The paper concerns testing long memory for fractionally integrated nonlinear processes. We show that the exact local asymptotic power is of order O[(logn)-1] for four popular nonparametric tests and is O(m-1/2), where m is the bandwidth which is allowed to grow as fast as n[kappa], [kappa][set...

Covariances play a fundamental role in the theory of stationary processes and they can naturally be estimated by sample covariances. There is a well-developed asymptotic theory for sample covariances of linear processes. For nonlinear processes, however, many important problems on their...

The paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models. Using a Gaussian approximation result for non-stationary multiple time series, we show that the constructed simultaneous confidence tubes have asymptotically...

We consider nonparametric estimation of the regression function g(*) in a nonlinear regression model Y_t = g(X_t) o(X_t)e_t, where the regressor X_t is a nonstationary unit root process and the error e_t is s sequence of independent and identically distributed (i.i.d.) random variables. With proper...

We show that the call-put implied volatility spread (IVS) outperforms many well-known predictors of the U.S. equity premium at return horizons up to six months over the period from 1996:1 to 2017:12. The predictive ability of the IVS is unrelated to the dividend yield and is useful in explaining...