Program for Kolmogorov Complexity Identification of Time Series

<p>The field of the graduation project is the development of the Kolmogorov complexity identification procedure for time series.</p><p>The main purpose of the work is time series analysis within the framework of Kolmogorov complexity aimed for further improvement of the quality of prediction and of statistical analysis.</p><p>During the project planning stage the comparative analysis of existing approaches and research of the effectiveness of the proposed bicriterial method were performed.</p><p>&nbsp;The paper proposes an approach to time series research based on the Kolmogorov complexity identification, which could be potentially used to improve the quality of data analysis and processing. The Kolmogorov complexity is a numeric characteristic of time series which represents the ratio of an original symbolic code of the data to a compressed code. The key issue of the proposed approach is a way of constructing a symbolic code that is obtained by using bicriterial method. The method uses two variables while constructing symbolic code: the reliability of encoded segments and the consistency of empirical and histogram distribution functions. The paper also suggests ideas for future research regarding clusterization issues of time series.</p><p>The final result of the graduation project is the developed program that:</p><p>1) For a given time series calculates the Kolmogorov complexity and the quality criterion of partitioning;</p><p>2) Visualizes the structure of time series decomposition into segments;</p><p>3) According to the results of test experiments classifies a given time series to an already studied time series under Kolmogorov complexity.</p><p>The result of the development is placed to open access on the Windows Azure cloud service and it is available at : <a href="http://kolmogorov.azurewebsites.net/">http://kolmogorov.azurewebsites.net/</a>. The program allows loading time series in text format and counting the Kolmogorov complexity and quality criteria, as well as information on previous experiments given in section &quot;Results of the experiments&quot;. Section &laquo;Cluster Analysis&quot; includes partitioning of previously calculated time series parameters and the quality criterion of Kolmogorov complexity.</p><p>The results of this study may be useful for researchers who are interested in effective data analysis. Time series can be initially investigated using the proposed program.</p><p>Future research in this area may be pursued in the context of the introduction of additional metrics for cluster space when evaluating the time series, which will improve the accuracy and efficiency of forecasts.</p><p><em><span id="result_box" lang="en"><strong><span class="hps">Keywords:</span></strong> <span class="hps">Kolmogorov complexity</span><span>, time series</span><span>,</span> <span class="hps">bicriterial</span> <span class="hps">method</span><span>,</span> <span class="hps">character code</span><span>, clustering</span><span>, forecasting.</span></span></em></p>