Unpredictable market? Per aspera ad astra


The total number of one-step forecasts is 50. Obviously, if so accurately forecast real price increments, it would be more than enough for practical gain. However, the formal application of a neural network to predict the number of real price increments gives the other - an unsatisfactory result.

So, the first problem that faced towards the application of deterministic chaos theory to financial series, is this: why superficially similar noise-series in different ways to forecast? Is there any specific feature that distinguishes these series? Were soon found answers to these questions.

Consider the phase portrait of the logistic map. It turns out that in the phase space defined detainees in time sequence of values, there is a set, beyond which <random> value of the series does not come out. In this case, the curve is a parabola. As the length of the sequence increases only the filling of the curve. Its position and shape are not changed.

Such sets in the phase space, which are attracted (or even do not deviate from them), the phase trajectory, and that portray a dynamic process, called attractors. Because the detainees are one step coordinates attractor is a parabola, it makes sense to look for the future value of the chaotic sequence as a quadratic function of the previous value. The coefficients of the quadratic dependence on the selected historical realization method of least squares. Then you can build a forecast. In fact, there are several problems associated with the accuracy of determining the internal parameters. The subsequent behavior of a number of highly sensitive to initial conditions as well as the importance of these control parameters. Therefore, a fairly accurate forecast for any number of steps possible. Estimate of the number of steps by which you can predict the chaotic series, is a subject of a separate study. Now we can say that after the effort made possible forecast a few steps forward. What is the attractor of a number of real price increments? The answer to this question lies in the picture.

As can be seen, a pronounced attractor, like a parabola in logistic map, no. Therefore, the forecast of the real price increments, made in the same way as for the logistic equation, has not brought the expected results. Thus, the presence or absence of an attractor explains good or bad predictability series. In deterministic chaos attractor is, in the real price it is not - this obvious conclusion is nA surface. There is a classic Russian question: what do you do?

What to do?

As popular wisdom, at any arbitrarily complex problem there is always a clear, easy to understand, wrong decision. This applies to our case. Conclude that there are a number of real attractor price increments was premature. Attractor is not in the same coordinates as for logistic sequence. But this does not mean that it is not at all! First, the attractor can exist in the same coordinates, but with a different delay. Secondly, why should he be one-dimensional, like a logistic equation? The future can not depend on a previous value, but from several.