Influence of Error Structures on Asymptotics for Explosive AR(1) Time Series
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초록
The first order autoregressive (AR(1)) process has been useful for analyzing serially correlated time series data. As a non-stationary time series, we discuss explosive AR(1) model focusing on the error structure generating the model. We have considered various errors such as Gaussian white noise, iid errors, martingale differences and stationary errors. It is noted that asymptotics are heavily influenced by the error structure of the model. The explosive bifurcating AR(1) process is also discussed. Based on the author’s works in the literature, this article reviews the explosive AR(1) process in terms of the error structure, bringing some perspectives to the future topics in this area.
Abstract
The first order autoregressive (AR(1)) process has been useful for analyzing serially correlated time series data. As a non-stationary time series, we discuss explosive AR(1) model focusing on the error structure generating the model. We have considered various errors such as Gaussian white noise, iid errors, martingale differences and stationary errors. It is noted that asymptotics are heavily influenced by the error structure of the model. The explosive bifurcating AR(1) process is also discussed. Based on the author’s works in the literature, this article reviews the explosive AR(1) process in terms of the error structure, bringing some perspectives to the future topics in this area.
참고문헌 (13)
- Fuller WA, "Introduction to statistical time series" (1996), Wiley
- Hall PG, "Martinegale limit theory and its applications" (1980), Academic Press
- Hwang SY, "Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors", Stat Probabil Lett, 83, pp.127~134 (2013)
- Hwang SY, "Generalized least squares estimation for eplosive AR(1) processes with conditionally heteroscedastic errors", Stat Probabil Lett, 77, pp.1439~1448 (2007)
- Hamilton JD, "Time series analysis" (1994), Princeton
- Nicholls DF, "Random coefficient autoregressive models: an introduction", Lecture Notes in Statistics, 11 (1982), Springer
- Hwang SY, "Explosive random coefficient AR(1) processes and related asymptotics for least squares estimation", J Time Ser Anal, 26, pp.807~824 (2005)
- 황선영, "Some characterizations of non-ergodic estimating functions for stochastic processes", Journal of the Korean Statistical Society, 44(4), pp.661~667 (2015), 한국통계학회
- S.Y.Hwang, "Non-stationary quasi-likelihood and asymptotic optimality", Journal of the Korean Statistical Society, 43(3), pp.475~482 (2014), 한국통계학회
- Cowan R, "The bifurcating autoregression model in cell lineage studies", Biometrics, 42, pp.769~783 (1986)
- Hwang SY, "Modeling and large sample estimation for multi-casting autoregression", Stat Probabil Lett, 79, pp.1943~1950 (2009)
- Hwang SY, "An overview on models for tree-indexed time series", Quantitative Bio-Sciences, 30, pp.9~11 (2011)
- 황선영, "Contemporary review on the bifurcating autoregressive models : Overview and perspectives", 한국데이터정보과학회지, 25(5), pp.1137~1149 (2014), 한국데이터정보과학회[DOI]