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持久时间序列中随机周期的估计AI 解读

A number of economic, financial, and climatic time series exhibit persistent cycles which are characterized by time-dependence patterns and peaks in the spectrum. In this article, we introduce a class of semiparametric cyclical–memory processes which enable the modeling of random cyclical patterns in stationary and non-stationary time series. We develop a theoretical background and asymptotic estimation theory for the frequency of a cycle represented by the location of a…

线性过程加权和的渐近正态性AI 解读

We establish asymptotic normality of weighted sums of linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and innovations. We also obtain weak convergence of weighted partial sum processes. The results are applicable to linear processes that have short or long memory or exhibit seasonal long memory behavior. In particular, they are…

重新审视 Nelson–Plosser：自相关函数方法AI 解读

We detect a new stylized fact that is common to the dynamics of all macroeconomic series, including financial aggregates. Their Auto-Correlation Functions (ACFs) share a common four-parameter functional form that arises from the dynamics of a general equilibrium model with heterogeneous firms. We find that, not only does our formula fit the data better than the ACFs that arise from auto-regressive and fractionally-integrated models, but it also yields the correct shape of…

两种长期方差估计量：超越短记忆AI 解读

This paper deals with the estimation of the long-run variance of a stationary sequence. We extend the usual Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator to deal with long memory and antipersistence. We then derive asymptotic expansions for this estimator and the memory and autocorrelation consistent (MAC) estimator introduced by Robinson [Robinson, P. M., 2005. Robust covariance matrix estimation: HAC estimates with long…

多元自回归序列中二次型的联合矩母函数AI 解读

Let { X t } follow a discrete Gaussian vector autoregression with deterministic components. We derive the exact finite-sample joint moment generating function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of functionals involving multivariate and univariate Ornstein–Uhlenbeck processes, drifts, and time trends. Such processes arise asymptotically from more general non-Gaussian processes and…

VAR 维度对估计量偏误的影响AI 解读

Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not address questions regarding the influence of the number and nature of the system's variates on parameter estimates. Clearly, both questions will have repercussions on the way VARs are…

协整分析中的两个混合正态密度AI 解读

We derive explicitly the exact density functions of two key mixed normal variates that arise from cointegration analysis. We also plot them, and analyze their analytical features and implications.

多变量自回归序列中二次型的联合矩母函数AI 解读

Let ( X 1 ) be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (m.g.f.) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of interest, including the m.g.f. of functional of multivariate Ornstein-Uhlenbeck processes that arise asymptotically from more general ( X 1 ) processes as well.

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以稳定过程为备择的非平稳性新检验AI 解读

It was recently shown (Abadir, 1993b) that nonstationarity causes the limiting distributions of the Wald ( W ) and Lagrange multiplier ( LM ) statistics to become different from each other. This paper demonstrates that such a divergence between the two distributions can be used as an indicator of the presence of a unit root. A test based on this idea is devised by modifying the normalized autocorrelation coefficient ( NAC ). It is then shown to be an improvement on NAC in…

单位根下自相关系数的极限分布AI 解读

The limiting distribution of the normalized autocorrelation coefficient in the case of a unit root is given in a closed form. It is found that high order transcendental functions such as the parabolic cylinder functions are indispensable to express this distribution, thus departing from the simple standard normal distribution that arises in the case of a stable root. Using the formulae derived in this paper, some numerical results available from previous studies are then…

单位根检验的渐近功效AI 解读

Closed forms for the distribution of some conventional statistics are given as a prelude to deriving their asymptotic power functions as unit root tests. In the process, an important distinction is drawn between two classes of statistics: one which relies on deterministic normalizations and the other which uses stochastic normalizations. When the data follow a driftless autoregression, a t test (which belongs to the second class) for a unit root is found to perform better…

非平稳自回归中的 OLS 偏差AI 解读

An analytical formula is derived to approximate the finite sample bias of the ordinary least-squares (OLS) estimator of the autoregressive parameter when the underlying process has a unit root. It is found that the bias is expressible in terms of parabolic cylinder functions which are easy to compute. Numerical evaluation of the formula reveals that the approximation is very accurate. The derived formula inspires a heuristic approximation, obtained by leastsquares fitting of…