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白噪声中的单位根AI 解读

We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T )/ p → 0 and p 3 / T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p , we…

具有随机波动的贝叶斯向量自回归AI 解读

This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate. Exact updating formulas are given to the nonlinear filtering of the precision matrix. Estimation of the autoregressive parameters requires numerical methods: an importance-sampling-based approach is explained here.

宏观经济学家应了解的单位根问题：贝叶斯视角AI 解读

This paper summarizes recent Bayesian research on unit roots for the applied macroeconomist in the way Campbell and Perron [8] summarized the classical unit roots perspective. The appropriate choice of a prior is discussed. In recognizing a consensus distaste for explosive roots, I find the popular Normal-Wishart priors centered at the unit root to be reasonable provided they are modified by concentrating the prior mass for the time trend coefficient toward zero as the…

使用精确似然函数时的 Jeffreys 先验AI 解读

In this paper, we calculate Jeffreys prior for an AR(1) process with and without a constant and a time trend when using the exact likelihood function. We show how this prior can be calculated for the explosive region, even though the unconditional variance of the process is infinite. The calculations lend additional support to the Schotman-van Dijk [6] procedure for restricting the location and the variance of the time trend coefficient. The results show that flat priors are…

理解单位根研究者：鸟瞰式导览AI 解读

For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient conditional on the estimate coexists with an asymmetric distribution for the estimate conditional on the coefficient. Prior densities implicit in treating classical significance levels…