with this command:  defaults write com.apple.dock workspaces-swoosh-animation-off -bool YES &amp;&amp; killall Dock   This new animation is even more slow than in Snow Leopard - nearly 1 second to switch - a real productivity killer.  Any help greatly appreciated! Let $\,f : \mathbb{R} \rightarrow \mathbb{R}$ be a infinitely differentiable function that is  increasing and bounded. Then is it true that $\lim_{x\to \infty}f'(x)=0$? How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$? Are the floor functions of $0.999\cdots$ and 1 equal?  It is true that $0.999\cdots=1$ but how does one justifies the integer part of $0.999\cdots$ being 1 , where it is not, or alternatively without using $0.999\cdots=1$ how can we show that  $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$ ?