Robust autoregressive modeling and its diagnostic analytics with a COVID-19 related application

References

• F.J. Anscombe and W.J. Glynn, Distribution of the kurtosis statistic b2 for normal samples, Biometrika 70 (1983), pp. 227–234.
   Web of Science ®Google Scholar
• A. Azzalini, A class of distribution which includes the normal ones, Scand. J. Stat. 12 (1985), pp. 171–178.
   Web of Science ®Google Scholar
• A. Azzalini, The Skew-Normal and Related Families, Cambridge University Press, Cambridge UK, 2014.
   Google Scholar
• A Azzalini, An overview on the progeny of the skew-normal family – a personal perspective, J. Multi. Anal. 188 (2022), 104851.
   Web of Science ®Google Scholar
• A. Azzalini and A. Capitanio, Distributions generated by perturbation of symmetry with emphasis on a multivariate Student-t distribution, J. R. Stat. Soc. 65 (2003), pp. 367–389.
   Google Scholar
• V.G. Cancho, V.H. Lachos, and E.M.M. Ortega, A nonlinear regression model with skew-normal errors, Stat. Pap. 51 (2010), pp. 547–558.
   Web of Science ®Google Scholar
• C.Z. Cao, J.G. Lin, and J.Q. Shi, Diagnostics on nonlinear model with scale mixtures of skew-normal and first-order autoregressive errors, Statistics 48 (2014), pp. 1033–1047.
   Web of Science ®Google Scholar
• B. Carmichael and A. Coën, Asset pricing with skewed-normal return, Finance Res. Lett. 10 (2013), pp. 50–57.
   Web of Science ®Google Scholar
• D. Cook, Assessment of local influence, J. R. Stat. Soc. B 48 (1986), pp. 133–169.
   Google Scholar
• R.B. D'Agostino, Transformation to normality of the null distribution of g1, Biometrika 57 (1970), pp. 679–681.
   Web of Science ®Google Scholar
• A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. B 39 (1977), pp. 1–38.
   Google Scholar
• M. Eling, Fitting asset returns to skewed distributions: Are the skew-normal and skew-Student good models? Insur. Mathem. Econom. 59 (2014), pp. 45–56.
   Web of Science ®Google Scholar
• C.S. Ferreira, G.A. Paula, and G.C. Lana, Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors, Comput. Stat. 37 (2022), pp. 445–468.
   Web of Science ®Google Scholar
• A.M. Garay, V.H. Lachos, F.V. Labra, and E.M.M. Ortega, Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions, J. Stat. Comput. Simul. 84 (2014), pp. 1761–1778.
   Web of Science ®Google Scholar
• H.J. Ho and T.I. Lin, Robust linear mixed models using the skew-t distribution with application to schizophrenia data, Biom. J. 52 (2010), pp. 449–469.
   PubMed Web of Science ®Google Scholar
• M. Huerta, V. Leiva, S. Liu, M. Rodriguez, and D Villegas, On a partial least squares regression model for asymmetric data with a chemical application in mining, Chemom. Intell. Lab. Syst. 190 (2019), pp. 55–68.
   Web of Science ®Google Scholar
• L. Jin, X. Dai, A. Shi, and L. Shi, Detection of outliers in mixed regressive-spatial autoregressive models, Commun. Stat.: Theory Methods 45 (2016), pp. 5179–5192.
   Web of Science ®Google Scholar
• T. Kollo and D. von Rosen, Advanced Multivariate Statistics with Matrices, Springer, Dordrecht, the Netherlands, 2005.
   Google Scholar
• J. Leao, V. Leiva, H. Saulo, and V Tomazella, Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data, Stat. Med. 37 (2018), pp. 4421–4440.
   PubMed Web of Science ®Google Scholar
• V. Leiva, S. Liu, L. Shi, and F.J.A. Cysneiros, Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics, J. Appl. Stat. 43 (2016), pp. 627–642.
   Web of Science ®Google Scholar
• V. Leiva, H. Saulo, R. Souza, R.G. Aykroyd, and R. Vila, A new BISARMA time series model for forecasting mortality using weather and particulate matter data, J. Forecast. 40 (2021), pp. 346–364.
   Web of Science ®Google Scholar
• W.K. Li, Diagnostic Checks in Time Series, Chapman and Hall/CRC, Boca Raton, 2004.
   Google Scholar
• T.I. Lin, J.C. Lee, and W.J. Hsieh, Robust mixture modeling using the skew t distribution, Stat. Comput. 17 (2007), pp. 81–92.
   Web of Science ®Google Scholar
• S. Liu, On diagnostics in conditionally heteroskedastic time series models under elliptical distributions, J. Appl. Probab. 41A (2004), pp. 393–405.
   Web of Science ®Google Scholar
• S. Liu and C.C. Heyde, On estimation in conditional heteroskedastic time series models under non-normal distributions, Stat. Pap. 49 (2008), pp. 455–469.
   Web of Science ®Google Scholar
• Y. Liu, G. Ji, and S. Liu, Influence diagnostics in a vector autoregressive model, J. Stat. Comput. Simul. 85 (2015), pp. 2632–2655.
   Web of Science ®Google Scholar
• S. Liu, V. Leiva, T. Ma, and A.H. Welsh, Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions, Stat. Methods Appl. 25 (2016), pp. 227–249.
   Web of Science ®Google Scholar
• S. Liu, V. Leiva, D. Zhuang, T. Ma, and J Figueroa-Zuniga, Matrix differential calculus with applications in the multivariate linear model and its diagnostics, J. Multivar. Anal. 188 (2022), 104849.
   Web of Science ®Google Scholar
• T. Liu, S. Liu, and L. Shi, Time Series Analysis Using SAS Enterprise Guide, Springer, Singapore, 2020.
   Google Scholar
• S. Liu, T. Ma, A. SenGupta, K. Shimizu, and M.Z. Wang, Influence diagnostics in possibly asymmetric circular-linear multivariate regression models, Sankhya B 79 (2017), pp. 76–93.
   Google Scholar
• Y. Liu, G. Mao, V. Leiva, S. Liu, and A Tapia, Diagnostic analytics for an autoregressive model under the skew-normal distribution, Mathematics 8 (2020), 693.
   Web of Science ®Google Scholar
• Y. Liu, C. Mao, V. Leiva, S. Liu, and W.A. Silva Neto, Asymmetric autoregressive models: Statistical aspects and a financial application under COVID-19 pandemic, J. Appl. Stat. 49 (2022), pp. 1323–1347.
   PubMed Web of Science ®Google Scholar
• S. Liu and H. Neudecker, On pseudo maximum likelihood estimation for multivariate time series models with conditional heteroskedasticity, Math. Comput. Simul. 79 (2009), pp. 2556–2565.
   Web of Science ®Google Scholar
• Y. Liu, R. Sang, and S. Liu, Diagnostic analysis for a vector autoregressive model under t distributions, Stat. Neerl. 71 (2017), pp. 86–114.
   Web of Science ®Google Scholar
• S. Liu and A.H. Welsh, Regression diagnostics, in International Encyclopedia of Statistical Science, M. Lovric, ed., Springer, Berlin, Heidelberg, 2011, pp. 1206–1208
   Google Scholar
• J. Lu, L. Shi, and F. Chen, Outlier detection in time series models using local influence method, Commun. Stat. Theory Methods 41 (2012), pp. 2202–2220.
   Web of Science ®Google Scholar
• J.R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 3rd ed. Wiley, Chichester, 2019.
   Google Scholar
• C. Marchant and V. Leiva, Robust multivariate control charts based on Birnbaum–Saunders distributions, J. Stat. Comput. Simul. 88 (2018), pp. 182–202.
   Web of Science ®Google Scholar
• S. Martinez, R. Giraldo, and V Leiva, Birnbaum–Saunders functional regression models for spatial data, Stoch. Environ. Res. Risk Assess 33 (2019), pp. 1765–1780.
   Web of Science ®Google Scholar
• G.A. Paula, Influence diagnostics for linear models with first-order autoregressive elliptical errors, Stat. Probab. Lett. 79 (2009), pp. 339–346.
   Web of Science ®Google Scholar
• W.Y. Poon and Y.S. Poon, Conformal normal curvature and assessment of local influence, J. R. Stat. Soc. Ser B 61 (1999), pp. 51–61.
   Google Scholar
• C.B. Zeller, V.H. Lachos, and F.E. Vilca-Labra, Local influence analysis for regression models with scale mixtures of skew-normal distributions, J. Appl. Stat. 38 (2011), pp. 348–363.
   Web of Science ®Google Scholar
• L. Sanchez, V. Leiva, M. Galea, and H. Saulo, Birnbaum–Saunders quantile regression models with application to spatial data, Mathematics 8 (2020), 1000.
   Web of Science ®Google Scholar
• The MathWorks Inc. MATLAB Version: 9.13.0 (R2022b), The MathWorks Inc, Natick, Massachusetts, 2022. Available at https://www.mathworks.com.
   Google Scholar
• A. Tapia, V. Leiva, M.P. Diaz, and V. Giampaoli, Influence diagnostics in mixed effects logistic regression models, TEST 28 (2019), pp. 920–942.
   Web of Science ®Google Scholar
• A. Tapia, V. Giampaoli, M.P. Diaz, and V. Leiva, Sensitivity analysis of longitudinal count responses: A local influence approach and application to medical data, J. Appl. Stat. 46 (2019), pp. 1021–1042.
   Web of Science ®Google Scholar
• R.S. Tsay, Analysis of Financial Time Series, Wiley, New York, 2010.
   Google Scholar
• R.S. Tsay, An Introduction to Analysis of Financial Data with R, Wiley, New York, 2013.
   Google Scholar
• I. Vidal and L.M. Castro, Influential observations in the independent student-t measurement error model with weak nondifferential error, Chil. J. Stat. 1 (2010), pp. 17–34.
   Google Scholar
• F.C. Xie, J.G. Lin, and B.C. Wei, Diagnostics for skew-normal nonlinear regression models with AR(1) errors, Comput. Stat. Data Anal. 53 (2009), pp. 4403–4416.
   Web of Science ®Google Scholar
• F. Zhu, S. Liu, and L. Shi, Local influence analysis for poisson autoregression with an application to stock transaction data, Stat. Neerl. 70 (2016), pp. 4–25.
   Web of Science ®Google Scholar
• F. Zhu, L. Shi, and S. Liu, Influence diagnostics in log-linear integer-valued GARCH models, AStA Adv. Stat. Anal. 99 (2015), pp. 311–335.
   Web of Science ®Google Scholar