scholarly journals Rescaled range analysis and conditional probability-based probe into the intrinsic pattern of rainfall over North Mountainous India

2021 ◽  
Author(s):  
Amith Sharma ◽  
Surajit Chattopadhyay
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Indian Summer Monsoon ◽  
Annual Rainfall ◽  
Conditional Probabilities ◽  
Autocorrelation Coefficient ◽  
Range Analysis ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
High Volatility

Abstract In work reported here, we have explored rainfall over North Mountainous India for pre-monsoon (MAM), Indian summer monsoon (JJAS), post-monsoon (OND) and Annual. The dependence of JJAS on MAM and OND on JJAS has been explored through conditional probabilities utilizing frequency distribution. An autocorrelation structure has shown that a low lag-1 autocorrelation coefficient characterizes all the time series. We have implemented rescaled range analysis. Through Hurst's exponent and fractal dimension, we have observed that the MAM time series of rainfall over North Mountainous India has a smooth trend and low volatility. We have further observed that for MAM and JJAS, we have , and D is closer to 1 than to 2. However, we have further observed that for OND and Annual rainfall over North Mountainous India and . Therefore, these two time series have been characterized by high volatility and randomness.

RANDOM WALK IN SHORTCUT MODELS

2008 ◽  
Vol 22 (10) ◽  
pp. 727-733 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Drift Velocity ◽  
System Size ◽  
Random Walk Process ◽  
Range Analysis ◽  
Sharp Transition ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Earlier studies of a parametrized class of models whose fractal dimension transitions from one to two indicated that the transition occurs infinitely sharply at the parameter value p=0, as the system size increases to infinity. We study a random walk process which is sensitive to dimension, and we find the same sharp transition at p=0. We use the tool of rescaled range analysis to analyze the drift velocity of the random walk process.

SUNSPOTS DATA ANALYSIS USING TIME SERIES

Fractals ◽  
2008 ◽  
Vol 16 (03) ◽  
pp. 259-265 ◽  
Author(s):  
YUSUF H. SHAIKH ◽  
A. R. KHAN ◽  
M. I. IQBAL ◽  
S. H. BEHERE ◽  
S. P. BAGARE
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
Sunspot Cycle ◽  
Fractal Dimensions ◽  
Data Sets ◽  
Range Analysis ◽  
Data Set ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
Sunspot Data

The record of the sunspot number visible on the sun is regularly collected over the centuries by various observatories for studying the different factors influencing the sunspot cycle and solar activity. Sunspots appear in cycles, and last several years. These cycles follow a certain pattern which is well known. We analyzed monthly and yearly averages of sunspot data observed from year 1818 to 2002 using rescaled range analysis. The Hurst exponent calculated for monthly data sets are 0.8899, 0.8800 and 0.8597 and for yearly data set is 0.7187. Fractal dimensions1 calculated are 1.1100, 1.1200, 1.1403 and 1.2813. From the study of Hurst exponent and fractal dimension, we conclude that time series of sunspots show persistent behavior. The fundamental tool of signal processing is the fast Fourier transform technique (FFT). The sunspot data is also analyzed using FFT. The power spectrum of monthly and yearly averages of sunspot shows distinct peaks at 11 years confirming the well known 11-year cycle. The monthly sunspot data is also analyzed using FFT to filter the noise in the data.

CHAOS, NOISE AND COMPLEX FRACTAL DIMENSIONS

Fractals ◽  
1993 ◽  
Vol 01 (01) ◽  
pp. 21-28 ◽  
Author(s):  
BRUCE J. WEST ◽  
X. FAN
Keyword(s):  
Time Series ◽  
Power Law ◽  
Colored Noise ◽  
Fractal Dimensions ◽  
Chaotic Time Series ◽  
Range Analysis ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
Power Law Index ◽  
Two Degree Of Freedom

Herein we propose a measure to distinguish a chaotic time series from one which is colored noise. We apply rescaled range analysis to the chaotic time series generated by a two-degree-of-freedom, nonintegrable Hamiltonian system, and find a modulated power-law for R/S. The combination of the power-law index and the period of modulation suggests a complex fractal dimension, which may be the signature of chaos. Some residual questions are collected.

scholarly journals The Nonlinear Time Sequence Analysis in the Alpine-Himalayan Earthquake Zone

2021 ◽  
Vol 299 ◽  
pp. 02001
Author(s):  
Jiemin Chen ◽  
Zelin Yan ◽  
Linfeng Xu ◽  
Zhixin Liu ◽  
Yan Liu ◽  
...  
Keyword(s):  
Time Series ◽  
Fractal Theory ◽  
Stable Region ◽  
Earthquake Activity ◽  
Range Analysis ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
Fractal Characteristics ◽  
Earthquake Zone ◽  
Himalayan Earthquake

The characteristics of the earthquake activity in the Eurasian earthquake zone, which is the second largest earthquake zone in the world, was investigated by researchers. The earthquake activity of the Eurasian earthquake zone was analysed in various disciplines, such as earth dynamics, rock mechanics, geology and tectonics. The emergence of fractal theory provided a new direction in exploring the characteristics of the earthquake activity in the Eurasian earthquake zone. This study processed the data on the earthquake activity in the Eurasian earthquake zone by self-similarity method and scaled invariant feature test and used the rescaled range analysis method to analyse the nonlinear time series fractal characteristics of the earthquake activity in the Eurasian earthquake zone. Results show that the time series of earthquake activity in the study area is not an independent Poisson process, which exhibits the characteristics of scale invariance and long-range correlation. Approximately 80% of the H values of the earthquake activity iteratively increase and decrease for moderate earthquakes, which is mainly concentrated during the increasing stage. The time difference of the H value between the two-neighbouring earthquake shows that the H value fluctuates in the active earthquake region and is stationary in the relatively stable region. Strong earthquakes will likely occur in the next few years because the H value fluctuates.

Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis

2011 ◽  
pp. 211-220 ◽  
Author(s):  
Georgios Balasis ◽  
Ioannis A. Daglis ◽  
Anastasios Anastasiadis ◽  
Konstantinos Eftaxias
Keyword(s):  
Time Series ◽  
Range Analysis ◽  
Dynamical Complexity ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Evaluating rescaled range analysis for time series

1994 ◽  
Vol 22 (4) ◽  
pp. 432-444 ◽  
Author(s):  
James B. Bassingthwaighte ◽  
Gary M. Raymond
Keyword(s):  
Time Series ◽  
Range Analysis ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Return Intervals Analysis of the Sunspot Time Series

2010 ◽  
Vol 29-32 ◽  
pp. 1144-1149
Author(s):  
Jie Fan ◽  
Wan Qing Li ◽  
Hong Zhang ◽  
Ke Qiang Dong
Keyword(s):  
Time Series ◽  
Long Range ◽  
Threshold Values ◽  
Range Analysis ◽  
Scaling Method ◽  
Long Range Correlations ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Rescaled range analysis (R/S) method is a scaling method commonly used for detecting the long-range correlations in many time series. The aim of this paper is to show that, using the rescaled range analysis on sunspot time series, how the threshold values q affects the correlations of the return intervals for events above a certain threshold q. We find that both the original records and the return intervals are long-range correlated.

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