$$d r = [\theta(t) - ar]d t + \sigma d W_t.$$
There is a statement in John Hull's book:
The advantage of making $a$ or $\sigma$, or both, functions of time is that the models can be fitted more precisely to the prices of instruments that trade actively in the market.
The disadvantage is that the volatility structure becomes nonstationary. The volatility term structure given by the model in the future is liable to be quite different from that existing in the market today.
$\theta(t)$ can already match the initial curve in the market, what's the meaning of
fitted more precisely to the prices?
$\sigma(t)$ can match today's implied vol of all maturities, it should be better than $\sigma.$ How to understand