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 COMPLEXITY-BASED ANALYSIS OF THE ALTERATIONS IN THE STRUCTURE OF CORONAVIRUSES

Fractals ◽  
2021 ◽  
Vol 29 (02) ◽  
pp. 2150123
Author(s):  
HAMIDREZA NAMAZI ◽  
ALI SELAMAT ◽  
ONDREJ KREJCAR
Keyword(s):  
Hurst Exponent ◽  
Complex Structure ◽  
Approximate Entropy ◽  
Sample Entropy ◽  
Long Term Memory ◽  
Complex Structures ◽  
Term Memory ◽  
The World ◽  
First Time

The coronavirus has influenced the lives of many people since its identification in 1960. In general, there are seven types of coronavirus. Although some types of this virus, including 229E, NL63, OC43, and HKU1, cause mild to moderate illness, SARS-CoV, MERS-CoV, and SARS-CoV-2 have shown to have severer effects on the human body. Specifically, the recent known type of coronavirus, SARS-CoV-2, has affected the lives of many people around the world since late 2019 with the disease named COVID-19. In this paper, for the first time, we investigated the variations among the complex structures of coronaviruses. We employed the fractal dimension, approximate entropy, and sample entropy as the measures of complexity. Based on the obtained results, SARS-CoV-2 has a significantly different complex structure than SARS-CoV and MERS-CoV. To study the high mutation rate of SARS-CoV-2, we also analyzed the long-term memory of genome walks for different coronaviruses using the Hurst exponent. The results demonstrated that the SARS-CoV-2 shows the lowest memory in its genome walk, explaining the errors in copying the sequences along the genome that results in the virus mutation.

Analysis of Long-Term Memory in the Mexican Exchange Market Using a Fuzzy Hurst Exponent: Does Intervention Matter?

2018 ◽  
Vol 26 (Suppl. 1) ◽  
pp. 71-92
Author(s):  
Klender Cortez ◽  
Martha Del Pilar Rodríguez
Keyword(s):  
Exchange Rate ◽  
Central Bank ◽  
Exchange Rates ◽  
Hurst Exponent ◽  
The Other ◽  
Long Term Memory ◽  
Exchange Market ◽  
Term Memory ◽  
Monetary Authorities

The following article aims to detect if long-term memory exists in the Mexican exchange rate market. This research was conducted between 1992 and 2016, during which time different intervention mechanisms were presented. The interventions were divided as follows: a) crawling bands (01/1992–12/1994), b) free flotation in crisis (01/1995–07/1996), c) mixed operations with purchases and sales of dollars by the Central Bank (08/1996–06/2001), d) free flotation (07/2001–04/2003), e) accumulation of international reserves (05/2003–02/2009, f) mixed auctions (03/2009–02/2016), and g) free flotation with interest rate increases (03/2016–12/2016). To detect the presence of long-term memory in the peso–dollar exchange rates, we proposed a fuzzy Hurst exponent. The results evidenced distinct types of behaviors depending on the grade of intervention. Compared to a free-floating regime, persistence and fuzzy Hurst values decreased when the Central Bank intervened in the exchange market. On the other hand, uncertainty increased when monetary authorities imposed a mechanism for buying and selling dollars without an exchange rate target.

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.

How the Efficiency of Mutual Funds in India Have Evolved over Time: A Study on Selected Mutual Funds in India

2020 ◽  
Vol 14 (1) ◽  
pp. 3-26
Author(s):  
Radhika Prosad Datta ◽  
Jayanta Kumar Seal ◽  
Jayanta Kumar Seal
Keyword(s):  
Market Efficiency ◽  
Mutual Funds ◽  
Hurst Exponent ◽  
Long Term Memory ◽  
Term Memory ◽  
Significant Difference ◽  
Over Time

This paper studies the long term memory of the returns from selected mutual funds from the large, mid & small cap and hybrid categories in India, over 10 years starting from 2008-09. The Hurst exponent is used to study the persistence and anti-persistent or mean-reverting trends and hence the market efficiency of the returns of the funds across various categories and periods are analyzed. The findings indicate, that there seems to be no significant difference in the market efficiency of various mutual funds across the categories studied over our period of interest. Although for certain periods all the categories do show persistent or anti-persistent behavior, there does not seem to be any particular pattern in such behaviour.

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.

Introducing a chaotic map with a wide range of long-term memory as a model of patch-clamped ion channels current time series

2019 ◽  
Vol 126 ◽  
pp. 361-368 ◽  
Author(s):  
Alireza Bahramian ◽  
Ali Nouri ◽  
Golnaz Baghdadi ◽  
Shahriar Gharibzadeh ◽  
Farzad Towhidkhah ◽  
...  
Keyword(s):  
Time Series ◽  
Ion Channels ◽  
Chaotic Map ◽  
Long Term Memory ◽  
Current Time ◽  
Term Memory ◽  
Wide Range

Forecasting the wind direction by using time series models with long-term memory (case study: Nayer region)

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Paria Soleimani ◽  
Bahareh Emami ◽  
Meysam Rafei ◽  
Hooman Shahrasbi
Keyword(s):  
Time Series ◽  
Wind Energy ◽  
Wind Direction ◽  
Fossil Fuels ◽  
Moving Average ◽  
Maximum Energy ◽  
Long Term Memory ◽  
Term Memory ◽  
Content Type

Purpose Today, because of the increasing need for the energy resources and the reduction of fossil fuels, renewable energy, especially wind energy, has attracted special attention. The precise forecasting of such energy will be the main factor in designing and investing in this field. On the other hand, the wind energy forecast provides the possibility of optimal use of available resources. In addition, the produce maximum energy would be possible by identifying wind direction and putting wind turbines in the best position. Design/methodology/approach Time series forecasting methods with long-term memory in this research have been used. Findings Eventually, the autoregressive fractionally integrated moving average (3,0,0)-FIGARCH (1,0,1) long-term memory model has more acceptable performance. The obtained error is based on the RMSE (0.2889) and the TIC (0.2605) values. Practical implications In this paper, the forecast wind direction belongs to Ardebil province and Nayer city in Iran. Originality/value The speed and direction of wind are variables that constantly change; hence, it will be difficult to predict the exact wind energy. In recent years, some studies have been conducted on wind speed forecasting, whereas wind direction forecasting has been done in a fewer number of studies. Most studies are related to low-lying areas. As the height of the wind turbine is directly related to the energy generation, 78 m height has been considered in this study.

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