Econometrics: one step ahead forecast - page 4

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I don't think extrapolating models apply to the market, as your article brilliantly proves. And what does it mean to "smooth out the noise"? It would really work if the markets were walking on your curve cluttered with noise, but the markets don't seem to be aware of the trend component that you believe.
 

For the model to be adequate, the price must return to the predicted value, rather than the predicted value moving to the price. That is, we need a mean reversion property to this "fair")) price. In that case the normality of the residuals will be there by itself.

This is a new idea, but not very clear. The forecast is made when the price does not exist. And the price moves in the channel from the forecast error.

 
Here is a simple example showing that a normal residual distribution is not a sufficient condition for the adequacy of the prediction model. We take a random walk graph and predict that the price will not change - i.e. forecast the last value. Let's assume the forecast for 10 periods. The residuals will be normally distributed, but the model does not predict anything. There is no return property, nor is there an opposite property.
 
C-4:
And what does it mean to "smooth out the noise"? It would really work if the markets were following your curve cluttered with noise, but the markets don't seem to be aware of the trend component that you believe.

I don't think extrapolating models apply to the market

We can't predict things that don't stem from the past, such as market crashes.

And what does it mean to "smooth out the noise"?

Of course not. A quotient is a random variable, but mathematical statistics is applicable to it if there is no deterministic component in the quotient. If it is present, then it will block out randomness. Hence, it is necessary to identify the deterministic component, and then analyse the residual, hoping that it does not have a deterministic component.

It would really work if the markets walked your curve cluttered with noise, but it seems the markets are not aware of the trend component that you consider.

They don't. In my forecasts I believe that the deterministic component will remain one step ahead. For this reason I do not recognise forecasts for several steps ahead.

 
Avals:
We take a random walk graph and predict that the price will not change - i.e. predict the last value.
Pure random walk (no drift or leverage) is not predicted - I haven't heard, if you can, a link.
 
faa1947:
Pure random wandering (no demolition or leverage) is not predicted - I haven't heard, if you can, a link.

it is possible to predict, only the prediction is meaningless, although the prediction error will be normally distributed. I don't have a link to the fact that the prediction is meaningless, but it comes from the definition of random walk (joint independence https://ru.wikipedia.org/wiki/Случайное_блуждание)
 
faa1947:

We cannot predict things that are not derived from the past, such as market crashes.

Well you can't, but other econometricians can:

How to predict financial market crashes.
 

Sufficient conditions for the adequacy of the forecast have not yet been devised. The necessary ones are plentiful. So we pick up new bricks at random, i.e. necessary conditions, in the hope that someday their set will be sufficient.

This seems to be the whole deep meaning of econometrics. But in fact it's just playing with spherical horse in a vacuum models: a completely hollowed out meaning - but a lot of statistical tests, giving a scientific quality to all this activity.

I don't see how you can take seriously a model that only takes into account the last few values - even if only for a few currencies. Here "a few" is one or two.

I am not at all against econometrics with its powerful staple apparatus. But let it work with meaningful models - not with some generalized (G)ARCH, ARIMA and other regression nonsense!

faa, you are in fact doing the same thing as Yusufhoja, the same regression. However, the latter doesn't justify them in any way (sorry, there's (18) deduced from nothing), but you have plenty of justification in the form of statistical tests.

This is all my humble and small imho, please don't take it too seriously.

Чистое случайное блуждание (без сноса или левериджа) не прогнозируется - я не слышал, если можно, то ссылку.

I don't know the link. It's in the terver textbooks. And it follows from the fact that the Wiener process is a martingale.

 
Avals:


it is possible to predict, only the prediction is meaningless, although the prediction error will be normally distributed.

I completely agree, but a quotient is not a random wandering, it can be seen with the naked eye, you can see quite specific trends. So we extrapolate them. And we only trust extrapolation if the residual is stationary (mo constant and variance) and not randomly distributed.

 
C-4:

Well you can't, but other econometricians can:

How to predict financial market crashes.

Thanks for the link. At first glance it is interesting, but for useless.

I am trying to predict one step ahead. Suppose my TS can not only predict the trend, but also predict outliers. So? Will you use such information or will you quit the market? I will, because it's not stability. This kind of forecast is interesting for politicians, as part of macroeconomic forecasts for the next few years. I am not.

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