Econometrics: let's discuss the CU balance sheet. - page 21

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Now, once again, the argument was that "in principle, by definition, an equity series cannot be stationary". Of course this is nonsense, it can be stationary and ergodic, because this series is nondeterministic and can have all the properties of a random series.
 
alsu:

Now to the row E. Suppose we have 100 rubles in our account. What is the expectation of the value of E for tomorrow? Right, 100+10=110 rubles, as equity increases by this amount on the average each day. In other words, expectation of equity for the given TS increases by RUB 10 every day, i.e. it is not constant in time - the series is non-stationary.

This is a revelation to me - I was taught if there are two random variables 100 and 110 with equal probabilities of 0.5, then MO = 105. I'll think about it tomorrow..........

And if today I have 100 p and tomorrow I expect it to be 120, then my MO will be 120? And if I change my mind and expect 150 tomorrow, in a second my MO is already 150?

And if I expect 150 tomorrow and it turns out to be 110, how much is my MO?

This is just a revelation......... I just got the sacred meaning of the word "waiting" in the phrase MO............

And if today I have 100, tomorrow I expect 100 and the day after that 100, is it a stationary series?

 
Demi:


And if I have 100 today and expect 100 tomorrow and 100 the day after that, is that a stationary series?

(2 pennies from me.)

Yes! A stationary series, roughly speaking, is always parallel to the X-axis.

 
alexeymosc:

(2 pennies from me.)

Yes! The stationary row is, roughly speaking, always parallel to the X-axis.


ideally yes.

In practice, a slight tilt angle is allowed

 
,
Demi:


why so many letters???

1. nobody touches ergodicity. And you don't need to touch it - that's how it all gets into such thickets now....

2. stationarity means constancy of MO

3. In practice, MO values cannot coincide - this is not a fairy tale, but real life. Therefore, for stationarity it is sufficient to change the MO within certain limits

MO is not the same as the sample mean you have in mind.

4. "by averaging over an ensemble of all possible realisations" - wrote above.... Well you can't "spell it out" without reading exactly what you're "spelling out". There are no implementations - there is only one implementation. Focus on an example - ONE implementation. ONE.

If it is in principle ONE, then no random variables, much less processes, are out of the question: everything is already known. The point of econometric calculations in this case is to estimate how equity may behave at other time intervals (in the future), which may be an infinite number. But since we naturally do not have such an ensemble, the only thing we can do is to estimate the equity by available realizations. This can be done in different ways, but when we have only ONE realization, almost all of them will require ergodicity of the series to some extent, and hence for non-stationary (non-ergodic) process will usually give biased estimates. In some methods the bias may be large (for example, when replacing MO by sample mean), while in some methods it may be much less noticeable (for example, for HP filter or more modern spline with a penalty). But one should always keep it in mind.

5. Once again I explain what to do in this case - chop a row, compare MO if it does not differ within 3 - 5% stationary.

6. the first difference - I do not need. Maybe someone needs it, but not me. Maybe I don't need it. Or maybe I do need it - maybe, but not for this example.

How could it not be? The MO of the trade written in the tester report is the estimation of the MO of the difference series


You worked your jaws vigorously, but why?

It never hurts to repeat the basics. What do you think university professors do year after year? They're getting smarter before their eyes!

 
Demi:


ideally, yes.

in practice, a slight tilt angle is allowed

then it is unsteady, that's the trick))
 

it is clear to the court - all this has nothing to do with real life

theoretical nonsense - with this approach there are no stationary processes in real life, as the MO of real processes differs by thousandths or millionths, at least, but

Thanks, but it was not worth wasting time - no use

But the methodology of calculating the MO as a value which the observer "expects" to get in the future without any calculations and fiddling with probabilities - liked it. amused!

 
MetaDriver:

The correlation between individual currencies(not pairs) is weak rather than strong.

no?

// EURCHF not suggested. ;)



Well, the price is always relative to another asset (or several). There is no other way around it.

For example, we take the EURUSD and GBPUSD increments on m15. From these two distributions, we generate EURGBP increments provided they are independent and compare them with the real EURGBP increments. I.e. we montegrate different increments of EURUSD and GBPUSD from their real distributions and calculate EURGBP cross

in blue - real, and in red - synthetic EURGBP increments. The synthetic ones are indeed similar to Cauchy. The real ones have of course more tails than the normal one, but they are far from Cauchy. And a pronounced spiciness.

For example, I haven't seen the distribution of increments in any currency asset like this synthetic. Be it a pair or a more complex one - the dollar index, for example. And the only condition introduced in this pseudocross is the independence of the increments of the majors. Therefore the conclusion is that all assets are dependent. Although not directly, but through other assets, but it does not change the essence.

 
Demi:


Why are there so many letters?

1. no one is touching ergodicity. And you don't need to touch it - that's how it all gets into such thickets now....

2. stationarity is the constancy of the MoD.


It would be very desirable not to propagandize selves at least on this thread. Your unwillingness to notice other, referenced points of view is particularly unpleasant.

Stationarity is mo + dispersion .

Without taking variance into account, you've made a fool of yourself in your reasoning about equity.

 

Let's get back to the topic of the thread.

So far, I've made one point: if we are discussing balance stationarity (note that I don't even have a balance - returns in pips!), then the most valuable thought is that balance detrending is only possible as a straight line and my smoothing with HP filter is not correct.

I will try to recalculate with that in mind.

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