In many applications, time series exhibit nonstationary behavior that might reasonably be modeled as a time-varying autoregressive (AR) process. In the context of such a model, we discuss the problem of testing for modality of the variance function. We propose a test of modality that is local...

We consider an autoregressive model where the variance is allowed to be a function of time, unconditional on the past. Pötscher (1989) has proven that, regardless of the shape of the variance function, order selection can be made consistently. However, this procedure does not account for the...

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed...

We consider a conditional empirical distribution of the form Fn(C | x)=[summation operator]nt=1 [omega]n(Xt-x) I{Yt[set membership, variant]C} indexed by C[set membership, variant], where {(Xt, Yt), t=1, ..., n} are observations from a strictly stationary and strong...

Multivariate mode hunting is of increasing practical importance. Only a few such methods exist, however, and there usually is a trade-off between practical feasibility and theoretical justification. In this paper we attempt to do both. We propose a method for locating isolated modes (or better,...