Study of autocorrelated samples of random variables

Abstract

Mathematical statistics is a branch of mathematics that deals with the collection, analysis, interpretation and presentation of data. It provides theoretical foundations and methods for conducting statistical studies that are used in various fields of science and technology. The role of mathematical statistics in the modern world is enormous. It allows researchers to draw conclusions from data, build predictive models, and make informed decisions in the face of uncertainty. In medicine, statistics help in developing new drugs and assessing their effectiveness; in economics, in analyzing financial markets and forecasting economic indicators; in sociology, in studying social phenomena and trends. In almost all areas of human endeavor, mathematical statistics plays a key role in transforming raw data into useful information that promotes progress and innovation. This study examines autocorrelated samples of random variables and their impact on statistical methods of data analysis. Autocorrelation occurs when the values of a random variable in a sample are not independent, as is often observed in time series and spatial data. This phenomenon can significantly influence the results of statistical analysis, leading to biased estimates and an increase in the rate of false conclusions. The purpose of this study is to draw attention to the issue of autocorrelation in statistical mathematics and the subsequent development of a method for detecting and correcting autocorrelation in samples of random variables. The analysis makes it clear that the use of specialized methods can significantly improve the accuracy of forecasts and the reliability of statistical conclusions, since ignoring autocorrelation when conducting research is a wrong decision. In summary, the results of this study highlight the importance of considering autocorrelation in data analysis and provide practical recommendations for statistics and data scientists.