The title pretty much says it all: is an AR(p) process with roots inside the unit circle non-stationary?
According to Theorem 8.8 in Time Series A.W. van der Vaart an ARMA process $$\phi (L)X_t=\theta(L)\epsilon_t$$ has a  unique stationary solution $X_t=\psi(L)\epsilon_t$ with $\psi=\theta/\phi$ if $\phi$ has no roots on the complex unit circle. This would imply that the explosive process, with $\rho&gt;1$, is a stationary process $$X_t=\rho X_{t-1}+\epsilon_t$$ with stationary solution $X_t=\sum_{i=1}^\infty \rho^{-i}\epsilon_{t+i}$.  Now indeed $\sum_{i=1}^{\infty} \rho^{-i} &lt; \infty$ so that weak stationarity can be proved by using this representation.   However, here on stackexchange I see a lot of question/answers that suggest that the process above is not stationary (see for example , ). In particular, the accepted answer of the latter question claims that the process is non-stationary by simulating a series and showing it displays explosive trending behaviour.  I think the only way to reconcile the theorem I mention above and the plots in the accepted answer of () is the following: the explosive process is indeed stationary but non-ergodic, that is, we cannot find the statistical properties of $X_t$ such as $\mathbb{E}(X_t)=\mu$ by observing a single infinitely long sample path of the explosive process, mathematically: $$\lim_{t \to \infty}\frac{1}{t}\sum_{t=1}X_t \neq\mathbb{E}X_t$$  Is this reading correct?
Spam gets fairly heavily punished - 100 reputation penalty, if I recall correctly, and the content itself gets hidden in the revision history.  Now if we just have some rubbish:     dfajiojaifojadiofjadhigaowkokaomdiovnuiyhioqejgioqejgio   I'm not talking about someone posting a question or comment as an answer (i.e. possibly just not knowing the rules or being frustrated with not having the required privileges), or someone making some really horrible attempt at answering the question, I'm talking about an answer that clearly shows absolutely no observation of any content on the page.  This, in my opinion, causes a similar amount of harm to the site - I'm inclined to say the fact that someone posts spam isn't as important as the fact that they're posting something that needs to be deleted, since we're likely going to delete it pretty quickly, and they're (likely) behaving maliciously, or am I wrong?  Why don't we treat this equally harshly, or why do we treat spam as harshly as we do?    Side notes:  I'm sure I've seen a few times where users get punished for posting spam when their link is likely actually relevant to the question and useful (should I flag these? They are still link-only answers, so they shouldn't really come back, and often I'm just not sure enough). While false positives are bad, it seems worse that we're treating worse behaviour better.  I'm assuming that's not what "abusive" in this reason is referring to: (I'm also not sure, off the top of my head, how this one gets treated)     It is offensive, abusive, or hate speech Is it possible to make signing up gracefully fail over to logging in if the SE OpenID account exists? For most OpenID options, it doesn't much matter if you pick the "Sign up" versus the "Log in" tab on the sign in page.  Whether you have an account on the site or not, it just does the right thing. Not so if you are using the Stack Exchange OpenID service:    (Bonus bug: the reCAPTCHA box is a bit too wide for the expanded "Sign up using Stack Exchange" container.)  Since we already have collected an email and password (well, two copies of the password), could we not check to see if they match and automagically log the user into their SE OpenID?  If not, the error needs to be reworded somehow to explain that while the email might have been used to create a Stack Exchange OpenID, that doesn't mean they can't log in with that OpenID to create an account.  Counterintuitively, they need to use the  even if they've never had an account there before.  The  link adds to the confusion since it sends an email that leads off with:     Someone requested an account recovery on The Workplace Stack Exchange for jericson@stackexchange.com, but we don't have an account on this site that matches this email address.   (For people with accounts on other sites and/or Stack Exchange OpenIDs, this paragraph is followed by other instructions that would probably work if followed. By that time I imagine many users are at wit's end.)  To simplify: If a user already has a Stack Exchange OpenID (likely because they have an account on another site) they should be able to use the  to sign up for an account or there should be clear instructions on what to do next if they fail. I cannot remember anyone writing the letter epsilon in any other way than \varepsilon in any math class; but in LaTeX \epsilon and \varepsilon are different symbols. Do any of you know why there are two different symbols? (I.e. if \epsilon is the correct way to write the letter epsilon, why aren't mathematicians using it, and when is, according to the standards today, the correct situation to use each of the symbols?) I received an email saying documents are /were What to do when my 3-year-old holds poop in and won't go in diaper or on potty? Is there a RegExp.escape function in JavaScript? When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$? $$\Bbb{Q} = \left\{\frac ab \mid \text{$a$ and $b$ are integers and $b \ne 0$} \right\}$$ In other words, a rational number is a number that can be written as one integer over another. For an integer, the denominator is $1$ in that case. For example, $5$ can be written as $\dfrac 51$.  Is $5$ a rational number? Or is $\dfrac 51$  a rational number? I'm not able to figure out what the definition is actually saying. What are the numbers that cannot be written as one integer over another?  Irrational numbers are the numbers that cannot be written as one integer over another. Roots of numbers that are not perfect squares are examples of irrational numbers.  However, what is this then: $\dfrac {\sqrt 7} {2}$? Google map only loading half of itself Prove : $p$(n│even number of ODD parts)=$p$(n│distinct parts ,number of ODD parts is even ) Find the representing matrix with the respect to the standard basis Let $\Bbb R^2$ be a finite-dimensional vector space and $T:\mathbb{R}^2\to \mathbb{R}^2$ a linear operator. Let $[T]_B =  \begin {bmatrix}0 &amp; 0 \\-1 &amp; 1 \end{bmatrix} $ be a matrix representation of $T$ in the basis $B= (1,1),(-1,0)$.   How can I find the matrix $[T]_E$ where $E$ is the standard basis $(1,0),(0,1)$ if the transformation isn't given in the question?  Thanks,  Alan Disable the activation of the menu bar when Alt is pressed in Windows 7 In Windows 7 how can I disable the function that activates the menu bar when Alt is pressed?  Are there some registry values to modify this behaviour? 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I have two questions about this:  1) is this possible?   2) If yes, how could I justify knowing I will lose my come-back flight during my first entry? (I would purchase round trip because one-way are too expensive, probably with less than 90 days difference) How to divide LaTeX table cells vertically? I want my table to have separated cells. Basically double lines but I can't figure how to have horizontal lines disconnected. I tried \hline and \cline but those connect too.  This is best I can do:    This is how I want my table to look:   \begin{tabular}{|c||c||c||c|}   \hline   \multicolumn{2}{|c||}{First Cell}&amp;   Second Cell&amp;   Third Cell\\   \hline   \hline   \begin{tabular}{@{}l@{}} Data\\ Data\\ Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}\\    \hline  \end{tabular} Photons acting as carriers of both attractive and repulsive forces I understand, in basic terms, how a photon, whilst not being electrically charged itself, is viewed as creating electrical repulsion by means of positive momomentum transfer between two negatively charged electrons.  In most introductory quantum mechanics and basic quantum field theory textbooks this repulsive momementum transfer picture is almost always used as a (in classical terms) billiard ball type illustration for electrical repulsion, the Compton effect and so on.  As a photon is a photon is a photon..... I would like to know how it also has the ability to produce atttraction and how negative momentum transfer (such as that between a positively charged object, say a positron and an electron) is explained in any sort of visualisable picture. I'm guessing this may involve Feymann diagrams and the use of time reversal but I'm on shaky ground from there on. How do I make an Bootable Ubuntu USB containing the the latest version of Ubuntu?  For completeness, how would I be able to do this on Ubuntu, Windows, OS X or another Linux distro? Possible Duplicate:          I know that I have to find the number of factors of $5$'s, $25$'s, $125$'s etc. in order to do this. But how can you derive such a formula for any number $n$?