This article is cited in 8 papers

On some probabilistic-statistical methods in technical analysis

S. V. Pastukhov

M. V. Lomonosov Moscow State University

Abstract: This paper gives a mathematical basis of some methods of technical analysis which are used in the financial market. In particular, with the help of the introduced notion of the $H$-volatility ($H>0$), the so-called renko- and kagi-models are founded and corrected. For a Wiener process the $H$-volatility has the properties which take place also in the financial market with some differences which indicate the existence of arbitrage possibilities. We obtain this arbitrage with the help of introduced renko-, and kagi-$H$-strategies.

Keywords: $\Delta$-variation, $\Delta$-volatility, $H$-variation, $H$-fluctuation, renko-$H$-inversion, kagi-$H$-inversion, renko-$H$-volatility, kagi-$H$-volatility, renko-$H$-strategy, kagi-$H$-strategy.

Received: 19.01.2004

DOI: 10.4213/tvp220

 English version: Theory of Probability and its Applications, 2005, 49:2, 245–260

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