Análise do Valor p Determinado pela Estatística τ na Aplicação do Teste de Dickey-Fuller Aumentado
DOI:
https://doi.org/10.5540/tcam.2022.023.02.00283Keywords:
Estacionariedade, raiz unitária, séries temporais, teste ADFAbstract
O presente artigo avaliou a interferência da quantidade de defasagens utilizadas no resultado do valor-p associado à estatística utilizada no teste de Dickey-Fuller aumentado (ADF), bem como identificou algumas propriedades das séries estudadas que interferem em seu resultado. Foram realizados três experimentos com séries de diferentes amplitudes, considerando estrutura do modelo em relação à presença ou não de constante e/ou tendência, e quantidade de defasagens como fatores. Modelos autorregressivos do tipo AR(1) foram considerados para a geração de dados pelo método de Monte Carlo, que poderiam apresentar diferentes intensidades para o coeficiente associado à primeira defasagem. Depois da aplicação do teste ADF, foram determinadas as proporções de rejeição da hipótese nula em cada condição experimental, sendo utilizada uma análise de variância com a estatística qui-quadrado para verificar a influência da quantidade de defasagens no valor-p. Os resultados mostram que se houver raiz unitária, o teste apresenta bons resultados, independentemente da quantidade de defasagens considerada. Entretanto, o mesmo não foi observado nos casos em que a série temporal não apresenta raiz unitária.
References
G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, Time Series Analysis: Forecasting and Control. Wiley, 2015.
P. A. Morettin and C. M. C. Toloi, An lise de S ries Temporais. Blucher, 2018.
C. R. Nelson and C. R. Plosser, “Trends and random walks in macroeconomic time series: some evidence and implications,” Journal of Monetary Economics, vol. 10, no. 2, pp. 139–162, 1982.
M. Arltov and D. Fedorov , “Selection of unit root test on the basis of length of time series and value of AR(1) parameter,” Statistika: Statistics and Economy Journal, vol. 96, no. 3, pp. 47–64, 2016.
D. A. Dickey and W. A. Fuller, “Distribution of the estimators for autoregressive time series with unit root,” Journal of the American Statistical Association, vol. 74, no. 366, pp. 427–431, 1979.
M. Caner and L. Kilian, “Size distortions of tests of the null hypothesis of
stationarity: evidence and implications for the PPP debate,” Journal of International Money and Finance, vol. 20, no. 5, pp. 639–657, 2001.
E. Aylar, S. Smeekes, and J. Westerlund, “Lag truncation and the local asymptotic distribution of the ADF test for a unit root,” Statistical Papers, vol. 60, pp. 2109–2118, 2019.
I. Choi, Almost all about unit roots: Foundations, Developments, and Applications. Cambridge University Press, 2015.
R. F. Engle and C. W. J. Granger, “Co-integration and error correction: representation, estimation, and testing,” Econometrica, vol. 55, no. 2, pp. 251–276, 1987.
D. A. Dickey and W. A. Fuller, “Likelihood ratio statistics for autoregressive time series with a unit root,” Econometrica, vol. 49, no. 4, pp. 1057–1072, 1981.
P. A. Morettin, Econometria Financeira: um Curso em Séries temporais Financeiras. Blucher, 2011.
S. Ng and P. Perron, “Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag,” Journal of the American Statistical Association, vol. 90, no. 429, pp. 268–281, 1995.
G. W. Schwert, “Tests for unit roots: a Monte Carlo investigation,” Journal of Business & Economic Statistics, vol. 7, no. 2, pp. 147–159, 1989.
R. J. Hyndman and G. Athanasopoulos, “Forecasting: principles and practice,” 2020.
H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716–723, 1974.
G. Schwarz, “Estimating the Dimension of a Model,” Annals of Statistics, vol. 6, no. 2, pp. 461–464, 1978.
E. J. Hannan and B. G. Quinn, “The determination of the order of an autoregression,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 41, no. 2, pp. 190–195, 1979.
H. Ferrer-P rez, M. I. Ayuda, and A. Aznar, “The sensitivity of unit root tests to the initial condition and to the lag length selection: A Monte Carlo Simulation Study,” Communications in Statistics - Simulation and Computation, 2019.
G. Cavaliere, P. C. B. Phillips, S. Smeekes, and A. M. R. Taylor, “Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility,” Econometric Reviews, vol. 34, no. 4, pp. 512–536, 2015.
J. H. Zar, Biostatistical Analysis. Pearson, 1999.
R Core Team, “R: a language and environment for statistical computing,” 2020.
R. J. Hyndman and Y. Khandakar, “Automatic time series forecasting: the
forecast package for r,” Journal of Statistical Software, vol. 26, no. 3, pp. 1 22, 2008.
B. Pfaff, Analysis of Integrated and Cointegrated Time Series with R. Springer, 2008.
A. Zeileis and T. Hothorn, “Diagnostic checking in regression relationships,” R
News, vol. 2, no. 3, pp. 7–10, 2002.
F. Mendiburu and M. Yaseen, agricolae: Statistical Procedures for Agricultural Research, 2020. R package version 1.4.0.
E. Paparoditis and D. N. Politis, “The asymptotic size and power of the augmented Dickey–Fuller test for a unit root,” Econometric Reviews, vol. 37, no. 9, pp. 955–973, 2018.
A. M. R. Taylor, “The finite sample effects of deterministic variables on conventional methods of lag-selection in unit root tests,” Oxford Bulletin of Economics and Statistics, vol. 62, no. 2, pp. 293–304, 2000.
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