On Sign Tests in ARMA Models with Possibly Infinite Error Variance

Sign tests for long-memory time series

“…We also consider testing composite hypothesis on the long-memory parameter for general ARFIMA(p, d, q) models, which yields, as a particular case, tests for the composite unit root hypothesis in the direction of long-memory alternatives. The basic result is a uniform approximation for the score statistic based on the sign of residuals, extending to long-range-dependent data results of Boldin (1996) and Boldin and Stute (2000) for weakly dependent processes.…”

“…We consider now the problem of hypothesis testing on parameters of general ARFIMA models extending Boldin and Stute's (2000) treatment for ARMA processes. Consider the ARFIMA (p, d, q) …”

“…Also one side tests can be set, such as whether the processes is trending nonstationary (d = O.S) against stationarity (d <O.S). For other composite hypotheses concerning ARMA parameters, see Boldin and Stute (2000).…”

“…is dealt with as in Proposition 2 and as in Boldin and Stute (2000), respectively. The contribution of (11) is the joint contribution of the locally in the memory parameter and the ARMA parameters, and is of smaller order as we now argue.…”

“…Sign-based inference on the parameters of an autoregressive process have been developed by Boldin (1995Boldin ( , 1996 and Boldin and Tyurin (1994), the ARMA case has been studied by Boldin and Stute (2000). Chapters 6 and 7 of the mentioned monograph by Boldin et al (1997) discuss sign-based inference on the parameter of the AR(I) process in stationary, instable and explosive situations.…”