On the use of 2-test to check serial independence
format: Article | STATISTICA & APPLICAZIONI - 2010 - 1
In this paper two tests of serial independence are proposed. The building block of these procedures is the definition of a component 2-test for testing independence between pairs of lagged variables. With reference to different component 2-tests, it is shown that the corresponding test statistics are independent. Taking advantage of this result, the component tests are used from both a simultaneous and a direct viewpoint to define two different test procedures denoted by SIS (Serial Independence Simultaneous) and SICS (Serial Independence Chi-Square). Simulations are used to explore the performance of these tests in terms of size and power. Our results underline that both the proposals are powerful against various types of alternatives. It is also shown, through what we call Lag Subsets Dependence Plot (LSDP), how to detect possible lag(s)-dependences graphically. Some examples are finally provided in order to evaluate the effectiveness of the LSDP. Keywords: Nonlinear Time Series, Serial Independence, Simultaneous Tests, 2-test.
Nonparametric ARCH with additive mean and multiplicative volatility: a new estimation procedure
format: Article | STATISTICA & APPLICAZIONI - 2009 - 1
Motivated by the misspecification problem in time series analysis, the nonparametric approach has quickly developed in the latest years. First models in literature were focused on the estimation of the conditional mean. It is well known that alongside the conditional mean it is important to study the series volatility (conditional variance). The following paper deals with nonparametric autoregression with multiplicative volatility and additive mean as studied by Yang et al. (1999). A new estimation procedure is here provided. The procedure uses the residual-based estimator, backfitting algorithm and the local polynomial estimation. Some applications with simulated and real data will be presented.