Santa Ana Winds: Fractal-Based Analysis in a Semi-Arid Zone of Northern Mexico

A fractal analysis based on the time series of precipitation, temperature, pressure, relative humidity, and wind speed was performed for 16 weather stations located in the hydrographic basin of the Guadalupe River in Baja California, Mexico. Days on which the phenomenon known as Santa Ana winds occurs were identified based on the corresponding criteria of wind speed (≥4.5 m/s) and wind direction (between 0° and 90°). Subsequently, the time series was formed with data representing the days on which this phenomenon occurs in each of the analyzed weather stations. A time series was additionally formed from the days in which the Santa Ana winds condition does not occur. Hurst exponents and fractal dimension were estimated applying the rescaled range method to characterize the established time series in terms of characteristics of persistence, anti-persistence, or randomness along with the calculation of the climate predictability Index. This enabled the behavior and correlation analysis of the meteorological variables associated with Santa Ana winds occurrence. Finally, this type of research study is instrumental in understanding the regional dynamics of the climate in the basin, and allows us to establish a basis for developing models that can forecast the days of occurrence of the Santa Ana winds, in such a way that actions or measures can be taken to mitigate the negative consequences generated when said phenomenon occurs, such as fires and droughts.

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

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.

Generalized Cauchy Process: Difference Iterative Forecasting Model

The contribution of this article is mainly to develop a new stochastic sequence forecasting model, which is also called the difference iterative forecasting model based on the Generalized Cauchy (GC) process. The GC process is a Long-Range Dependent (LRD) process described by two independent parameters: Hurst parameter H and fractal dimension D. Compared with the fractional Brownian motion (fBm) with a linear relationship between H and D, the GC process can more flexibly describe various LRD processes. Before building the forecasting model, this article demonstrates the GC process using H and D to describe the LRD and fractal properties of stochastic sequences, respectively. The GC process is taken as the diffusion term to establish a differential iterative forecasting model, where the incremental distribution of the GC process is obtained by statistics. The parameters of the forecasting model are estimated by the box dimension, the rescaled range, and the maximum likelihood methods. Finally, a real wind speed data set is used to verify the performance of the GC difference iterative forecasting model.

INVESTMENT RISK MANAGEMENT BASED ON QUOTATIONS OF OIL COMPANIES, OIL AND DOLLAR

With the non-random movement of the prices of exchange trading objects in mind, by means of the methods and tools of chaos theory, it is possible to show that price changes are subject to the laws of deterministic chaos. This is a new look at this subject compared to the statistical methods that have been used for years, which in most cases assume that the distribution of the rate of returns of the examined series is normal. The aim of the study is to determine the nature of the changes in oil, dollar and Polish fuel prices: whether they are random or determined. In addition, the second aim is to investigate the cause and effect relationship between the price changes of the above-mentioned stocks. Tools such as rescaled range analysis, mean and variance stability analysis and technical analysis will be used. Conclusions resulting from the examination of the three indicated values should be interesting for capital market participants. The article ends with a short-term forecast for WIG-oil&gas.