Abstract
This chapter adresses some domains of technical analysis and is devoted to the design of the VIMADES Extrapolator for forecasting mechanisms of lower bounds of risky returns, the VIMADES Trendometer for detecting the trend reversals of time series and related issues.
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Notes
- 1.
See [24, Sect. 1.3, p. 23], for further comments on this crucial issue.
- 2.
The two sisters Mnemosyne and Lesmosyne, daughter of Heaven (Ouranos) and Earth (Gaia), are respectively the goddesses of memory and forgetting. Clio, muse of history, and the eight other muses, were born of the same breath out of the love between Zeus and Mnenosyne.
- 3.
See Nonoscillation Theory of Functional Differential Equations with Applications, [4] by Agarwal, Berezansky, Braverman and Domoshnitsky (of the Nikolai Viktorovich Azbelev’s school) for a recent account of this field.
- 4.
The software of the Robot-Extrapolator of VIMADES has been registered on May 21, 2010, at the INPI, the French Institut National de la Propriété Industrielle.
- 5.
This terminology is used for describing moving averages of all kinds. Here, this is the tube itself which is moved instead of an average of one of its unknown evolution.
- 6.
Recall that the tensor product \(p \otimes q\) of two vectors \(p := (p_{i} )_{i} \in \mathbb {R}^{\ell } \) and \(q :=(q_{j} )_{j} \in \mathbb {R}^{\ell } \) is the rank one linear operator
$$p \otimes q \in \mathcal {L}(\mathbb {R}^{\ell }, \mathbb {R}^{\ell }) : x \mapsto \left\langle p, x \right\rangle q $$the entries of which (in the canonical basis) are equal to \((p_{i} q_{j}) _{i, j}\).
- 7.
The software of the Tensor Trendometer of VIMADES has been registered on November 25, 2013, at the INPI, the French Institut National de la Propriété Industrielle.
- 8.
It is calculated daily volume (number of shares traded) or by value of transactions. The volume used here is the volume of securities, not their values. The volume is an important activity indicator because it measures the interest of investors.
- 9.
The non-parametric statistical Friedman test was developed in 1937 by the Milton Friedman for detecting differences in treatments of several discrete-time series, which was integrated in many statistical software packages. It is related to the Durbin test and the Kruskal-Wallis analysis of variance by ranks (see for instance Rank Correlation Methods, [125] by Maurice Kendall).
- 10.
One can take other tubes, such as the tube made of a “snake” of a given (large) “radius” around it. For instance, the radius can be an error or a relative threshold imposed a priori. For instance, the Keltner channels, introduced in the 1960s by Chester Keltner is the tube surrounding a time series of “radius” equal to twice the average of the High, Low and Last Prices which could be used as a tube instead of the price tube.
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Aubin, JP., Chen, L., Dordan, O. (2014). Technical and Quantitative Analysis of Tubes. In: Tychastic Measure of Viability Risk. Springer, Cham. https://doi.org/10.1007/978-3-319-08129-8_2
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DOI: https://doi.org/10.1007/978-3-319-08129-8_2
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