Analysis and Forecasting of Parameters for p-Order Autoregressive Process

Sherstneva A.A.

Abstract


Several assumptions are made while solving the problems of calculating the performance and reliability metrics of info-communication systems using classical methods – for instance, the exponential distribution of source variables does not always correspond to real data. Moreover, source variables are random variables collected and processed by the monitoring system. To obtain the most accurate results of the indicator calculation, it is necessary to conduct a large number of measurements of random variables. In this sense, the well-known formulas of teletraffic theory have some inaccuracy. One of the effective ways to solve this problem is the use of regression analysis. The paper purposes for estimating the metrics in info-communication systems for data trend forecasting.

The paper aims to identify the autoregressive process for parameters forecasting for info-communication systems. The use of a classical regression analysis method, such as least squares estimation, has several limitations. The paper proposes an alternative approach to solving the indicated problem through the filtration theory.

Along with the classical least squares estimation, an alternative opportunity is to solve the empirical Yule-Walker equations. The paper presents a solution technique using the Levinson-Durbin algorithm. In addition to theoretical calculations, a program has been developed to automate the computation process.

Depending on the number of observations, a criterion is selected, its minimization leads to the model’s real order. The estimation is carried out using the mathematical modeling program Matlab. In this regard, the paper considers the possibility of choosing a criterion from a theoretical point of view and its practical implementation. The conditions of use are also given; the most effective method for criterion choosing is shown depending on the number of observations.

Keywords


regression, analysis, least squares estimation, Yule-Walker equations, Levinson-Durbin algorithm

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DOI: http://dx.doi.org/10.22213/2413-1172-2020-4-77-84

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