Econometrics: one step ahead forecast - page 56

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faa1947:
as the stationary residual can be replaced by a constant equal to any of the values: mean, skew, variance, spread - anything and everything is possible in the case of stationarity.

Are they constants?
 
Vinin:

Are they constants?
No, strictly speaking. Above I gave a graph of such an almost stationary residual. Weak change in mo and sko along the sample. and most importantly a spread of about 10 pips.
 

For some reason it seems to me lately that stationarity is not to be found there, i.e. not directly in the residuals from the regression on the series of quotes, but in something else.

But it must be found in any case. Otherwise the application of statistics is doomed.

 
faa1947:
I'm talking about the methodology (not invented by me) of model building: the initial non-stationary quotient must be decomposed into components until you get a stationary residual. This requirement for me is well understood on an intuitive level (which is very important), because the stationary residual can be replaced by a constant equal to any of the values: mean, skew, dispersion, spread - anything and everything is possible in the case of stationarity.
The whole question is with what period or hindsight to take this stationary residual, in your opinion. If you change the retrospective, the characteristics of the stationary residue will change as well, how are you trying to solve this question? By optimising it?
 
Mathemat:

For some reason it seems to me lately that the stationarity should not be looked for there, i.e. not directly in the residuals from the regression on the series of quotes, but in something else.

But it must be found in any case. Otherwise the application of statistics is doomed.

Right, this residual depends on the hindsight in question; this is where the dog is buried. The optimal hindsight is hard to find.
 
As for the proverbial hindsight, I have it too, but in a different sense. It's not a smoothing period, just a period where the data is extracted. There are no irons.
 
yosuf:
The whole question is with what period or retrospective to take this stationary, in your opinion, residual. If you change the retrospective, the characteristics of the stationary residual will also change, how are you trying to solve this question? By optimising it?

An extremely unpleasant question. The original model: quotier = trend + noise + seasonality + periodicity + outliers.

We are discussing the first two members of the model. there is no seasonality in Forex. Well, the outliers (news) are neglected, but the periodicity, by which I mean the presence of a wave in quotire, the period of which changes. For a very long time I have considered this periodicity to be the main source of non-stationarity. I don't have an approach to it.

I solve it very simply. I take a model with a small number of lags. Evaluation of regression coefficient. I make a 1-step forecast in hope(?) that the regression coefficients will not change by at least one step. And in addition to coefficients there is a set of regression properties (see table above). Upon the arrival of the bar we will again estimate the regression - here the very fashionable word adaptation is appropriate.

 
yosuf:
That's right, this residual depends on the hindsight in question; this is where the dog is buried. The optimal retrospective is hard to find.
What is "optimal window width"? The window width is used to estimate the regression coefficient. I made calculations: I changed window width and compared coefficients. They change very much up to 30, less after 40 and practically do not change after 70 for H1. By the way, there is an opinion, that with more than 30 observations t-statistics converges to z-statistics in terms of probability.
 
faa1947:

An extremely unpleasant question. The original model: quotient = trend + noise + seasonality + periodicity + outliers.

We discuss the first two terms of the model. Well, neglected outliers (news), but periodicity, by which I mean the presence of a wave in a quotient, the period of which changes. For a very long time I have considered this periodicity to be the main source of non-stationarity. I don't have an approach to it.

I solve it very simply. I take a model with a small number of lags. Evaluation of regression coefficient. I make a 1-step forecast in hope(?) that the regression coefficients will not change by at least one step. And in addition to coefficients there is a set of regression properties (see table above). When the bar arrives, regression estimation again - here the very fashionable word adaptation is appropriate.

Let's break down this model:

1) Trend - which trend are we talking about, because there are many of them;

2) Noise - it depends on the parameters of the trend in question and often the noise itself has a trend;

3. Periodicity - sine is inevitable, but it should be kept in mind that two consecutive Gamma functions also yield almost ideal full-period sine, which means that it is not yet clear;

4. Emissions are unpredictable, but apparently a corridor can be delineated.

 
yosuf:

Let's break down this model:

1. trend - which trend are we talking about, as there are many of them;

2) Noise - it depends on the parameters of the trend in question and often the noise itself has a trend;

3. Periodicity - sine is inevitable, but it should be kept in mind that two consecutive Gamma functions also yield almost ideal full-period sine, which means that it is not yet clear;

4. Outliers are unpredictable, but apparently a corridor can be delineated.


why all this...if you can't even predict the "trend" )))
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