scholarly journals A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 117
Author(s):  
Jonathan Blackledge ◽  
Marc Lamphiere
Keyword(s):  
Financial Time Series ◽  
Scaling Law ◽  
Market Price ◽  
Scaling Properties ◽  
Times Series ◽  
Machine Learning Approach ◽  
Times Series Analysis ◽  
Historical Developments ◽  
Price Differences ◽  
Fractal Market Hypothesis

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ scaling law, where γ>0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values.

scholarly journals Characterizing the Foreshock, Main Shock, and Aftershock Sequences of the Recent Major Earthquakes in Southern Alaska, 2016–2018

2020 ◽  
Vol 8 ◽  
Author(s):  
B. G. Bukchin ◽  
A. S. Fomochkina ◽  
V. G. Kossobokov ◽  
A. K. Nekrasova
Keyword(s):  
Control Parameter ◽  
Empirical Distribution ◽  
Scaling Law ◽  
Plate Boundary ◽  
Scaling Properties ◽  
Second Moments ◽  
The Pacific ◽  
Unified Scaling Law ◽  
Aftershock Sequences ◽  
Integral Estimation

For each of three major M ≥ 7.0 earthquakes (i.e., the January 24, 2016, M7.1 earthquake 86 km E of Old Iliamna; the January 23, 2018, M7.9 earthquake 280 km SE of Kodiak; and the November 30, 2018, M7.1 earthquake 14 km NNW of Anchorage, Alaska), the study considers characterization of the foreshock and aftershock sequences in terms of their variations and scaling properties, including the behavior of the control parameter η of the unified scaling law for earthquakes (USLE), along with a detailed analysis of the surface wave records for reconstruction of the source in the approximation of the second moments of the stress glut tensor to obtain integral estimation of its length, orientation, and development over time. The three major earthquakes at 600 km around Anchorage are, in fact, very different due to apparent complexity of earthquake flow dynamics in the orogenic corner of the Pacific and North America plate boundary. The USLE generalizes the classic Gutenberg-Richter relationship taking into account the self-similar scaling of the empirical distribution of earthquake epicenters. The study confirms the existence of the long-term periods of regional stability of the USLE control parameter that are interrupted by mid- or even short-term bursts of activity associated with major catastrophic events.

Times Series Analysis Without Model Identification

1984 ◽  
Vol 19 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Wayne F. Velicer ◽  
Roderick P. McDonald
Keyword(s):  
Model Identification ◽  
Times Series ◽  
Series Analysis ◽  
Times Series Analysis

Seismic coda Q and scaling law of the source spectra at the Aeolian Islands, southern Italy

1983 ◽  
Vol 73 (1) ◽  
pp. 97-108
Author(s):  
E. Del Pezzo ◽  
F. Ferulano ◽  
A. Giarrusso ◽  
M. Martini
Keyword(s):  
Southern Italy ◽  
Scaling Law ◽  
Coda Wave ◽  
Corner Frequency ◽  
Volcanic Complex ◽  
Coda Q ◽  
Aeolian Islands ◽  
Scaling Properties ◽  
Linear Pattern ◽  
Seismic Coda

abstract The model developed by Aki and Chouet for the coda wave generation and propagation has been used to calculate the quality factor Q for the zone of the Aeolian Islands, southern Italy, in the frequency range of 1 to 12 Hz, and the scaling properties of the seismic spectrum in the magnitude range of 0.4 to 4.7. The Q found for the Aeolian area has a frequency dependence of the form Q = qfv. The absolute values of Q seem to be dependent on the station and location of the seismic events, confirming the strong lateral heterogeneities in the geological structure beneath the Aeolian Arc. A temporal variation has been noted in the Q calculated at Vulcano station (VPL) in a period of 3 weeks soon after the occurrence of a main shock of ML = 5.5 located near the station. The scaling behavior of this sequence is similar to that obtained in two areas of California and one portion of Japan, with a corner frequency that remains constant with an increasing seismic moment between magnitudes 1 and 4. It differs substantially from the scaling properties of the Hawaian earthquakes that show a linear pattern, without an increase of the stress drop with magnitude. The fact that Vulcano is an active volcano seems not to influence the scaling properties of the seismic sequence localized very near it. It probably indicates that the aftershocks used for calculating the scaling law are generated out of the volcanic complex Lipari-Vulcano, in a zone with a good capability of accumulating the stress.

scholarly journals Heads and Tails of Earnings Management: Quantitative Analysis in Emerging Countries

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 57 ◽  
Author(s):  
Pavol Durana ◽  
Katarina Valaskova ◽  
Darina Chlebikova ◽  
Vladislav Krastev ◽  
Irina Atanasova
Keyword(s):  
Quantitative Analysis ◽  
Earnings Management ◽  
Unit Root ◽  
Developed Countries ◽  
Emerging Countries ◽  
Bankruptcy Risk ◽  
Discretionary Accrual ◽  
Times Series ◽  
Times Series Analysis

Earnings management is a globally used tool for long-term profitable enterprises and for the apparatus of reduction of bankruptcy risk in developed countries. This phenomenon belongs to the integral and fundamental part of their business finance. However, this has still been lax in emerging countries. The models of detections of the existence of earnings management are based on discretionary accrual. The goal of this article is to detect the existence of earnings management in emerging countries by times series analysis. This econometric investigation uses the observations of earnings before interest and taxes of 1089 Slovak enterprises and 1421 Bulgarian enterprises in financial modelling. Our findings confirm the significant existence of earnings management in both analyzed countries, based on a quantitative analysis of unit root and stationarity. The managerial activities are purposeful, which is proven by the existence of no stationarity in the time series and a clear occurrence of the unit root. In addition, the results highlight the year 2014 as a significant milestone of change in the development of earnings management in both countries, based on homogeneity analyses. These facts identify significant parallels between Slovak and Bulgarian economics and business finance.

scholarly journals Scaling properties of planetary calderas and terrestrial volcanic eruptions

2012 ◽  
Vol 19 (6) ◽  
pp. 585-593 ◽  
Author(s):  
L. Sanchez ◽  
R. Shcherbakov
Keyword(s):  
Solar System ◽  
Scaling Law ◽  
Geographical Location ◽  
Internal Heat ◽  
Volcanic Eruptions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Caldera Formation ◽  
Planetary Bodies ◽  
Terrestrial Planetary Bodies

Abstract. Volcanism plays an important role in transporting internal heat of planetary bodies to their surface. Therefore, volcanoes are a manifestation of the planet's past and present internal dynamics. Volcanic eruptions as well as caldera forming processes are the direct manifestation of complex interactions between the rising magma and the surrounding host rock in the crust of terrestrial planetary bodies. Attempts have been made to compare volcanic landforms throughout the solar system. Different stochastic models have been proposed to describe the temporal sequences of eruptions on individual or groups of volcanoes. However, comprehensive understanding of the physical mechanisms responsible for volcano formation and eruption and more specifically caldera formation remains elusive. In this work, we propose a scaling law to quantify the distribution of caldera sizes on Earth, Mars, Venus, and Io, as well as the distribution of calderas on Earth depending on their surrounding crustal properties. We also apply the same scaling analysis to the distribution of interevent times between eruptions for volcanoes that have the largest eruptive history as well as groups of volcanoes on Earth. We find that when rescaled with their respective sample averages, the distributions considered show a similar functional form. This result implies that similar processes are responsible for caldera formation throughout the solar system and for different crustal settings on Earth. This result emphasizes the importance of comparative planetology to understand planetary volcanism. Similarly, the processes responsible for volcanic eruptions are independent of the type of volcanism or geographical location.

scholarly journals Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 441 ◽  
Author(s):  
Maria C. Mariani ◽  
Peter K. Asante ◽  
Md Al Masum Bhuiyan ◽  
Maria P. Beccar-Varela ◽  
Sebastian Jaroszewicz ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Series Data ◽  
Financial Time Series ◽  
Seismic Station ◽  
Volcanic Eruptions ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Properties ◽  
Long Range Correlations

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

scholarly journals Scaling properties of gravity-driven sediments

1995 ◽  
Vol 2 (3/4) ◽  
pp. 178-185 ◽  
Author(s):  
D. H. Rothman ◽  
J. P. Grotzinger
Keyword(s):  
Critical Thickness ◽  
Sedimentary Basin ◽  
Scaling Law ◽  
Scaling Exponent ◽  
Power Law Distribution ◽  
Scaling Properties ◽  
Number Of Layers ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
Open Question

Abstract. Recent field observations of the statistical distribution of turbidite and debris flow deposits are discussed. In some cases one finds a good fit over 1.5-2 orders of magnitude to the scaling law N(h) α h-B, where N(h) is the number of layers thicker than h. Observations show that the scaling exponent B varies widely from deposit to deposit, ranging from about 1/2 to 2. Moreover, one case is characterized by a sharp crossover in which B increases by a factor of two as h increases past a critical thickness. We propose that the variations in B, either regional or within the same deposit, are indicative of the geometry of the sedimentary basin and the rheological properties of the original gravity-driven flow. The origin of the power-law distribution remains an open question.

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