Застосування методу серій для дослідження взаємної кореляції спостережень

Abstract

Запропоновано метод обчислення автокореляції, а також ефективної кількості спостережень. Для генерування корельованих спостережень використовується метод рухомого середнього. За допомогою методу серій можливе спрощене обчислення ефективної кількості спостережень для визначення стандартної непевності середнього значення корельованих спостережень. Предложен метод вычисления автокорреляции, а также эффективного числа наблюдений. Для генерирования коррелированных наблюдений используется метод подвижного среднего. С помощью метода серий возможно упрощенное вычисление эффективного числа наблюдений для определения стандартной неопределенности среднего значения коррелированных наблюдений. When processing the results of measurements big role important presence of correlation values. To find the standard uncertainty need to know the effective number of uncorrelated observations. No correlation can consider could lead to incorrect evaluation of the standard uncertainty of the mean. Not always known autocorrelation function monitoring, and evaluation of the autocorrelation function on observations characterized by low accuracy, which can lead to incorrect finding effective number. There are indirect methods of evaluating the impact assessment on observations correlation standard deviation. This method is recorded sample of N divided into k sub-samples (groups) up to n samples each (N = n · k). Each subsample are partial mean and variance estimation, and find the settings for the entire sample. Then compare the ratio of the variance between groups and within the group. Using the F distribution at a significance level α determined whether the observations are correlated or not. These methods are quite complex and require significant additional computing. The purpose of research is to study simple method of testing autocorrelation and consideration in calculating the Neff. The proposed method is based on calculating the number of series. Series is a sequence of observed values equal before which or after which the values observed are another category or no supervision at all. Set the number of series or observation results are correlated or not. To determine whether correlated observations required to determine the median of the sample and calculate the number of deviations from the median values. Research performed by theMonte Carlo. For research use two types of observations: first – with uncorrelated observations, the second – generated correlated observations, including the method ofmoving average. To find the index of correlation function used exponential autocorrelation function. An effective dependence theoretical number and effective number determined by the method episodes from different bias moving average on a constant number of observations. Based on these studies show that increasing the number of observations (N> 50) to simplify the calculation of the possible number of effective using the method of series. At least 50 the number of observations can be effective calculating numbers with a small biasmoving average.To investigate the cross-correlation of observations of the method is appropriate series and simplifies the calculation of the standard uncertainty.