scholarly journals Analysis of Epidemic Situation of New Coronavirus Infection at Home and Abroad Based on Rescaled Range (R / S) Method

2020 ◽  
Author(s):  
Xiaofeng Ji ◽  
Zhou Tang ◽  
Kejian Wang ◽  
Xianbin Li ◽  
Houqiang Li
Keyword(s):  
Time Series ◽  
Hubei Province ◽  
Long Term Memory ◽  
Analysis Method ◽  
Second Stage ◽  
Rescaled Range ◽  
The Future ◽  
Coronavirus Infection ◽  
At Home

1Summary1.1BackgroundThe outbreak of the new coronavirus infection broke out in Wuhan City, Hubei Province in December 2019, and has spread to 97 countries and regions around the world. Apart from China, there are currently three other severely affected areas, namely Italy, South Korea, and Iran. This poses a huge threat to China’s and even global public health security, challenges scientific research work such as disease surveillance and tracking, clinical treatment, and vaccine development, and it also brings huge uncertainty to the global economy. As of March 11, 2020, the epidemic situation in China is nearing its end, but the epidemic situation abroad is in the outbreak period. Italy has even taken measures to close the city nationwide, with a total of 118,020 cases of infection worldwide.1.2MethodThis article selects the data of newly confirmed cases of COVID-19 at home and abroad as the data sample. Among them: the data of newly confirmed cases abroad is represented by Italy, and the span is from February 13 to March 10. The data of newly confirmed cases at home are divided into two parts: Hubei Province and other provinces except Hubei Province, spanning from January 23 to March 3, and with February 12 as the cutting point, it”s divided into two periods, the growth period and the recession period. The rescaled range (R / S) analysis method and the dimensionless fractal Hurst exponent are used to measure the correlation of time series to determine whether the time series conforms to the fractal Brownian motion, that is, a biased random process. Contrast analysis of the meaning of H value in different stages and different overall H values in the same stage.1.3ResultsBased on R / S analysis and calculated Hurst value of newly confirmed cases in Hubei and non-Hubei provinces, it was found that the H value of Hubei Province in the first stage was 0.574, which is greater than 0.5, indicating that the future time series has a positive correlation and Fractal characteristics; The H value in the second stage is 1.368, which is greater than 1, which indicates that the future epidemic situation is completely preventable and controllable, and the second stage has a downward trend characteristic, which indicates that there is a high probability that the future time series will decline. The H values of the first and second stages of non-Hubei Province are 0.223 and 0.387, respectively, which are both less than 0.5, indicating that the time series of confirmed cases in the future is likely to return to historical points, and the H value in the second stage is greater than that in the first stage, indicating that the time series of confirmed cases in the second stage is more long-term memory than the time series of confirmed cases in the first stage. The daily absolute number of newly confirmed cases in Italy was converted to the daily growth rate of confirmed cases to eliminate the volatility of the data. The H value was 1.853, which was greater than 1, indicating that the time series of future confirmed cases is similar to the trend of historical changes. The daily rate of change in cases will continue to rise.1.4ConclusionAccording to the different interpretation of the H value obtained by the R / S analysis method, hierarchical isolation measures are adopted accordingly. When the H value is greater than 0.5, it indicates that the development of the epidemic situation in the area has more long-term memory, that is, when the number of confirmed cases in the past increases rapidly, the probability of the time series of confirmed cases in the future will continue the historical trend. Therefore, it is necessary to formulate strict anti-epidemic measures in accordance with the actual conditions of various countries, to detect, isolate, and treat early to reduce the base of infectious agents.

scholarly journals ERROR ASSESSMENT IN MODELING WITH FRACTAL BROWNIAN MOTIONS

Fractals ◽  
2013 ◽  
Vol 21 (03n04) ◽  
pp. 1350018 ◽  
Author(s):  
BINGQIANG QIAO ◽  
SIMING LIU
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Hurst Exponent ◽  
Long Term Memory ◽  
Error Assessment ◽  
Data Sampling ◽  
Brownian Motions ◽  
Term Memory ◽  
Rescaled Range

To model a given time series F(t) with fractal Brownian motions (fBms), it is necessary to have appropriate error assessment for related quantities. Usually the fractal dimension D is derived from the Hurst exponent H via the relation D = 2-H, and the Hurst exponent can be evaluated by analyzing the dependence of the rescaled range 〈|F(t + τ) - F(t)|〉 on the time span τ. For fBms, the error of the rescaled range not only depends on data sampling but also varies with H due to the presence of long term memory. This error for a given time series then can not be assessed without knowing the fractal dimension. We carry out extensive numerical simulations to explore the error of rescaled range of fBms and find that for 0 < H < 0.5, |F(t + τ) - F(t)| can be treated as independent for time spans without overlap; for 0.5 < H < 1, the long term memory makes |F(t + τ) - F(t)| correlated and an approximate method is given to evaluate the error of 〈|F(t + τ) - F(t)|〉. The error and fractal dimension can then be determined self-consistently in the modeling of a time series with fBms.

scholarly journals Effectiveness of Electricity Derivatives Market Based on Hurst Exponent

2019 ◽  
Vol 118 ◽  
pp. 02061
Author(s):  
Yunzhi Fei ◽  
Xufang Shao ◽  
Gang Wang ◽  
Li Zhou ◽  
Xue Xia ◽  
...  
Keyword(s):  
Hurst Exponent ◽  
Long Term Memory ◽  
Analysis Method ◽  
Random Walk Process ◽  
Range Analysis ◽  
Rescaled Range ◽  
Electricity Derivatives ◽  
Rescaled Range Analysis ◽  
Method R

The Rescaled Range Analysis method (R/S Analysis method) is applied to analyze the PJM electricity derivatives market through calculating V statistics and Hurst Exponent of three types of products. The study finds that there is no obvious average cycle in the PJM electricity derivatives market. The price fluctuation of various products is not a non-random walk process but has a long-term memory. It shows that the PJM electricity derivatives market is not completely effective. The study also finds that PJM electricity option market is more effective than PJM electricity futures market.

Modeling the risk-return characteristics of the SB1 Mexican private pension fund index

2016 ◽  
Vol 5 (2) ◽  
pp. 70
Author(s):  
Roberto J. Santillán- Salgado ◽  
Marissa Martínez Preece ◽  
Francisco López Herrera
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Financial Time Series ◽  
Private Pension ◽  
Long Term Memory ◽  
Investment Funds ◽  
Risk Return ◽  
Time Series Modelling ◽  
Figarch Model

This paper analyzes the returns and variance behavior of the largest specialized private pension investment funds index in Mexico, the SIEFORE Básica 1 (or, SB1). The analysis was carried out with time series techniques to model the returns and volatility of the SB1, using publicly available historical data for SB1. Like many standard financial time series, the SB1 returns show non-normality, volatility clusters and excess kurtosis. The econometric characteristics of the series were initially modeled using three GARCH family models: GARCH (1,1), TGARCH and IGARCH. However, due to the presence of highly persistent volatility, the series modeling was extended using Fractionally Integrated GARCH (FIGARCH) methods. To that end, an extended specification: an ARFIMA (p,d,q) and a FIGARCH model were incorporated. The evidence obtained suggests the presence of long memory effects both in the returns and the volatility of the SB1. Our analysis’ results have important implications for the risk management of the SB1. Keywords: Private Pension Funds, Time Series modelling, GARCH models, Long Term memory series

Research on the Long-Term Memory of Commodity Housing Price Volatility Based on the FIGARCH Model

2014 ◽  
Vol 1079-1080 ◽  
pp. 1194-1198
Author(s):  
Feng Lan ◽  
Bao Hua Chen
Keyword(s):  
Housing Price ◽  
Price Volatility ◽  
Future Price ◽  
Long Term Memory ◽  
Term Memory ◽  
The Future ◽  
The Government ◽  
Figarch Model ◽  
And Control

The purpose of this paper is to test whether there exists a long-term memory volatility characteristics of housing price. The paper based on the data ranging of Zhengzhou from January 2004 to May 2014, by adopting the FIGARCH model, empirically studies and analysis this characteristics. The research results indicate that the price fluctuation of Zhengzhou commodity homes exist effect of cluster and long-term memory characteristic. FIGARCH model can capture the long memory well, and can predict the future price of commodity residential house for a period of time .Therefore, FIGARCH model can well catch long-term memory and forecast the commodity housing price in the future period of time, which illustrates that external shocks have long-standing impact on the volatility of commodity housing price as well, reaching the conclusion that long-effect Mechanism of regulation and control should be set and developed during the macro-control of the government.

scholarly journals Optimal prediction with resource constraints using the information bottleneck

2020 ◽  
Author(s):  
Vedant Sachdeva ◽  
Thierry Mora ◽  
Aleksandra M. Walczak ◽  
Stephanie Palmer
Keyword(s):  
Resource Constraints ◽  
Internal Representation ◽  
Motion Prediction ◽  
Long Term Memory ◽  
Resource Limitations ◽  
Information Bottleneck ◽  
Trade Offs ◽  
Markovian Dynamics ◽  
The Future

Responding to stimuli requires that organisms encode information about the external world. Not all parts of the signal are important for behavior, and resource limitations demand that signals be compressed. Prediction of the future input is widely beneficial in many biological systems. We compute the trade-offs between representing the past faithfully and predicting the future for input dynamics with different levels of complexity. For motion prediction, we show that, depending on the parameters in the input dynamics, velocity or position coordinates prove more predictive. We identify the properties of global, transferrable strategies for time-varying stimuli. For non-Markovian dynamics we explore the role of long-term memory of the internal representation. Lastly, we show that prediction in evolutionary population dynamics is linked to clustering allele frequencies into non-overlapping memories, revealing a very different prediction strategy from motion prediction.

ASSESSMENT persistent time series hryvnia to the dollar US

2019 ◽  
Author(s):  
Serhii Ternov ◽  
Vasyl Fortuna
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Efficient Market Hypothesis ◽  
Long Term Memory ◽  
Characteristic Time Scale ◽  
Term Memory ◽  
Dollar Exchange Rate ◽  
Study Process ◽  
Daily Changes

Contemporary literature suggests that the effective market hypothesis is not substantiated. Instead, it suggests the Fractal Market Hypothesis (FMH). Fractal markets are characterized by long-term memory. The main feature of the fractal market is that the frequency distribution of the indicator looks the same across diffe­ rent investment horizons. In such cases, it is said that for an appropriate indicator, the phenomenon of scale invariance is observed. All daily changes are correlated with all future daily changes, all weekly changes are correlated with all future weekly changes. There is no characteristic time scale, a key characteristic of the time series. The presence of memory in the time series can be characterized by the Hearst indicator. This paper analyzes the hryvnia to US dollar exchange rate for the period 04.06.14-04.01.15. Finding the Hearst index made it possible to conclude that there is or is not long-term memory in this series. The presence of long-term memory indi­ cates that the efficient market hypothesis is unjustified. The hypothesis was tested that the longer the averaging intervals are taken into account in the model, the Hearst's index decreases. The analysis does not have great predictive power, however, it allows to identify the presence or absence of long-term memory in the study process and thus to accept or reject the hypothesis of an effective market. That is, the series under study is persistent, thus demonstrating long-term me­ mory availability. Thus, since persistence is revealed, the hypothesis of an effective market for the exchange rate yield is not confirmed, but instead can be argued for the fractality of the hryvnia / dollar exchange rate yield. Therefore, the application of the proposed approach made it possible to find the Hearst rate for the hryvnia / dollar exchange rate. The value found indicates that the effective market hypothesis is not substantiated for at least such an exchange rate.

scholarly journals Aspects of the Theory of Comprehension, Memory and Attention

1973 ◽  
Vol 25 (1) ◽  
pp. 22-40 ◽  
Author(s):  
Donald G. Mackay
Keyword(s):  
Dichotic Listening ◽  
Short Term Memory ◽  
Long Term Memory ◽  
Linguistic Processing ◽  
Short Term ◽  
Term Memory ◽  
Memory And Attention ◽  
Second Stage ◽  
Additional Support

This paper proposed a two-stage model to capture some basic relations between attention, comprehension and memory for sentences. According to the model, the first stage of linguistic processing is carried out in short-term memory (M1) and involves a superficial analysis of semantic and syntactic features of words. The second stage is carried out in long-term memory (M2) and involves application of transformational rules to the analyses of M1 so as to determine the deep or underlying relations among words and phrases. According to the theory, attention is an M2 process: preliminary analyses by M1 are carried out even for unattended inputs, but final analyses by M2 are only carried out for attended inputs. The theory was shown to be consistent with established facts concerning memory, attention and comprehension, and additional support for the theory was obtained in a series of dichotic listening experiments.

scholarly journals Investigating the signatures of long-range persistence in seismic sequences along Circum-Pacific subduction zones

2019 ◽  
Vol 37 (4) ◽  
pp. 407
Author(s):  
Daniel Freitas ◽  
George França ◽  
Thais Scherrer ◽  
Carlos Vilar ◽  
Raimundo Silva
Keyword(s):  
Long Range ◽  
Subduction Zones ◽  
Active Fault ◽  
Long Term Memory ◽  
Seismic Sequences ◽  
Rescaled Range ◽  
The Pacific ◽  
Q Index ◽  
National Earthquake Information Center

AbstractIn the present paper, we analyze the signatures of long-range persistence in seismic sequences along Circum-Pacific subduction zones, from Chile to Kermadec, extracted from the National Earthquake Information Center (NEIC) catalog. This region, known as the Pacific Ring of Fire, is the world’s most active fault line, containing about 90% of the world’s earthquakes. We used the classical rescaled range (R/S) analysis to estimate the long-term persistence signals derived from a scaling parameter called the Hurst exponent, H. We measured the referred exponent and obtained values of H > 0.5, indicating that a long-term memory effect exists. We found a possible fractal relationship between H and the bs(q)-index, which emerges from the non-extensive Gutenberg-Richter law as a function of the asperity. Therefore, H can be associated with a mechanism that controls the level of seismic activity. Finally, we concluded that the dynamics associated with fragment-asperity interactions can be classified as a self-affine fractal phenomenon.Keywords: Applied geophysics; Fault and Fracture Analysis; Mathematics applied to geohysics; Seismology; Statistics;geostatistics ResumoNo presente artigo, analisamos as assinaturas de persistência long-range nas sequências sísmicas ao longo das zonas de subducção Circum-Pacific, do Chile até Kermadec, extraídas do catálogo do Centro Nacional de Informações sobre Terremotos (NEIC). Esta região, conhecida como Anel de Fogo do Pacífico, é a linha de falhas mais ativa do mundo, contendo cerca de 90% dos terremotos do mundo. Usamos a análise clássica R / S para estimar a assinatura de persistência a longo prazo derivada do parâmetro de escalonamento chamado expoente de Hurst, H. Como principal objeto de estudo}, medimos o referido expoente e obtivemos todos os valores de H> 0,5, indicando que existe um efeito de memória de longo prazo. A principal contribuição do nosso artigo foi encontrar uma possível relação entre H e o índice bs (q) - que emerge da lei de Gutenberg-Richter não-extensiva como uma função da aspereza, isto é, H pode estar associado ao mecanismo que controla o nível de atividade dos terremotos. Finalmente, concluímos que a dinâmica associada às interações fragilidade-aspereza pode ser classificado como um fenômeno fractal auto-afim.Palavras-chaves: Geofisica Aplicada; Analise de falhas e fraturas; Matematica Aplicada a Geofisica; Sismologia; Estatistica;geoestatistica

Sign in / Sign up

Export Citation Format

Share Document