A Dimensionless Scenario Framework for Technical Analysis
Summary
The document proposes a probabilistic way to classify market behavior from price velocity and acceleration. It describes departures from a random walk using two dimensionless quantities: a Froude number comparing acceleration with velocity, and a forecast horizon scaled by the training period. The resulting scenario framework is designed to be invariant to changes in price units and to account for multiple possible paths given the same price history.
Trend-following and contrarian patterns can both arise, depending on the scaled forecast horizon. The described approach assesses the stability of predicted market trajectories to choose between them. Tests use daily returns across major equity indices, bonds, and currencies, spanning roughly nine to thirty years of data. The authors report statistically significant predictive power across essentially all market phases, while separate trend and trend-plus-acceleration strategies perform well only in particular phases. The summary provides no detailed methodology, transaction costs, or out-of-sample protocol, so the reported results do not by themselves establish tradable profitability.
Key ideas
- The framework characterizes price history through velocity and acceleration.
- A dimensionless Froude number and scaled forecast horizon define the scenario classification.
- Trend-following and contrarian behavior may coexist, with their relevance depending on forecast horizon.
- The empirical tests span equity indices, bonds, and currencies, and report predictive power across market phases.
- The description does not provide transaction cost or detailed out-of-sample evidence.
Tags
Full text
# Fundamental Framework for Technical Analysis # Fundamental Framework for Technical Analysis Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price velocity and price acceleration, we construct a general classification of the possible patterns characterizing the deviation or defects from the random walk market state and its time-translational invariant properties. The classification relies on two dimensionless parameters, the Froude number characterizing the relative strength of the acceleration with respect to the velocity and the time horizon forecast dimensionalized to the training period. Trend-following and contrarian patterns are found to coexist and depend on the dimensionless time horizon. The classification is based on the symmetry requirements of invariance with respect to change of price units and of functional scale-invariance in the space of scenarii. This ``renormalized scenario'' approach is fundamentally probabilistic in nature and exemplifies the view that multiple competing scenarii have to be taken into account for the same past history. Empirical tests are performed on on about nine to thirty years of daily returns of twelve data sets comprising some major indices (Dow Jones, SP500, Nasdaq, DAX, FTSE, Nikkei), some major bonds (JGB, TYX) and some major currencies against the US dollar (GBP, CHF, DEM, JPY). Our ``renormalized scenario'' exhibits statistically significant predictive power in essentially all market phases. In constrast, a trend following strategy and trend + acceleration following strategy perform well only on different and specific market phases. The value of the ``renormalized scenario'' approach lies in the fact that it always finds the best of the two, based on a calculation of the stability of their predicted market trajectories.
Shown in full with attribution under the source's licence. Licence: abstract CC0
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.