Efficient detection of random coefficients in autoregressive models

Optimal tests for random effects in linear mixed models

“…As an alternative to LR-test, Bayesian and permutation test, particularly concerning detecting the randomness in the coefficients of individual effects in longitudinal and clustered data, we present a parametric and non-parametric test locally and asymptotically optimal. Practical examples of a model building using Uniform Local Asymptotic Normality (ULAN) optimal test models can be found in [1,4,10,19] among many others.…”

“…(z j ) . As inAkharif and Hallin (2003), the proof is decomposed into three parts. (a) y 2 → l z,x (y) := R G z,x (η, y)h(η) dη ,with G z,x (η, y) = m j=1 f (z j − x j yη) isabsolutely continuous in a right-neighborhood of y = 0 with a.e.…”

Essays in financial econometrics

“…First, we identify all those state variables (elements of Z t ) that are I (1). Assume that the number of such I(1) variables is n 0 .…”

“…Robinson (1978), Nicholls and Quinn (1980, 1982, Basawa (1993,1998), Koul and Schick (1996) and Schick (1996) have studied the problem of asymptotic inference for these models. Nicholls and Quinn (1982), Ramanathan and Rajarshi (1994), Lee (1998) and Akharif and Hallin (2003) have investigated the issue of testing whether the autoregressive coef-ficients are, indeed, random. Finally, Bera, Higgins and Lee (1992) and Tsay (1987) have proved that the autoregressive conditional heteroskedastic (ARCH) processes may be viewed as autoregressive processes with zero-mean random coefficients, thus establishing a link between two areas of the econometrics literature which, until then, were being studied independently of each other.…”

“…Moreover, the constraints on the model parameters that this sufficient condition implies are not explicit and depend on the sample size. Weiss also established a necessary condition for second-order stationarity of the AR(1)/AR (1) process, which is useful in the sense that its violation ensures that the underlying process is not second-order stable. Tjostheim derived necessary and sufficient conditions for the underline process y t to be asymptotically second order stationary in the case where v t are Gaussian, not allowing for deviations from symmetric and mesokurtic random errors.…”