We consider statistical inference of trends in mean non-stationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct...

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...