On the Complexity and Behaviour of Cryptocurrencies Compared to Other Markets

We show that the behaviour of Bitcoin has interesting similarities to stock and precious metal markets, such as gold and silver. We report that whilst Litecoin, the second largest cryptocurrency, closely follows Bitcoin's behaviour, it does not show all the reported properties of Bitcoin. Agreements between apparently disparate complexity measures have been found, and it is shown that statistical, information-theoretic, algorithmic and fractal measures have different but interesting capabilities of clustering families of markets by type. The report is particularly interesting because of the range and novel use of some measures of complexity to characterize price behaviour, because of the IRS designation of Bitcoin as an investment property and not a currency, and the announcement of the Canadian government's own electronic currency MintChip.Comment: 16 pages, 11 figures, 4 table

Estimating the Algorithmic Complexity of Stock Markets

Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why it is particularly relevant to Finance, and potentially to other sub-fields of Economics as well. We develop a generic method to estimate the Kolmogorov complexity of numeric series. This approach is based on an iterative "regularity erasing procedure" implemented to use lossless compression algorithms on financial data. Examples are provided with both simulated and real-world financial time series. The contributions of this article are twofold. The first one is methodological : we show that some structural regularities, invisible with classical statistical tests, can be detected by this algorithmic method. The second one consists in illustrations on the daily Dow-Jones Index suggesting that beyond several well-known regularities, hidden structure may in this index remain to be identified

Input–output maps are strongly biased towards simple outputs

This is the final version. Available from Nature Research via the DOI in this record. The data sets generated during and/or analysed during the current study are available from the corresponding authors on reasonable request.Many systems in nature can be described using discrete input–output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity K(x) of that output. These input–output maps are biased towards simplicity. We derive an upper bound P(x) ≲ 2^−aK(x)−b, which is tight for most inputs. The constants a and b, as well as many properties of P(x), can be predicted with minimal knowledge of the map. We explore this strong bias towards simple outputs in systems ranging from the folding of RNA secondary structures to systems of coupled ordinary differential equations to a stochastic financial trading model.Engineering and Physical Sciences Research Council (EPSRC)Clarendon Fun

An algorithmic information-theoretic approach to the behaviour of financial markets

International audienceUsing frequency distributions of daily closing price time series of several financial market indexes, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information theory, may account for some of the deviation of financial markets from log-normal, and if so for how much of said deviation and over what sequence lengths. We do so by comparing the distributions of binary sequences from actual time series of financial markets and series built up from purely algorithmic means. Our discussion is a starting point for a further investigation of the market as a rule-based system with an algorithmic component, despite its apparent randomness, and the use of the theory of algorithmic probability with new tools that can be applied to the study of the market price phenomenon. The main discussion is cast in terms of as- sumptions common to areas of economics in agreement with an algorithmic view of the market

An algorithmic information-theoretic approach to the behaviour of financial markets

Using frequency distributions of daily closing price time series of several financial market indexes, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information theory, may account for some of the deviation of financial markets from log-normal, and if so for how much of said deviation and over what sequence lengths. We do so by comparing the distributions of binary sequences from actual time series of financial markets and series built up from purely algorithmic means. Our discussion is a starting point for a further investigation of the market as a rule-based system with an 'algorithmic' component, despite its apparent randomness, and the use of the theory of algorithmic probability with new tools that can be applied to the study of the market price phenomenon. The main discussion is cast in terms of assumptions common to areas of economics in agreement with an algorithmic view of the market.

The Archetypal Market Hypothesis; A Complex Psychology Perspective on the Market’s Mind

The thesis introduces the Archetypal Market Hypothesis (AMH). Based on complex psychology and supported by insights from other (mind) sciences it describes the unconscious nature of investing and how it shapes price patterns. Specifically, it emphasises the central role of numerical archetypes in price discovery. Its ontological premise is the market’s mind, a complex adaptive system in the form of collective consciousness which originates from the collective unconscious. This premise suggests that investing involves more than cognition and reaches beyond rationality and logic. Among others, the thesis clarifies the affective impact of price discovery: it is not only what we can do with prices, but also what they can do with us. Numbers receive their affective powers from the numerical archetypes. They preconsciously create order in the mind by facilitating the dynamics of symbolic mapping as the mind attempts to make sense of what it senses, bridging the imaginative with the real. This autonomous and often dominating impact of the numerical archetypes manifests itself: • in individual consciousness via numerical intuition, and • in crowd consciousness via participation mystique which underlies intersubjectivity. The thesis will argue that both are supported cerebrally. The collective intersubjective nature of the market’s mind and its symbolic expression via prices make it an exemplary phenomenon to be researched because the archetypal dynamics are strongest in such spheres. The PhD’s goal, as part of the AMH proposition, is twofold. First, to formalise theoretically the concept of the market’s mind, in particular the collective experience of market states, generally known as market moods, and how these shift as a result of herd instinct. Second, to propose a framework for further empirical research to show that representing market data in a non-traditional way, based on Jung’s active imagination and similar techniques, can improve investors’ understanding of those states. If successful, the method (including bespoke software) can complement analytical investment research methods currently used by investor