Sensitivity analysis of error-contaminated time series data under autoregressive models with the application of COVID-19 data. (English) Zbl 07716694
Summary: Autoregressive (AR) models are useful in time series analysis. Inferences under such models are distorted in the presence of measurement error, a common feature in applications. In this article, we establish analytical results for quantifying the biases of the parameter estimation in AR models if the measurement error effects are neglected. We consider two measurement error models to describe different data contamination scenarios. We propose an estimating equation approach to estimate the AR model parameters with measurement error effects accounted for. We further discuss forecasting using the proposed method. Our work is inspired by COVID-19 data, which are error-contaminated due to multiple reasons including those related to asymptomatic cases and varying incubation periods. We implement the proposed method by conducting sensitivity analyses and forecasting the fatality rate of COVID-19 over time for the four most populated provinces in Canada. The results suggest that incorporating or not incorporating measurement error effects may yield rather different results for parameter estimation and forecasting.
MSC:
| 62-XX | Statistics |
Keywords:
autoregressive model; COVID-19; forecasting; measurement error; sensitivity analysis; time seriesSoftware:
itsmrReferences:
| [1] | Baud, D.; Qi, X.; Nielsen-Saines, K.; Musso, D.; Pomar, L.; Favre, G., Real estimates of mortality following covid-19 infection, Lancet Infect. Dis., 20, 773 (2020) |
| [2] | Box, G. E.; Jenkins, G. M.; Reinsel, G. C.; Ljung, G. M., Time Series Analysis: Forecasting and Control (2015), John Wiley & Sons: John Wiley & Sons, Hoboken, NJ |
| [3] | Brockwell, P. J.; Davis, R. A., Introduction to Time Series and Forecasting (2002), Springer-Verlag: Springer-Verlag, New York · Zbl 0994.62085 |
| [4] | Chanda, K. C., Asymptotic properties of estimators for autoregressive models with errors in variables, Ann. Stat., 24, 423-430 (1996) · Zbl 0853.62070 |
| [5] | Cheung, Y.-W.; Lai, K. S., Lag order and critical values of the augmented dickey-fuller test, J. Bus. Econ. Stat., 13, 277-280 (1995) |
| [6] | Day, M., COVID-19: Four fifths of cases are asymptomatic, China figures indicate, BMJ, 369, m1315 (2020) |
| [7] | Dedecker, J.; Samson, A.; Taupin, M.-L., Estimation in autoregressive model with measurement error, ESAIM Probab. Stat., 18, 277-307 (2014) · Zbl 1307.62171 |
| [8] | Dong, E.; Du, H.; Gardner, L., An interactive web-based dashboard to track COVID-19 in real time, Lancet Infect. Dis., 20, 533-534 (2020) |
| [9] | Granger, C. W.J.; Morris, M. J., Time series modelling and interpretation, J. R. Stat. Soc. Ser. A, 139, 246-257 (1976) |
| [10] | He, W.; Yi, G. Y.; Zhu, Y., Estimation of the basic reproduction number, average incubation time, asymptomatic infection rate, and case fatality rate for COVID-19: Meta-analysis and sensitivity analysis, J. Med. Virol., 92, 2543-2550 (2020) |
| [11] | Hurvich, C. M.; Tsai, C. -L., Regression and time series model selection in small samples, Biometrika, 76, 297-307 (1989) · Zbl 0669.62085 |
| [12] | Kanchan, T., Kumar, N., and Unnikrishnan, B, Mortality: Statistics, in Encyclopedia of Forensic and Legal Medicine, J. Payne-James and R.W. Byard, eds., 2nd ed., Elsevier, Oxford, 2015, pp. 572-577. |
| [13] | Kimball, A., Asymptomatic and presymptomatic SARS-CoV-2 infections in residents of a long-term care skilled nursing facility-King County, Washington, March 2020, Morb. Mortal. Wkly Rep., 69, 377-381 (2020) |
| [14] | Lahiri, S. N., Theoretical comparisons of block bootstrap methods, Ann. Stat., 27, 386-404 (1999) · Zbl 0945.62049 |
| [15] | Nagata, S., Edgeworth approximation of a finite sample distribution for an AR(1) model with measurement error, Open. J. Stat., 2, 383-388 (2012) |
| [16] | Pagano, M., Estimation of models of autoregressive signal plus white noise, Ann. Stat., 2, 99-108 (1974) · Zbl 0317.62059 |
| [17] | Staudenmayer, J.; Buonaccorsi, J. P., Measurement error in linear autoregressive models, J. Am. Stat. Assoc., 100, 841-852 (2005) · Zbl 1117.62430 |
| [18] | Tanaka, K., A unified approach to the measurement error problem in time series models, Econ. Theory, 18, 278-296 (2002) · Zbl 1109.62352 |
| [19] | Tripodis, Y.; Buonaccorsi, J. P., Prediction and forecasting in linear models with measurement error, J. Statist. Plann. Inference, 139, 4039-4050 (2009) · Zbl 1183.62161 |
| [20] | Yi, G. Y., Statistical Analysis With Measurement Error or Misclassification: Strategy, Method and Application (2017), Springer: Springer, New York · Zbl 1377.62012 |
| [21] | Zhang, Q. and Yi, G.Y, Sensitivity analysis of error-contaminated time series data under autoregressive models with application of covid-19 data, preprint (2020). Available at arXiv:2008.05649, |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
