Testing parametric assumptions of trends of a nonstationary time series

Abstract

SUMMARYThe paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series.

Testing for Parallelism Among Trends in Multiple Time Series

“…The points of , suitably rescaled by , become increasingly dense in as . By the local stationarity (14), the process can be approximated by the stationary process in the sense that (24) Denote by the sample auto-covariance of at lag and average these quantities over to estimate the autocovariance (16) by (25) Then, can be simply estimated by (26) for some truncation parameter with bandwidth and . Indeed, will be close to zero for large and for all under the local stationarity condition (14) and the short-range dependence assumption (19).…”

Testing additive assumptions on means of regular monitoring data: a multivariate nonstationary time series approach

“…Unlike data-driven bandwidth selectors, this does not introduce an extra amount of randomness into the testing procedure; the asymptotic results developed in Sections 3.1−3.3 remain unharmed and theoretically rigorous tests are feasible. In addition, it produces practically reasonable bandwidths for nonparametric hypothesis testing problems, as suggested by Zhang and Wu (2011).…”

“…Condition (A2) can be interpreted as the stochastically Lipschitz continuous condition, under which the underlying data generating mechanism evolve smoothly over time; see Zhang and Wu (2011) for more discussion.…”

Semiparametric model building for regression models with time-varying parameters

“…1. Wu and Zhao (2007) assumed that the error process is stationary and accepted the quadratic trend without considering any explanatory variable; see Zhang and Wu (2011) for a test with nonstationary errors. A rigorous generalization of their tests to partially time-varying coefficient models is left as a possible topic for future research.…”

“…trend function contaminated by random errors. This special case is useful in studying mean nonstationary processes, and has been extensively used in nonparametric trend estimation and testing problems; see for example Johnstone and Silverman (1997), Wu and Zhao (2007), Zhang and Wu (2011) and references therein. As another important example, let x i = (y i−1 , .…”