Matstat Econometrics Matan - page 3
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By the way, it would be interesting to see pictures similar to the one you gave at https://www.mql5.com/ru/forum/368720/page2#comment_22207994,
for the particular case where the exchange rate changed almost by leaps and bounds.
Basically, which is to be expected.
But at least now I understand what's what.
Alexei, such a question has arisen.
I have dug into econometric formulas, and in many formulas there is a variable that is white noise.
By definition, white noise has perfect characteristics, the presence of normality with a constant variance of one.
Obviously such white noise is probably not to be found in reality. So the question is:
in practice, what is used as white noise?
Does this white noise have anything to do with the input data? For example, take residuals as noise, but then the normality and dispersion conditions would be violated.
Or should it really be extraneous noise which can simply be randomly generated with specified characteristics?
Or is that the point, to get white noise characteristics from the residuals? That is, normality is there, variance is constant, no autocorrelation.
What does normality and dispersion have to do with it? White noise is characterised by a Dirac autocorrelation delta function. Does that make you feel better? Just kidding... although true (about the Dirac delta function).
A generator of uniformly distributed random numbers - that's white noise for you - that's all. Range - whatever you want, do it: A*2.0*(MathRand()/32767-0.5).
In general, there is Google and you can find a lot of interesting things with it: https://ru.wikipedia.org/wiki/Белый_шум
What does normality and dispersion have to do with it? White noise is characterised by a Dirac autocorrelation delta function. Does that make you feel better?
Just kidding... although true (about the Dirac delta function).
A generator of uniformly distributed random numbers - that's white noise for you - that's all. Range - whatever you want, do it: A*2.0*(MathRand()/32767-0.5).
Actually, you can google it and find a lot of interesting stuff: https://ru.wikipedia.org/wiki/Белый_шум
Not convincing.
I have different information about it.
If the elements of the series wt are independent equally distributed (i.i.d.) values with mean equal to 0 and variation equal to σ2,
and no autocorrelation Cor(wi,wj)≠0, ∀i≠j, then the series wt is white noise.
As I assume, the oscillator is needed for test simulations, so to speak, for checking.
Maybe I misunderstood the expression equally distributed (i.i.d)?In practice the generator should not be used.
And it does not mean that theyare normally distributed ?
Not convincing.
I have different information on this.
If the elements of the series wt are independent equally distributed (i.i.d.) values with mean equal to 0 and variation equal to σ2,
and no autocorrelation Cor(wi,wj)≠0, ∀i≠j, then the series wt is white noise.
As I assume, the oscillator is needed for test simulations, so to speak, for checking.
Maybe I misunderstood the expression equally distributed (i.i.d)?In practice, however, the oscillator should not be used.
And it does not mean that theyare normally distributed ?
White noise is constant MO, constant variance and zero autocovariance function (the observations are not correlated with each other). A weakly stationary process.
If the observations have a normal distribution, the process becomes strictly stationary and the autocorrelation coefficients will also have a normal distribution.
White noise - constant MO, constant variance and zero autocovariance function (observations are uncorrelated). A weakly stationary process.
If the observations have a normal distribution, the process becomes strictly stationary and the autocorrelation coefficients will also have a normal distribution.
There you go. Thank you.
A weakly stationary process.
Strictly stationary process.
There is a difference. Depending on whether the observations have a normal distribution or not.
But the question was a little different.
What is used as noise in practice? Residuals?
There. Thank you.
Slightly stationary process.
Strictly stationary process.
There is a difference. Depending on whether the observations have a normal distribution or not.
But the question was a little different.
What is used as noise in practice? Residuals?
I don't quite understand the question - why use white noise?
If you want such a series, you can generate a SB series in Excel or some other program and take its first differences - that would be white noise.
If a rough estimate is appropriate - the first differences of the price series are also quasiWhite Noise
What is the expectancy of white noise? It is constant and the same at all range values. If you calculate it by the formula, it will be 0 - no arguments here, mathematics is a silent science - you won't swear back.
White noise is stationary. Although it's rather silly to say it's stationary, it's white noise - that says it all.
The word "equal" is closer in meaning to"uniform" than to "normal". And anyway, how can a single element be somehow distributed? An absurd definition. Or what are the elements? Pieces of a row? Why the hell are we even talking about chunks (elements)?
I don't quite understand the question - why use white noise?
If you need such a series, you can generate a SB series in Excel or another program and take its first differences - that would be white noise.
If a rough estimate fits - the first differences of a price series is also quasiWhite Noise.
If there is a white noise component in the formula, it should be isolated... even if the useful signal is already visible))
All numerical series are divided into three types - deterministic, random and stochastic.
TheorWer deals with random series - the task is to decompose a random series into a deterministic and a stochastic component. Roughly speaking, model + white noise.