Econometrics: one step ahead forecast - page 42
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I completely agree with this, but for me the interesting question is, what happens outside the sample?
If your prediction has the property of robustness, then the parameters of the predicted distribution will hold, both mo (predicted value) and sk (error).
The fact that you require the error to be stationary on history is the test for the robustness of the prediction.
What do you need to analyse inside the sample to increase the probability of out-of-sample predictions being fulfilled?
Is the calculation of the error and the requirement of stationarity to it sufficient?
And one last question. What is the forecast horizon? By one step or by several steps? If several steps, how is such a possibility determined?
I don't think these questions are solved without introducing a forecast target function (quality score). For example, the profit factor. And further estimation of its change depending on changes in system parameters (and everyone has them). Monotonic growth of the target function when approaching an extremum.
I don't understand how you can expect a stationary error on non-stationary data? In the chart you posted above the magnitude of the error obviously does not possess the properties of the finite variance, which makes it at least questionable to apply to it estimations based on the dispersion of results (of s.c.o. or the square root of N).
The model used in this thread does not use my idea, which is as follows: initially we consider that kotir = trend + noise + cyclicality.
Cyclicality cannot be dealt with, then it is discarded
If there is no trend, then no forecast is possible.
We select the trend (HP indicator 4 lags) and take into account the noise (2 lags). Now look at the residual from this model. This is pure noise, or is there a trend left in it? If there is a trend left, we extract the trend from this residual. As long as there is no noise left. It cannot be predicted. Now what noise? This is where your question comes in. On the chart there is a noise with the range of 25 pips. You can't predict the minutes, but you can predict the days.
If your prediction has the property of robustness, then the parameters of the predicted distribution will hold, both mo (predicted value) and sk (error).
The fact that you require the error to be stationary on history is the test for robustness of the prediction.
Robustness on the profit factor is the final estimate, but some constructiveness at the analysis stage would be desirable.
TAP has a Taylor decomposition. It is argued that the forecast horizon is equal to the number of derivatives in this decomposition.
If we make an analogy: the derivative is the residual from the model, then the forecast horizon is the number of iterations of the residual. We stop when we get a residual that we can neglect or model, e.g. GARCH.
Robustness on the profit factor is the final estimate, but I would like some constructiveness in the analysis phase.
There is a Taylor decomposition in TAP. It is argued that the forecast horizon is equal to the number of derivatives in this decomposition.
If we make an analogy: the derivative is the residual from the model, then the forecast horizon is the number of iterations of the residual that we can neglect or model, e.g. GARCH.
the forecast horizon depends on the size of the sample to be analysed. As a rule the horizon is smaller than this sample. I.e. if you analyze a window of N bars and make a forecast based on it, it would be logical that the forecast horizon is <N bars. Of course it would be naive to look for a universal dependence like a forecast should be made for half of the analyzed data size, but within a particular system we can look for such a dependence in purely statistical terms.
1) Robustness on the profit factor is a finite estimate, but I would like some construction on the analysis stage.
2) TAP has a Taylor decomposition. It is argued that the forecast horizon is equal to the number of derivatives in this decomposition.
3) If we make an analogy: the derivative is the residual from the model, the forecast horizon is the number of iterations of the residuals. We stop when we get a residual that we can neglect or model, e.g. GARCH.
1) Make a target function --- what it is and how it is - look in a book on optimization theory. (although it's unlikely to help you).
2) Bullshit!!! This is the first time I've heard such statements, and only here and from you. To avoid making such bloopers from now on, read the definitions at least twice. (What do you call TAR? Are you referring to automatic control theory?)
3) And again: Bullshit!!!
.
Econometrician, understand the basics first (e.g. what a derivative is) before you move on. And you need incomparably more prior knowledge to be able to deal with the space of states.
the forecast horizon depends on the size of the sample to be analysed. As a rule, the horizon is smaller than this sample. I.e. if you analyze a window of N bars and make a forecast based on it, it's logical that the forecast horizon is <N bars. Of course it would be naive to look for a universal dependence like a forecast should be made for half of the analyzed data size, but within a particular system we can look for such a dependence in purely statistical terms.
I cannot fully agree.
The sample size should be taken from other considerations.
We shall take a sample and estimate model parameters, and then we shall divide the sample into 2 parts and estimate model parameters on these parts. If model parameters haven't changed, OK, if they have, we split them again. If there is something left as a result, prognosis is possible, and if not, we wait.
1) Make up a target function --- what it is and how it is - look it up in a book on optimisation theory. (although it's unlikely to help you).
2) Bullshit!!! This is the first time I've heard such statements, and only here and from you. To avoid making such bloopers from now on, read the definitions at least twice. (What do you call TAR? Are you really referring to automatic control theory?)
3) Again: Bullshit!!!
I cannot fully agree.
The sample size should be taken from other considerations.
We take the sample and estimate the model parameters, and then we divide the sample into 2 parts and estimate the model parameters on these parts. If model parameters haven't changed, OK, if they have, we again divide them. If there is something left as a result, prognosis is possible, and if not, we wait.
It was not a question of selecting a sample size for the analysis, but of the forecast horizon. I don't think it should be fixed in time, but if you really want to discuss what it depends on, then the sample size is one of the factors
Econometrician, get the basics first (e.g., what is a derivative), and then move on. And you need a lot more prior knowledge to be able to deal with the space of states.