An rescaled range analysis on the characteristics of coal seam development in the Eastern depression of the Liaohe Basin

The characteristics of coal seam development,and the prospects of a favorable coal-forming area,were evaluated for the Liaohe Basin located in China.The Number 3 and Number 9 coal seam thickness series from 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined by a rescaled range analysis.The results indicate that the Hurst exponents of the Number 3 and Number 9 coal seam thickness series are 0.69 and 0.68,respectively.This suggests the presence of persistence.As the bore spacing increases the Hurst exponent of the Number 3 series gradually decreases（H changes from 0.69 to 0.52） and shifts from persistence to randomness.The Hurst exponent of the Number 9 thickness data gradually increases（H changes from 0.68 to 0.91） and always shows the characteristic of persistence.A combination of geological characteristics and the series data allow the conclusion that it is more suitable for the Number 9 coal seam to form in the Northeastern part of the Eastern depression than the Number 3 coal seam.

The Law of Iterated Logarithm of Rescaled Range Statistics for AR(1) Model

Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.

Prediction and calculation for new energy development

Some important questions for new energy development were discussed, such as the prediction and calculation of sea surface temperature, ocean wave, offshore platform price, typhoon track, fire status, vibration due to earthquake, energy price, stock market’s trend and so on with the fractal methods (including the four ones of constant dimension fractal, variable dimension fractal, complex number dimension fractal and fractal series) and the improved rescaled range analysis (R/S analysis).

Forecasting Diabetes Patients Attendance at Al-Baha Hospitals Using Autoregressive Fractional Integrated Moving Average (ARFIMA) Models

Diabetes has become a concern in the developed and developing countries with its growing number of patients reported to the ministry of health records. This paper discusses the use of the Autoregressive Fractional Moving Average (ARFIMA) technique to modeling the diabetes patient’s attendance at Al-Baha hospitals using monthly time series data. The data used in the analysis of this paper are monthly readings of diabetes patients data covered the period January 2006-December 2016. The data were collected from the General Directorate of Health Affairs, Al-Baha region. The autoregressive fractional moving average approach was applied to the data through the model identification, estimation, diagnostic checking and forecasting. Hurst test results and ACF confirmed that there is a long memory behavior in diabetic patient’s data. Also, the fractional difference to diabetes series data revealed that (d = 0.44). Moreover, unit root tests indicated that the fractional difference of diabetes series level is stationary. Furthermore, according to AIC and BIC of model selection criteria ARFIMA (1, 0.44, 0) model shown the smallest values, hence this model was chosen as an adequate represents the data. Also, a diagnostic check confirmed that ARFIMA was appropriate and highly recommended in modeling and forecasting this type of data.

Empirical Study on Long Memory Feature in Chinese Stock Market

The notion of long memory, or long-term dependence, has received considerable attention in empirical finance. While many empirical works were done on the detection of long memory in return series, very few investigations focused on the market volatility, though the long-term dependence in volatility may lead to some types of volatility persistence as observed in financial markets and affect volatility forecasts and derivative pricing formulas. So, using modified rescaled range analysis and ARFIMA model testing, this study examined long-term dependence in Chinese stock market returns and volatility. The results show that although the returns themselves contain little serial correlation, the variability of returns has significantly long-term dependence. It would be beneficial to encompass long memory structure to assess the behavior of stock prices and research on financial market theory.