  Autocovariance of the error term in a time series model plays a key role in
the estimation and inference for the model that it belongs to. Typically, some
arbitrary parametric structure is assumed upon the error to simplify the
estimation, which inevitably introduces potential model-misspecification. We
thus conduct nonparametric estimation of it. To avoid the difficult bandwidth
selection issue under the traditional nonparametric truncation approach, this
paper conducts the Bayesian estimation of its spectral density in a frequency
domain. To this end, we consider two cases: fixed error variance and
time-varying one. Each approach is taken to estimate the spectral density of
the autocovariance and the model parameters. The methodology is applied to
exchange rate forecasting and proves to compete favorably against some
benchmark models, including the random walk without drift.
