in the answers given to this question  it is said that a stationary time series is not allowed to have regular cycles. According to my search a stationary time series has 3 properties:  Expactation value is constant for every t Variance is constant for every t Autocovariance is constant for every t  Which of those is violated by a time series with regular cycles? I'd appreciate every comment.
I just started trying to undestand the notion of stationary in time series. Basically I have 2 questions:  Can stationary time series contain regulary cycles and thus seasonality patterns? For exmaple in this tutorial it is stated that stationary time series can not have seasonal components (predicitable cycles)  whereas in this figures () the green time series that clearly has cycles (and thus seasonality) is labeled as 'stationary' (and I have seen these kind of figures quite often if you just google 'stationary time series) Can a stationary time series have periods with no fluctuations and periods with high fluctuations? As far as I understood the variance and the (aut)covarianz should not change over time making such a time series not stationary. But here in this picture () the time series below is labeld as stationary altough it has periods with changing fluctuations.  I hope you can help me as I am confused about the concept of stationarity. I'd appreciate every comment. The bounty is to expire quite soon. So I'd be happy if some could at least give me one answer to my questions. It will help me a lot. Why is nobody answering the questions? Are they not clear enough? If so, please tell me. I think they are important and fundamental as the concept of stationarity is quite important.
Ragged Right linebreaking, such that the last line is fullest, and the first most empty I am trying to get a better feel for the topology of ordinals and just received a great answer to this  where the Cantor-Bendixson rank and degree turn out to be a complete homeomorphism invariant of countable compact spaces. Now I am curious about what is going on within homeomorphism classes of ordinals. In particular, I want to know how to characterize countable ordinals $\alpha$ which are minimal among all ordinals homeomorphic to $\alpha$.   Certainly finite ordinals and $\omega$ are easy. Next, if $\alpha\cong \omega+1$, then it seems like we would have to have $\omega+1\leq \alpha&lt;\omega +\omega$ since there can only be one limit point in $\alpha$. Things become a little fuzzier for me with ordinals that have infinitely many limit points.  For instance, suppose $\alpha$ is an ordinal homeomorphic to $\omega^{\omega}$. Is it necessarily true that $\alpha\geq \omega^{\omega}$? Is there a general rule for knowing when an ordinal is the smallest among all ordinals homeomorphic to it? QM without complex numbers I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier? Why there isn't reputation points for successful flagging? By helping the site by flagging successfully (and therefore gaining higher flag weight), you typically inform that you are able to understand the system and be helpful.  Similarly, when you are helpful by editing posts (not necessarily even understanding anything, just making it better), you gain 2 points for each edit. Good flagging may require even more understanding; while editing just fixing spelling and/or formatting gives reputation points. You don't have to understand whether question (or answer) is on-topic, or even meaningful.  So, why there isn't for example 2 points for each flag that was acted on, in the same way flag weight increase is determined? $1+x+\ldots+x^n$ perfect square Let $p$ be the polynomial $p(x)=1+x+\ldots+x^n$. For which couples $(a, n)\in\mathbb{N}^2$, $p(a)$ is a perfect square? I'm particularly interested in $p(3)$. List of PDOStatement::bindParam data_type parameters How can we remove the launcher that come with Unity on this new Ubuntu version ? Solve $$\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$$ without complex integration.  This integral can be very easily solved with contour integration, but how can you solve it without taking a tour in the complex plane? Explaining different Standard Deviation results from same data in ArcGIS Desktop and MS Excel? I have done some interpolation in Geostatistical Analyst in ArcGIS and I got the Standard Deviation (SD) a bit different from the SD that I calculated in Excel Spreadsheet.   What algorithm does each package use? Why are the results different? I am trying to install chrome browser via command line.  I tried this:  $ apt-cache search chrome browser   The results show that the proper term is "chrome-browser," so I tried that:  $ sudo apt-get install chrome-browser   And then "Y" for the Y/n question.  But the installation threw errors.  Does someone see anything wrong with the commands I issued? Calling PHP functions within HEREDOC strings In PHP, the HEREDOC string declarations are really useful for outputting a block of html.  You can have it parse in variables just by prefixing them with $, but for more complicated syntax (like $var[2][3]), you have to put your expression inside {} braces.  In PHP 5, it is possible to actually make function calls within {} braces inside a HEREDOC string, but you have to go through a bit of work.  The function name itself has to be stored in a variable, and you have to call it like it is a dynamically-named function.  For example:  $fn = 'testfunction'; function testfunction() { return 'ok'; } $string = &lt;&lt;&lt; heredoc plain text and now a function: {$fn()} heredoc;   As you can see, this is a bit more messy than just:  $string = &lt;&lt;&lt; heredoc plain text and now a function: {testfunction()} heredoc;   There are other ways besides the first code example, such as breaking out of the HEREDOC to call the function, or reversing the issue and doing something like:  ?&gt; &lt;!-- directly output html and only breaking into php for the function --&gt; plain text and now a function: &lt;?PHP print testfunction(); ?&gt;   The latter has the disadvantage that the output is directly put into the output stream (unless I'm using output buffering), which might not be what I want.  So, the essence of my question is: is there a more elegant way to approach this?  Edit based on responses: It certainly does seem like some kind of template engine would make my life much easier, but it would require me basically invert my usual PHP style.  Not that that's a bad thing, but it explains my inertia..  I'm up for figuring out ways to make life easier though, so I'm looking into templates now. Linear regression not fitting well I do a linear regression using R lm function:  x = log(errors) plot(x,y) lm.result = lm(formula = y ~ x) abline(lm.result, col="blue") # showing the "fit" in blue     but it does not fit well. Unfortunately I can't make sense of the manual.  Can someone point me in the right direction to fit this better?  By fitting I mean I want to minimize the Root Mean Squared Error (RMSE).    Edit: I have posted a related question (it's the same problem) here:   and the raw data here:    except that on that  x is what is called errors on the present page here, and there are less samples (1000 vs 3000 in the present page plot). I wanted to make things simpler in the other question. DEF file syntax error in visual studio 2012 Compound literals in MSVC Why are heatmaps on qgis 2.8.1 produced in the wrong CRS? How to illuminate the darkness inside glass objects in Cycles? My model has a clear plastic (or glass) dome with objects inside.  The objects appear dark.  I've tried the glass shader with color 100% RGB, with very small IOR, and using just a refraction shader.    I know Cycles has problems with caustics, but I just want broad illumination to fall clean through the glass.  The light-to-column path can ignore refraction, but is blocked or tremendously attenuated. The camera-column path needs refraction, and seems to work fine anyway.  This demo image offers all optical paths of interest:   light upon object, seen directly light upon object, seen through glass (looks okay) light through glass onto object, seen directly. This is the shadow on the lit side of the column just below the glass tubing.  I expect full illumination, but there is shadow.  There is some light, but it's diffuse light from the floor. light through glass onto object, seen through glass. This     I did at one point try non-progressive rendering, and find extremely coarse light where there shouldn't be shadow, but this is not a practical way to make nice images. I've even tried cranking up certain sampling settings to many thousands, but still get bad noise though less, at the cost of long render times. I  would like to finish my creations sometime before "Star Trek, the Generation After the Next" becomes real life, if you know what I mean.  The next image is an example. I think Transmission in Sampling was 5000, but not sure.    I'm using Cycles in Blender 2.67 on a quad core Linux machine, 16GB RAM. Machine limits have never been a problem for 3D rendering.  Possibly, I screwed up some setting when I made my startup file, and just need to fix it. OTOH maybe this is just a limitation of path tracing, or of the way Cycles does it. If that's the case, what to real-world Blender artists do when they need to produce images on a budget and schedule?  What is the practical real-world fix? Etymology of "dong" and "dongle" Dong as in ding-dong is clearly onomatopoetic as confirmed by :     ding dong        imitative of the sound of a bell, c.1560.   and similarly for :     ding (v.)       1819, "to sound as metal when struck," possibly abstracted from ding-dong, of imitative origin. The meaning "to deal heavy blows" is c.1300, probably from Old Norse dengja "to hammer," perhaps also imitative. Meaning "dent" is 1960s. Related: Dinged; dinging.   What, then, is the origin of dong to mean penis? Etymonline.com is  here:     dong (n.)        "penis," 1891, of unknown origin.   We also have a much more recent word, dongle, which has no entry at etymonline.com but  claims it is:     Apparently from dangle.   This leads me to the theory that the anatomical and onomatopoetic dongs  are not related and that the former usage, like dongle, derives from dangle. So, my questions are:   Is that so? Does dong (penis) derive from dangle? Sounds reasonable enough but I have found no definitive sources for it. Does dongle derive from dangle? It makes perfect descriptive sense for dong but the USB devices called dongles do not dangle but instead protrude quite rigidly, so I feel that dongle being derived from the cruder meaning of dong makes more sense. Which "href" value should I use for JavaScript links, "#" or "javascript:void(0)"? The following are two methods of building a link that has the sole purpose of running JavaScript code. Which is better, in terms of functionality, page load speed, validation purposes, etc.?    function myJsFunc() {     alert("myJsFunc"); } &lt;a href="#" onclick="myJsFunc();"&gt;Run JavaScript Code&lt;/a&gt;     or    function myJsFunc() {     alert("myJsFunc"); }  &lt;a href="javascript:void(0)" onclick="myJsFunc();"&gt;Run JavaScript Code&lt;/a&gt; This question is about the net speed.  I'm from China, and I find that opening pages on Stack Overflow is very fast, normally within a range of 1 to 4 seconds. This speed is very good for a website outside China; it's even faster than some native websites.  Not every website outside China has such good speed, so I am wondering why and how Stack Overflow manages to be so quick. How can I programmatically pause an NSTimer? I'm using an NSTimer to do some rendering in an OpenGL based iPhone app.  I have a modal dialog box that pops up and requests user input.  While the user is providing input I'd like to "pause" i.e. something like this:  [myNSTimer pause];   I'm using this syntax because I've been doing things like:  [myNSTimer invalidate];   when I want it to stop.  How can I programmatically pause the NSTimer?