Quantifying the randomness of the stock markets

Delgado-Bonal, Alfonso

doi:10.1038/s41598-019-49320-9

Cited by 29 publications

(15 citation statements)

References 22 publications

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“…The comparison of the results must be made, continuing with the example, between two time series of human heartbeats since they have similar alphabets; the direct comparison of the complexity of the heartbeat of two different species would not provide meaningful information. For an application of complexity measures to series with different alphabets, see 7 .…”

Section: Resultsmentioning

confidence: 99%

On the use of complexity algorithms: a cautionary lesson from climate research

Delgado-Bonal

2020

Sci Rep

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Complexity algorithms provide information about datasets which is radically different from classical moment statistics. Instead of focusing on the divergences from central values, they quantify other characteristics such as order, pattern repetitions, or the existence of attractors. However, those analyses must be done with the proper statistical treatment, which is, unfortunately, not always the case. In this contribution, I provide an example of the hazards of applying complexity measures without sufficient care by correcting a previously published analysis that aimed to quantify the complexity of climate. I clarify some misconceptions about the use of Sample Entropy and revise the incorrect assessments and conclusions drawn from the previous misapplication of the methods.An attempt to contrast the complexity of the climate of the past 122,000 years and the recent 2,000 years has been developed recently 1 . The idea behind the research was to use the Oxygen isotopic (δ 18 O) record of ice cores, a proxy for the temperature at the accumulation site through history, to determine the levels of complexity of the two different periods. The author obtained values of Sample Entropy (SampEn) of 0.7 ± 0.1 for the long record and 2.2 ± 0.2 for the short one, and values of Lempel-Ziv complexity (LZC) of 0.29 ± 0.03 and 0.99 ± 0.05 for the long and short records respectively, attributing those differences to changes in the complexity of climate. In this paper, I use the same data to show that the reported differences are attributable to the incorrect use of the algorithms rather than to actual changes in climatic complexity.Complexity algorithms are statistical tools, and as such, the conclusions drawn from them are as good as the robustness of their application. The first issue with the previous research was related to the use of the data. The author used two different datasets of the δ 18 O record with different time resolution: the data record for the last 2,000 years had a time resolution of τ = 1 year, while the record for 122,000 years had a time resolution of τ = 20 years. The complexity algorithms used in this research require measurements equally spaced in time 2 , 3 and, in general, the comparison of different time resolutions is impractical and lacks any statistical significance. In the second figure of the same research, the author also determined the complexity for the recent past 2,000 years by sampling the annually resolved record every τ = 20 years, obtaining a mean value of SampEn = 2.3 ± 0.5 and LZC = 1.16 ± 0.08. However, the NGRIP δ 18 O data set spanning the entire past 122,000 years consists of 20-year binned averages of the higher-resolution measurements. In order to avoid erroneous conclusions, instead, this data should have been compared to 20-year binned averages of the annually resolved record.The second issue with the previous research was the misapplication of the complexity algorithms. The complexity of climate was determined by making use of Sample Entropy 4 and Lempel-Ziv complexity 5 .SampE...

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Section: Resultsmentioning

confidence: 99%

On the use of complexity algorithms: a cautionary lesson from climate research

Delgado-Bonal

2020

Sci Rep

Self Cite

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“…Furthermore, since it can be applied to digital and analog signals, one can measure the randomness of a binary key, a speech signal, an image, an ECG signal, the first k digits of π, or other mathematical special number, economic and biological data, among others. There are also other randomness measures based on entropy [15][16][17]; however, they require the estimation of the probability density function and one of them was proposed to be used only with images [15].…”

Section: Discussionmentioning

confidence: 99%

Estimation of the Randomness of Continuous and Discrete Signals Using the Disentropy of the Autocorrelation

Ramos

2021

SN COMPUT. SCI.

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“…For example, the approximated entropy method described in [41] could be used, which has already been applied to i.e. stock prices in [42]. Additionally, instead of a deterministic prediction, one could perform a probabilistic prediction and/or work with confidence intervals for the predicted power values.…”

Section: Discussionmentioning

confidence: 99%

A Non-Intrusive Load Monitoring Approach for Very Short Term Power Predictions in Commercial Buildings

Brucke¹,

Arens²,

Telle³

et al. 2020

Preprint

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This paper presents a new algorithm to extract device profiles fully unsupervised from three phases reactive and active aggregate power measurements. The extracted device profiles are applied for the disaggregation of the aggregate power measurements using particle swarm optimization. Finally, this paper provides a new approach for short term power predictions using the disaggregation data. For this purpose, a state changes forecast for every device is carried out by an artificial neural network and converted into a power prediction afterwards by reconstructing the power regarding the state changes and the device profiles. The forecast horizon is 15 minutes. To demonstrate the developed approaches, three phase reactive and active aggregate power measurements of a multi-tenant commercial building are used. The granularity of data is 1 s. In this work, 52 device profiles are extracted from the aggregate power data. The disaggregation shows a very accurate reconstruction of the measured power with a percentage energy error of approximately 1 %. The developed indirect power prediction method applied to the measured power data outperforms two persistence forecasts and an artificial neural network, which is designed for 24h-day-ahead power predictions working in the power domain.

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Quantifying the randomness of the stock markets

Cited by 29 publications

References 22 publications

On the use of complexity algorithms: a cautionary lesson from climate research

On the use of complexity algorithms: a cautionary lesson from climate research

Estimation of the Randomness of Continuous and Discrete Signals Using the Disentropy of the Autocorrelation

A Non-Intrusive Load Monitoring Approach for Very Short Term Power Predictions in Commercial Buildings

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