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

• Pages: 24-31

34

Vol. 9 No.2

September, 2023

Balkan Journal of

Interdisciplinary Research

E-ISSN 2411-9725

ISSN 2410-759X

Some empirical results using block bootstrap in estimating the coecients of

a periodic autoregressive model

Lorena Margo Zeqo

Fan S. Noli University, Korca, Albania

DOI: hps://doi.org/10.2478/bjir-2023-0004

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 eective 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 coecients 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.

Keywords: Block bootstrap, periodicity, Periodic Autoregressive (PAR) models, estimation,

condence interval, resampling.

1. Introduction

Periodically correlated (or cyclostationary) processes are random processes that have

a periodic structure but are also random. Many processes encountered in nature and

in human activity possess periodic properties such as in meteorology, communication

systems, econometrics etc.

Periodically correlated random processes are random processes in which a periodic

rhythm exists in the structure that is generally more complicated than periodicity in

the mean function. An important class of periodically correlated sequences are the

Research Article

© 2023 Lorena Margo Zeqo

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