An extensive literature in econometrics focuses on finding the exact and approximate first and second moments of the least-squares estimator in the stable first-order linear autoregressive model with normally distributed errors. Recently, Kiviet and Phillips (2005) developed approximate moments...

It is well documented in the literature that the sample skewness and excess kurtosis can be severely biased in finite samples. In this paper, we derive analytical results for their finite-sample biases up to the second order. In general, the bias results depend on the cumulants (up to the sixth...

The sample average is an unbiased estimator of the population mean, so it may seem innocuous that for estimating model parameters that do not involve the population mean, the data can be demeaned first. Using a first-order moving average (MA) model for example, we derive the analytical...

The quasi-maximum likelihood estimator (QMLE) of parameters in the first-order moving average model can be biased in finite samples. We develop the second-order analytical bias of the QMLE and investigate whether this estimation bias can lead to biased feasible optimal forecasts conditional on...

We derive a neat and compact representation of the asymptotic Fisher information matrix of a vector ARMA process. Its inverse can be used immediately as the asymptotic covariance matrix of the Gaussian maximum likelihood estimator. We also provide the robust sandwich covariance estimator when...

Spatial econometric analyses abound in spatial sciences such as regional and urban economics, geography, and planning. Although the origins of spatial econometrics can be largely traced back to the disciplines of economics and geography, the field of application has by now stretched out as far...

I derive the finite-sample bias of the conditional Gaussian maximum likelihood estimator in ARMA models when the error follows some unknown nonnormal distribution. The general procedure relies on writing down the score function and its higher-order derivative matrices in terms of quadratic forms...

A compact analytical representation of the asymptotic covariance matrix, in terms of model parameters directly, of the quasi maximum likelihood estimator (QMLE) is derived in ARMA models with possible non-zero means and non-Gaussian error terms. For model parameters excluding the error variance,...

We investigate predictive abilities of nonlinear models for stock returns when density forecasts are evaluated and compared instead of the conditional mean point forecasts. The aim of this paper is to show whether the in-sample evidence of strong nonlinearity in mean may be exploited for...

We develop the analytical second-order bias and variance of the estimated Sharpe ratio when the return series is not IID. We show that the bias and variance formulae depend upon the covariance structure of the data generating process