Monte Carlo evaluation of asymptotic and bootstrap tests for residual autocorrelation

Vânia de Fátima Lemes de MIRANDA[1]

Daniel Furtado FERREIRA1

§                     ABSTRACT: Autocorrelation diagnosis can be formally made by using Durbin-Watson's test (DW). This study aimed to evaluate through Monte Carlo simulation, the Durbin-Watson's bootstrap approach (DWB), direct bootstrap test for autocorrelation parameter (ρ) with (Bρ) and without accelerated bias (BρCa) correction, t test (tρ), bootstrap t test (tρB), normal ρ test (Nρ), normal ρ with bias correction (Nρc), normal test for Young´s C statistics (NC) and bootstrap C test approach (BC). Additionally, the quality of the three estimators (r, r1+ and C) of ρ was studied by evaluating bias and the mean square error. An autocorrelation structure of first order was simulated. As an evaluation criterion type-I error rate and the power of these tests were compared with the test of DW. The main conclusions are: the bias of the r, r1+ and C estimators increase with the increase of the number of k covariates and ρ autocorrelation parameter; the variance of the three estimators are not affected by increasing k and ρ; DW, Nρ, tρ, Bρ and BρCa tests are rigorous and less powerful than their competitors; the DW test is the most rigorous of all and presented the smallest power; DWB and BC tests are equivalents; DWB, BC, tρB, Nρc and NC tests are considered the best because they have sizes that are not significantly different from the nominal level (a), larger power and because they are robust; NC test was considered rigorous for small values of a and of sample size n; Nρc test is recommended here due to its simplicity and ease of application.

§    KEYWORDS: Autocorrelation; Durbin-Watson's test; bootstrap; Monte Carlo.



[1]Departamento de Ciências Exatas, Universidade Federal de Lavras – UFLA, CEP 37200-000, Lavras, MG. E-mail: vaniafatima@bol.com.br / danielff@ulfa.br