The Northern Hemisphere mean surface temperature has shown a significant positive trend over the past two centuries. On the basis of the well-known reconstructions of global climate from proxy data, the conclusion is made that the current warming has been unprecedented during at least the past two millennia. On the other hand, it was demonstrated in [6] that the existing statistical models strongly underestimate the low-frequency variability of global annual mean temperature, thus making the conclusion drawn above questionable. At present, the results of [6] are interpreted as evidence that the Mann reconstruction is invalid [1]. To our knowledge, however, it is too early to draw such conclusions. What is the cause of smoothing low-frequency variability? To what extent are various statistical models used for paleoclimate reconstruction that is subject to this effect? To answer these questions, numerical experiments are performed with data sets of annual mean surface temperature over the past millennium that are simulated with the ECHO-G coupled ocean-atmosphere general circulation model.