<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The bootstrap proposed by Efron (1979) resulted a useful method in estimating the distribution of an estimator or a test statistic by resampling the data in the case of independent and identically distributed observations. Although it was not as effective in the case of dependent data as in the case of independent and identically distributed data, an adaptation was obtained using the block bootstrap. The block bootstrap consists in dividing the data into blocks of observations and then resampling these blocks with replacement. When resampling periodic data, we must take in consideration the periodicity present.</p>
<p>Periodically correlated time series and in particular those related with PAR processes have been object of many recent studies due to numerous applications in real data problems. The aim of this paper is to use a block bootstrap procedure proposed, Block Bootstrap of the Residuals, in the case of PAR (Periodic Autoregressive) models. The results obtained in the case of estimating the coefficients in a PAR model studied are very good and are characterized by small values of Bias, Mean Squared Error and Standard Deviation. Also the bootstrap estimations obtained are closer to the true values than the usual classic point estimations.</p>
</abstract>

The bootstrap proposed by Efron (1979) resulted a useful method in estimating the distribution of an estimator or a test statistic by resampling the data in the case of independent and identically distributed observations. Although it was not as effective in the case of dependent data as in the case of independent and identically distributed data, an adaptation was obtained using the block bootstrap. The block bootstrap consists in dividing the data into blocks of observations and then resampling these blocks with replacement. When resampling periodic data, we must take in consideration the periodicity present.
Periodically correlated time series and in particular those related with PAR processes have been object of many recent studies due to numerous applications in real data problems. The aim of this paper is to use a block bootstrap procedure proposed, Block Bootstrap of the Residuals, in the case of PAR (Periodic Autoregressive) models. The results obtained in the case of estimating the coefficients in a PAR model studied are very good and are characterized by small values of Bias, Mean Squared Error and Standard Deviation. Also the bootstrap estimations obtained are closer to the true values than the usual classic point estimations.

Some empirical results using block bootstrap in estimating the coefficients of a periodic autoregressive model

Balkan Journal of Interdisciplinary Research

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

The bootstrap proposed by Efron (1979) resulted a useful method in estimating the distribution of an estimator or a test statistic by resampling the data in...

Some empirical results using block bootstrap in estimating the coefficients of a periodic autoregressive model

Published Online: Sep 21, 2023

Page range: 34 - 41

DOI: https://doi.org/10.2478/bjir-2023-0004

Keywords
Block bootstrap, periodicity, Periodic Autoregressive (PAR) models, estimation, confidence interval, resampling

© 2023 Lorena Margo Zeqo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

Some empirical results using block bootstrap in estimating the coefficients of a periodic autoregressive model

Published Online: Sep 21, 2023

Page range: 34 - 41

DOI: https://doi.org/10.2478/bjir-2023-0004

KeywordsBlock bootstrap, periodicity, Periodic Autoregressive (PAR) models, estimation, confidence interval, resampling

© 2023 Lorena Margo Zeqo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords
Block bootstrap, periodicity, Periodic Autoregressive (PAR) models, estimation, confidence interval, resampling