مدل تکامل مشترک اقتصاد خرد برای سیگنال های تجزیه و تحلیل فنی مالی

Technical analysis (TA) has been used for a long time before the availability of more sophisticated instruments for financial forecasting in order to suggest decisions on the basis of the occurrence of data patterns. Many mathematical and statistical tools for quantitative analysis of financial markets have experienced a fast and wide growth and have the power for overcoming classical TA methods. This paper aims to give a measure of the reliability of some information used in TA by exploring the probability of their occurrence within a particular microeconomic agent-based model of markets, i.e., the co-evolution Bak–Sneppen model originally invented for describing species population evolutions. After having proved the practical interest of such a model in describing financial index so-called avalanches, in the prebursting bubble time rise, the attention focuses on the occurrence of trend line detection crossing of meaningful barriers, those that give rise to some usual TA strategies. The case of the NASDAQ crash of April 2000 serves as an illustration.

Quantitative analysis of financial market data has well assessed several properties like the long term memory in volatility [1], [2], [3] and [4], returns [5], [6] and [7], speculative bubbles [8], and the presence of fractals [9] that has been extensively studied since a pioneering paper [10]. Many mathematical and statistical models [11], [12], [13], [14], [15] and [16] are available nowadays for a phenomenological description of financial data, while rigorous theoretical frameworks have shown to be able to encapsulate some conjectures like the Elliot waves [17]. Alongside the descriptive analysis of macroeconomic quantities, theories derived for complex systems can explain the aggregate behavior of markets through the analysis of its components at the microeconomic level. Microeconomic models of financial markets rank in complexity from the simplest models, typically considering the interaction of two main types of agents—the fundamentalists and the chartists [18], [19], [20] and [21]—to the most heterogeneous types of agents; an intermediate step considering the presence of noise traders that act either without market information or not caring about the fundamentals, thus creating white noise, while mean reversion effects [22] can be accounted due to the activity of fundamentalists. The first question to be raised is whether a microeconomic approach can be found based on insight about the mechanism of the formation of financial quantities. If investigations of micro- or macroeconomic models rely on simulation frameworks whenever more theoretical tools are not available, the evaluation of investment strategies driven by models, even empirical ones, like those leading to technical analysis (TA) is a need. Nevertheless, it is difficult to implement them, even through simulations of multiagent systems, because of the lack of reliability of the parameters. Indeed it is not easy to perform computer simulations of markets with interacting agents that trigger their orders on the basis of TA patterns because TA rules are more complex than those commonly assigned to chartists and fundamentalists in computer simulations. Moreover, to get the best trading decision is still an art, independently from a model sophistication; indeed the interpretation of charts heavily relies on the expertise of the analyst. Therefore, we study model property and statistics instead of trying to draw results relying on heavy computer simulations of a multiagent system. On the other hand, a decision based on financial signal TA must take into account the temporary occurrence of several patterns. However, to start the study of the occurrence and of the reliability of the simplest components is a compulsory step towards the comprehension of more complex configurations. This can in turn lead to a systematic assessment of the expertise of such a kind of market analysts. A cornerstone for TA comes from the expertise of Charles H. Dow that developed the set of methods that are gathered under the name of Dow theory. Dow theory [23] considers major trends as those lasting more than one year. Intermediate trends are those that range from a minimum of three weeks to a maximum of several months, as those which can be useful in futures markets. Short trends can be identified for time intervals shorter than two or three weeks. Thus, it is very important to decide upon a reliable time interval for implementing a strategy, before trying to define any trend. Statistics of trend lines will be exploited on the aggregate of the proposed microeconomic model and compared with the results obtained on raw data. Such analyzes should show their power at their best when performed during periods of high risk exposure. Among them the rising part of speculative bubbles of market indices, due to endogenous causes, has been chosen below because of the availability of already well assessed theories [24], [25], [26], [27] and [28]. It is worth remarking that stock market indices actually are a weighted mean of stock prices. To perform buy/sell strategies on stock market indices (eventually triggered by TA signals) has the meaning to buy/sell a previous selected financial product replica of the index (Exchange Traded Funds, ETF, certificates). Therefore, the aim of this paper is twofold. The first task is to set up a microeconomic approach based on insight about the mechanism of the formation of financial quantities; the second target is to show how to use the property of the aggregate rising from the model structure in order to evaluate the reliability of already often used methods like those found by chartists in so-called TA [29]. In particular, the analysis will focus on the probability estimate of the occurrence of trend lines slopes and on the estimate the probability of trend lines crossing. The paper is organized as follows. The next section shortly gives an overview of the main properties of the NASDAQ July 2000 crash, of its statistical properties, and shows the bases of the models that we are going to apply and how to combine them for data modeling. Section 3 introduces TA signals of interest, in particular so-called barriers. Section 4 shows how to use the model information in order to set up a tool in order to estimate both the occurrence of barrier crossing and the formation of a trend line. Section 5 serves as a conclusion and suggestions for going beyond the present work. It will appear that the numerical values used to build the agent-based model describing the financial index are those of the two-dimensional square lattice Bak–Sneppen (BS) co-evolution model [30]. For completeness the one-dimensional case is treated in the Appendix.

Any automatic trading system can trigger buy/sell orders when some either upper or lower barrier is crossed. Rules like these, even so simple, have been able to cause crashes in markets. Technical analysis studies concern a more complex structure of signals and often rely on the sensitivity of the analyst. We have observed an analogy between statistical properties of a co-evolution model, in particular the avalanche content description, with the residuals of a financial index signal like the NASDAQ 100 Composite—residuals obtained from the latter signal first order approximation obtained by the theory of large financial crashes. In view of the analytical properties of the superposition of such a microscopic models, we have been able to derive estimates for avalanche and recovery duration time. We have pointed out the qualitative features helping technical analysts to elaborate more refined approached than classical ones. Several quantitative features are also available. Other indices could be used for a search on universality properties. We stress that we have discussed not only degradation, but also recovery features. The suitability of the mean fitness properties for bubble models as they emerge from the BS model dynamics does not stop at the level of numerical analysis of correlations, but goes further into the dependence structure of avalanches, making this approach a sound complement to the fBm approach. Moreover, the BS model furnishes an agent-based model for an explanation of the cooperative behavior that leads to the earthquake and large financial crashes phenomena, thus embracing simulations into a theoretical framework that allows to state the reliability of the results apart from numerical instabilities. The set up of a model for the residuals provides a further insight on the formation of trend lines. Statistics drawn on the BS model about the occurrence of trend lines slopes provide market analyst by bounds of the probability of the occurrence of trend lines on market index data. Moreover, once trend lines are drawn, the probability of their crossing can be estimated from the model. This is a first step towards other signal TA and to the assessment of the usage of TA rules that supersede the skill of the single analyst. In addition the two-dimensional model, necessarily implying the existence of more than two nearest neighbor agents, obviously four for the square lattice data examined here above, finds some correspondence in the sand pile model on a fractal basis simulating financial avalanches before a crash as studied in Ref. [24] and [39] where the periodicity of the log-periodic oscillations indicate that the relevant number of agents is between three and four. For further work, it could be suggested that more complex signals be examined, together with a deeper analysis of the fractal and multifractal structure both of the microscopic model and of market data.