  We propose a panel ARMA-GARCH model to capture the dynamics of large panel
data with $N$ individuals over $T$ time periods. For this model, we provide a
two-step estimation procedure to estimate the ARMA parameters and GARCH
parameters stepwisely. Under some regular conditions, we show that all of the
proposed estimators are asymptotically normal with the convergence rate
$(NT)^{-1/2}$, and they have the asymptotic biases when both $N$ and $T$
diverge to infinity at the same rate. Particularly, we find that the asymptotic
biases result from the fixed effect, estimation effect, and unobservable
initial values. To correct the biases, we further propose the bias-corrected
version of estimators by using either the analytical asymptotics or jackknife
method. Our asymptotic results are based on a new central limit theorem for the
linear-quadratic form in the martingale difference sequence, when the weight
matrix is uniformly bounded in row and column. Simulations and one real example
are given to demonstrate the usefulness of our panel ARMA-GARCH model.
