Global Conference on Mathematics and Applications (GCMA)

We propose a local linear estimator of the conditional spectral density of a stationary time series with functional covariates and responses missing at random. The estimator uses a tapered local periodogram, correcting diagonal terms with individual inclusion probabilities and off-diagonal terms with joint inclusion probabilities. Under specified assumptions, we establish an almost-complete convergence rate and, under additional conditions, a pointwise central limit theorem. Two simulation studies, each with 500 replications, show lower bias and root mean squared error than individual weighting or an incorrect independence assumption for the observation indicators.