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Estimation and Forecasting of Russian Macroeconomic Indicators through ARFIMA Models

Student: Atlasova Mariya

Supervisor: Elena V. Kossova

Faculty: Faculty of Economic Sciences

Educational Programme: Master

Year of Graduation: 2014

<p>This paper examines autoregressive fractionally integrated moving average (ARFIMA) processes and considers their applications in estimation and forecasting the time series dynamics. Recursive forecasting through ARFIMA models are investigated in case of main Russian macroeconomic indicators: the consumer price index for goods and services, GDP, unemployment rate and industrial production index. Adequacy of forecasts of fractionally integrated stochastic processes based on time series data are compared with simpler models.</p><p>The main goals of research are:</p><p style="margin-left:57.3pt;">&middot;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; study of estimation the time series through ARFIMA models;</p><p style="margin-left:57.3pt;">&middot;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; analysis of prognostic features of the Russian main macroeconomic indicators.</p><p>To achieve these aims examples of estimating of time series including macroeconomic indicators through fractionally integrated processes are described. In addition, the properties and methods for estimating the parameters of these models are studied and recursive forecasts of the best ones are compared with simpler models.</p><p>The analysis of indicators revealed that, firstly, considered time series have a long memory, and, secondly, the construction of recursive forecasts does not justify its efforts compared to simpler in realization models. Analysis of root-mean-square error (RMSE) statistics showed that for only two indicators (CPI and IPI) of the four &nbsp;ARFIMA models provide the best forecasts.</p><p>It was worked out that all indicators except IPI have structural breaks, which were modeled in testing for the presence of unit roots. Also for these indicators obtained estimate of the parameter d&nbsp;belongs to the interval (0, 0.5)&nbsp;which confirms the presence of long memory. Estimates of the fractional integration indicator through semi-parametric methods are different from MLE estimates, and it can be explained by small sample sizes, or correlated to the residuals. It should be noted that the obtained results are comparable with the estimates in studies of other authors.&nbsp;</p>

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