Error terms are calculated when you already have a model, and you calculate them as predicted values - actual values. Now you want to fit MA process to predict future data points (means you still don't have any MA model, so don't have predicted values and thus don't have past forecast errors)  MA model says ...   The model will try to learn parameters theta's, but how do derive these error terms?  (Please refrain heavy mathematical equations to answer this question, if possible, please provide answer with simple example; lets say my time series is 2,5,7,9 ..how the fifth element will be calculated based on MA(1) process?)
This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the observation $Y$ is first regressed against its previous values $Y_{t-1}, ..., Y_{t-n}$ and then one or more $Y - \hat{Y}$ values are used as the error terms for the MA model.  But how are the error terms calculated in an ARIMA(0, 0, 2) model? If the MA model is used without an autoregressive part and thus no estimated value, how can I possibly have an error term?
I put some alias commands in my .bashrc file, so that they might be loaded everytime I open a new Terminal window. Yet this doesn't happen. I have to select run script: in the Terminal&gt;Preferences&gt;&quot;MyDefaultTheme&quot;&gt;Shell prefpane and add: source .bashrc &amp;&amp; clear for it to work... This seems odd since many tutorials only say you just have to add to the .bashrc file and all is good. Note that I don't run in bash when using the terminal, I like the other (default) one (don't know what it is) better, because it show me where I am all the time eg: &gt;&gt;d54c6b47b:~ romeo$  in stead of: &gt;&gt;bash$  In bash all is loaded as should be. So my question is, why didn't my .bashrc file load automatically and did I have to add the option to call it everytime? Also some tutorial told me to do something like: $alias la=’ls -la’ &gt;&gt; ~/.bashrc  which should write the alias to my .bashrc, this doesn't work either... Note that I'm a UNIX novice, so be gentle. What is the difference between dpkg and aptitude/apt-get? When installing a software via dpkg -i packageA.deb, will the dependencies required by packageA be downloaded and installed automatically? How is this different from using apt-get or aptitude? What to look for in a starter-level off-camera flash? I have zero experience with flash and want to learn how to use it from zero, for example by following the Strobist blog.  What are the absolutely necessary specifications I should look for when shopping for a flash, and can I find something in a price range less than $200.00?  My camera is a Nikon DSLR. Suppose $\lim \limits_{n \to ∞} a_n=L$. Prove that $\lim\limits_{n \to ∞} \frac{a_1+a_2+\cdots+a_n}{n}=L$ Proving $A+A'B=A+B$ without truth tables How can I prove the Boolean algebraic rule $$A+A'B=A+B$$ without using a truth table?  With the truth table, it is easy to see that the two are equal, but how can I prove it using lesser Boolean identities? When should I use can? When should I use could? What is right under what context? "big enough to do this" My question is what is the difference among these three sentences.   He is big enough to do such  heavy works. He is not big enough to do such heavy works. He is small enough to do such  heavy works.   I am so much confused between 2 and 3.Also, I don't get what the 3rd one means. How do I diagnose not being able to reach a specific website as an end user? Finding distance between points in two different layers along route in ArcMap? I need to find the distance between points in separate layers along a stream network. I have source sites for macro-invertebrates and sites where they are lacking. I need to find the distance between the source sites and the sites where they are not through the stream network.   I tried the linear referencing toolbox but the locate features along route tool can only use one layer of points and has not way to differentiate between sources and not source sites.  Any ideas?  I am using ArcMap 10.3? What can I do if I forgot my Windows password? Apparently, there are $\frac{(2n)!}{2^nn!}$ ways to break $2n$ people into partnerships. Why?   An explanation reads that there are $2n!$ ways to line people up. If we just pair adjacent people in the line up, we would have overcounted. So we must divide by $2^n n!$.  My question is why do we divide by $2^n n!$ specifically to adjust for overcounting?  Furthermore, this problem can apparently be solved by taking a skip factorial of odd values:  $(2n-1)(2n-3)(2n-5) ... (5)(3)(1)$  Why is that so? What does this skip factorial have to do with the problem? Windows 8 OEM Reinstalling I know this question is a repetition but I didn't find any solution of my problem from any of the previous questions. Recently I formatted my Laptop HDD and now I want to re install windows 8 I've a Windows 8 OEM license but the problem is I don't have a disc , I downloaded en_windows_8_x64_dvd_915440 from msdn , but when I boot the windows it shows the error that the current version is not suitable with my serial key, so where I can find an OEM Windows 8 and also I've a retail windows 8 disc so if I install that windows 8 in my pc and is there any way to activate it using my OEM key Is the oil thrown on a creature consumed when it's dealt fire damage and lit? I had the idea of throwing oil flasks on enemies at level 1, then hitting them with a torch to deal a bunch of bonus fire damage.  PHB 152:     If the target takes any fire damage before the oil dries (after 1 minute), the target takes an additional 5 fire damage from the burning oil.   PHB 152:     If you make a melee attack with a burning torch and hit, it deals 1 fire damage.   A flat 6 fire damage is pretty potent at level 1, but does the oil remain or does it burn out in a flash when hit (since it has no damage over time) when hit?  If not there is potential for a dual torch wielding PC to throw down 12 fire damage per round, or for multiple PCs to deal 6 damage per torch per PC per round. An interesting exercise about converging positive series, involving $\sum_{n\geq 1}a_n^{\frac{n-1}{n}}$ SOQL result ordering in the absence of an Order By clause In the absence of an  in a SOQL query, what order will Salesforce return results in?  Clearly if ordering is important then Order By should be specified, but I recently encountered a question about what the order would be if it was undefined.  My initial thoughts were Salesforce would return them in whatever order suited them. Much like .  For simple queries this would typically line up with the creation date descending and the Id ascending. For more complex queries it would depend on the joins being performed. What would happen to a star if a Dyson sphere lined with mirrors reflected a significant portion of the stars light back to the star I have looked for similar questions here on stack exchange. The closest example to this that I found is . That question assumed less than perfect absorption of material lining the inside of the sphere, and the effect of thermally re-radiating it inside the sphere.  A lot of the answers focused on that much of the thermal radiation would not be reflected back to the star, and is likely to be reabsorbed by the sphere at another location. On the other hand, this question asks what would happen if the Dyson sphere, using mirrors, deliberately refocus a significant portion of the rays directly back at the star. I am getting this message every time I do something like starting or stopping a service.  perl: warning: Setting locale failed.    perl: warning: Please check that your locale settings:            LANGUAGE = "en_US:en",            LC_ALL = (unset),            LC_MESSAGES = "en_US.UTF-8",            LANG = "en_US.UTF-8"        are supported and installed on your system.    perl: warning: Falling back to the standard locale ("C").    locale: Cannot set LC_CTYPE to default locale: No such file or directory    locale: Cannot set LC_MESSAGES to default locale: No such file or directory    locale: Cannot set LC_ALL to default locale: No such file or directory    (Reading database ... 21173 files and directories currently installed.)   Removing bind9 ...    * Stopping domain name service... bind9                                        [ OK ] Processing triggers for man-db ...    locale: Cannot set LC_CTYPE to default locale: No such file or directory    locale: Cannot set LC_MESSAGES to default locale: No such file or directory    locale: Cannot set LC_ALL to default locale: No such file or directory      How do I fix this error ? Divisibility Rule for 9 I'm working through an elementary number theory course right now and I think I've come up with a proof here but wanted some feedback on my logic.    Question:  If the sum of the digits in base 10 is divisible by 9, then the number itself is divisible by 9.    Proof: Suppose that $9|d_1+d_2+...+d_n$ then $d_1+d_2+...+d_n=0\mod9$  Now consider $d_1(10^{n-1})+d_2(10^{n-2})+...+d_{(n-1)}(10^1)+d_n(10^0)$ Each power of $10$ is equivalent to $1\mod9$   therefor  $d_1(10^{n-1})+d_2(10^{n-2})+...+d_{(n-1)}(10^1)+d_n(10^0)=(1\mod9)(d_1+d_2+...d_n)$  $9|(d_1+d_2+...d_n)$ by our assumption, thus $9|(1\mod9)(d_1+d_2+...d_n)$  Thus we have shown that if 9 divides the sum of the digits in base 10, 9 divides the number itself.    The only question I really have is whether I'm jumping the gun on my assumption concerning the powers of 10 being $1\mod 9$.  I think this is fair game here but not 100% confident.  Thanks. What is the origin of elements heavier than iron? In all the discussions about how the heavy elements in the universe are forged in the guts of stars and especially during a star's death, I usually hear that once the star begins fusing lighter atoms to produce iron (Fe) that's the end of the star's life and the whole system collapses onto itself; and based on how massive the star was initially, it has different outcome - like a white dwarf, a neutron star or a black hole. I have rarely heard a detailed explanation of how the elements heavier than iron are produced. I would appreciate a convincing explanation of this process. What function satisfies $ f(x)+f\left(\frac{1-x}x\right)=x$ ?