  We produce new reconstructions of Northern Hemisphere annually averaged
temperature anomalies back to 1000 AD, and explore the effects of including
external climate forcings within the reconstruction and of accounting for
short-memory and long-memory features. Our reconstructions are based on two
linear models, with the first linking the latent temperature series to three
main external forcings (solar irradiance, greenhouse gas concentration and
volcanism), and the second linking the observed temperature proxy data (tree
rings, sediment record, ice cores, etc.) to the unobserved temperature series.
Uncertainty is captured with additive noise, and a rigorous statistical
investigation of the correlation structure in the regression errors is
conducted through systematic comparisons between reconstructions that assume no
memory, short-memory autoregressive models, and long-memory fractional Gaussian
noise models. We use Bayesian estimation to fit the model parameters and to
perform separate reconstructions of land-only and combined land-and-marine
temperature anomalies. For model formulations that include forcings, both
exploratory and Bayesian data analysis provide evidence against models with no
memory. Model assessments indicate that models with no memory underestimate
uncertainty. However, no single line of evidence is sufficient to favor
short-memory models over long-memory ones, or to favor the opposite choice.
When forcings are not included, the long-memory models appear to be necessary.
While including external climate forcings substantially improves the
reconstruction, accurate reconstructions that exclude these forcings are vital
for testing the fidelity of climate models used for future projections.
