scholarly journals Generalization of Higuchi’s Fractal Dimension for Multifractal Analysis of Time Series with Limited Length

2021 ◽  
Author(s):  
Carlos Carrizalez-Velazquez ◽  
Reik Donner ◽  
Lev Guzmán-Vargas
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Multifractal Analysis ◽  
Multifractal Spectrum ◽  
Reliable Estimate ◽  
New Approach ◽  
Anal Ysis ◽  
Univariate Time Series ◽  
Limited Length ◽  
Short Time

Abstract We introduce a generalization of Higuchi’s estimator of the fractal dimension as a new way to characterize the multifractal spectrum of univariate time series. The resulting multifractal Higuchi dimension anal ysis (MF-HDA) method considers the order-q moments of the partition function provided by the length of the time series graph at different levels of subsampling. The results obtained for different types of stochastic processes as well as real-world examples of word length series from fictional texts demonstrate that MF-HDA provides a reliable estimate of the multifractal spectrum already for moderate time series lengths. Practical advantages as well as disadvantages of the new approach as compared to other state-of-the-art methods of multifractal analysis are discussed, highlighting the particular potentials of MF-HDA to distinguish mono from multifractal dynamics based on relatively short time series.

MIXED MULTIFRACTAL ANALYSIS OF CRUDE OIL, GOLD AND EXCHANGE RATE SERIES

Fractals ◽  
2016 ◽  
Vol 24 (04) ◽  
pp. 1650046 ◽  
Author(s):  
MEIFENG DAI ◽  
SHUXIANG SHAO ◽  
JIANYU GAO ◽  
YU SUN ◽  
WEIYI SU
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Exchange Rate ◽  
Crude Oil ◽  
Multifractal Analysis ◽  
Multifractal Spectrum ◽  
Price Series ◽  
The Us ◽  
Multifractal Spectra ◽  
Us Dollar

The multifractal analysis of one time series, e.g. crude oil, gold and exchange rate series, is often referred. In this paper, we apply the classical multifractal and mixed multifractal spectrum to study multifractal properties of crude oil, gold and exchange rate series and their inner relationships. The obtained results show that in general, the fractal dimension of gold and crude oil is larger than that of exchange rate (RMB against the US dollar), reflecting a fact that the price series in gold and crude oil are more heterogeneous. Their mixed multifractal spectra have a drift and the plot is not symmetric, so there is a low level of mixed multifractal between each pair of crude oil, gold and exchange rate series.

INFLUENCE OF SAMPLING LENGTH AND SAMPLING INTERVAL ON CALCULATING THE FRACTAL DIMENSION OF CHAOTIC ATTRACTORS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250145
Author(s):  
CUICUI JI ◽  
HUA ZHU ◽  
WEI JIANG
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Sampling Interval ◽  
Computational Time ◽  
Chaotic Attractors ◽  
Computation Efficiency ◽  
Univariate Time Series ◽  
Saturation Method ◽  
Different Chaotic Systems

This paper intends to study the influences of the sampling length and sampling interval of time series on the chaotic attractors' fractal dimension calculation. Four kinds of univariate time-series signals from different chaotic systems were chosen, and then fractal dimensions of attractors under different sampling lengths and sampling intervals were calculated by the method of correlation dimension. The results show clearly that the chaotic attractors' fractal dimension is related to both the sampling length and the sampling interval. With the increase of the sampling length, all attractors' fractal dimensions tend to increase gradually first and then become stable. However, the fractal dimension remains stable only in a suitable range of the sampling interval, in which the attractor of the chaotic system can be reconstructed from one univariate time-series signal; if the sampling interval is unusually large or small, the fractal dimension will be unstable and the reconstructed attractor will be seriously distorted. Therefore, the dimension saturation method and the delay-coordinate's time difference method for determining the sampling length and the sampling interval were proposed separately, which are significant for improving the calculation accuracy for the chaotic attractor's dimension, reflecting the dynamics of complicated systems correctly, saving computational time as well as enhancing the computation efficiency.

scholarly journals An Improved Brown's Method Applying Fractal Dimension to Forecast the Load in a Computing Cluster for Short Time Series

2016 ◽  
Vol 9 (19) ◽  
Author(s):  
Vladimir Vyacheslalovich Kopytov ◽  
Viacheslav Ivanovich Petrenko ◽  
Fariza Bilyalovna Tebueva ◽  
Natalia Vasilievna Streblianskaia
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Short Time Series ◽  
Brown's Method ◽  
Short Time ◽  
Computing Cluster

A COMPARATIVE STUDY BETWEEN UNIVARIATE AND BIVARIATE TIME SERIES MODELS FOR CRUDE PALM OIL INDUSTRY IN PENINSULAR MALAYSIA

2020 ◽  
Vol 5 (1) ◽  
pp. 374
Author(s):  
Pauline Jin Wee Mah ◽  
Nur Nadhirah Nanyan
Keyword(s):  
Time Series ◽  
Palm Oil ◽  
Moving Average ◽  
Forecast Accuracy ◽  
Peninsular Malaysia ◽  
Time Series Models ◽  
Crude Palm Oil ◽  
Univariate Time Series ◽  
Import And Export ◽  
Bivariate Time Series

The main purpose of this study is to compare the performances of univariate and bivariate models on four time series variables of the crude palm oil industry in Peninsular Malaysia. The monthly data for the four variables, which are the crude palm oil production, price, import and export, were obtained from Malaysian Palm Oil Board (MPOB) and Malaysian Palm Oil Council (MPOC). In the first part of this study, univariate time series models, namely, the autoregressive integrated moving average (ARIMA), fractionally integrated autoregressive moving average (ARFIMA) and autoregressive autoregressive (ARAR) algorithm were used for modelling and forecasting purposes. Subsequently, the dependence between any two of the four variables were checked using the residuals’ sample cross correlation functions before modelling the bivariate time series. In order to model the bivariate time series and make prediction, the transfer function models were used. The forecast accuracy criteria used to evaluate the performances of the models were the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The results of the univariate time series showed that the best model for predicting the production was ARIMA  while the ARAR algorithm were the best forecast models for predicting both the import and export of crude palm oil. However, ARIMA  appeared to be the best forecast model for price based on the MAE and MAPE values while ARFIMA  emerged the best model based on the RMSE value.  When considering bivariate time series models, the production was dependent on import while the export was dependent on either price or import. The results showed that the bivariate models had better performance compared to the univariate models for production and export of crude palm oil based on the forecast accuracy criteria used.

scholarly journals The Use of Odd and Even Class Wind Speed Time Series of Distribution Histogram to Estimate Weibull Parameters

2018 ◽  
Vol 7 (2) ◽  
pp. 139-150 ◽  
Author(s):  
Adekunlé Akim Salami ◽  
Ayité Sénah Akoda Ajavon ◽  
Mawugno Koffi Kodjo ◽  
Seydou Ouedraogo ◽  
Koffi-Sa Bédja
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Time Series Data ◽  
Empirical Method ◽  
Likelihood Method ◽  
Series Data ◽  
New Approach ◽  
Weibull Parameters ◽  
Distribution Histogram ◽  
Mean Wind Speed

In this article, we introduced a new approach based on graphical method (GPM), maximum likelihood method (MLM), energy pattern factor method (EPFM), empirical method of Justus (EMJ), empirical method of Lysen (EML) and moment method (MOM) using the even or odd classes of wind speed series distribution histogram with 1 m/s as bin size to estimate the Weibull parameters. This new approach is compared on the basis of the resulting mean wind speed and its standard deviation using seven reliable statistical indicators (RPE, RMSE, MAPE, MABE, R2, RRMSE and IA). The results indicate that this new approach is adequate to estimate Weibull parameters and can outperform GPM, MLM, EPF, EMJ, EML and MOM which uses all wind speed time series data collected for one period. The study has also found a linear relationship between the Weibull parameters K and C estimated by MLM, EPFM, EMJ, EML and MOM using odd or even class wind speed time series and those obtained by applying these methods to all class (both even and odd bins) wind speed time series. Another interesting feature of this approach is the data size reduction which eventually leads to a reduced processing time.Article History: Received February 16th 2018; Received in revised form May 5th 2018; Accepted May 27th 2018; Available onlineHow to Cite This Article: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K. , Ouedraogo, S. and Bédja, K. (2018) The Use of Odd and Even Class Wind Speed Time Series of Distribution Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development 7(2), 139-150.https://doi.org/10.14710/ijred.7.2.139-150

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