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?
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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.
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How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access?
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What is the precise difference between the Mean, Average and Expectation ? Is there any mathematical formaulation to show the difference ? I see that often they are used interchangeably.
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I have tried to explore the information but still not very clear on the exact difference between ,  and . Can anyone help me out to clear my concept?
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The variance of a random variable $X$ is defined as $E[(x-\mu )^2]$. Why can't it be defined as $E[|x-\mu |]$. i.e., What is the basic idea behind this definition. Thank you.
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I'm new to statistics and reading stats books I found different definitions for Variance.  Definition1: $ s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2 $  Definition2: $ s^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2 $  I would like to know why is used different definition for same thing?
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I was recently looking at some code that confused me because it works and I didn't expect it to. The code reduces to this example  #!/bin/bash for var; do   echo "$var" done   When run with command line arguments is prints them  $ ./test a b c a b c   It is this, that is (to me) unexpected. Why does this not result in an error because var is undefined ? Is using this considered 'good practice' ?
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I finished my test and there is a question I completely failed but that my teacher did not go over, so I was hoping someone could post a correction of it, so that I understand what I was supposed to do for next time.  Suppose that A is a countable set of real numbers. Show that there exists a real number a such that $(a+A)\cap A=\varnothing$. (Note: By definition, $a+A= \{a+r\mid r\in A\}$.)
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I am currently investigating the impact of certain indicators such as GDP and inflation on the stock market. However some of my variables are non-stationary and some stationary in levels. All variables are stationary in first differences.  My question:   Since I have a mix of I(0) and I(1), I need to take the first difference of the I(1) variables and then use VAR. Say that I have a dependent variable $y$ which is I(0) and independent variables $x_1$ which is I(1) and $x_2$ which is I(0). Do I take the first differences of only $x_1$ and then apply the VAR model? Is that correct?  If I take the first differences, then might I lose the long-run relationship between the variables? Is ARDL the better method in this case?   If you have any references regarding the above I would be grateful.
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Is it the same convention as those used in known programming languages such as Java and C? I'm trying to create a lot of variables and I want it to start with a number, but I'm not sure if it's okay.
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Can someone please explain me what's the difference between Swing and AWT?  Are there any cases where AWT is more useful/advised to use than swing or vice-versa?
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I do not understand how dummy variables work in math.   Suppose we have:  $$I_1 = \int_{0}^{\infty} e^{-x^2} dx$$  How is this equivalent to:  $$I_2 = \int_{0}^{\infty} e^{-y^2} dy$$  How does this dummy variable system work?   Since $y$ is the dependent variable for $I_1$ How can $y$ itself be and independent variable for $I_2$  ??  Thanks!
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I am not familiar with PHP at all and had a quick question.  I have 2 variables pricePerUnit and InvoicedUnits. Here's the code that is setting these to values:  $InvoicedUnits = ((string) $InvoiceLineItem-&gt;InvoicedUnits); $pricePerUnit = ((string) $InvoiceLineItem-&gt;PricePerUnit);   If I output this, I get the correct values. Lets say 5000 invoiced units and 1.00 for price.  Now, I need to show the total amount spent. When I multiply these two together it doesn't work (as expected, these are strings).  But I have no clue how to parse/cast/convert variables in PHP.  What should I do?
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If you want to test whether two variables follow the same distribution, would it be a good test to simply sort both variables, and then check their correlation? If it is high (at least 0.9?), then the variables most likely come from the same distribution.  With distribution here I mean "normal", "chi-square", "gamma" etc.
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Most languages have naming conventions for variables, the most common style I see in shell scripts is MY_VARIABLE=foo.  Is this the convention or is it only for global variables?  What about variables local to the script?
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This may seem like a very basic question, but:  What exactly is the difference between a root of a polynomial, and a zero?  Of course I realise that they are technically exactly the same thing, but there seem to be subtle rules as to when to use each term, and a couple of times in the past I have been told I am using "root" where I should be using "zero".  Is it generally accepted that one should use "root" in an algebraic context,  and "zero" in a analytic context? If not, when should one use one or the other...and does it really matter?!
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Could someone explain? I understand the basic concepts behind them but I often see them used interchangeably and I get confused.   And now that we're here, how do they differ from a regular function?