Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence
Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence
复制标题
具有长程相关性的时间序列回归中的半参数估计
DOI：
10.1111/j.1467-9892.2005.00401.x
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发表时间：
2005
影响因子：
0.9
通讯作者：
M. Nielsen
中科院分区：
文献类型：
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作者：
M. Nielsen
抽象的。 我们考虑在误差和随机回归量都存在长期依赖性的情况下，时间序列回归中的半参数估计。针对一类半参数频域加权最小二乘估计建立了中心极限定理，其中包括窄带普通最小二乘和窄带广义最小二乘作为特例。这些估计是半参数的，因为焦点集中在原点附近，并且仅使用原点周围退化带中的周期图坐标。这种设置不同于早期关于具有长程依赖性的时间序列回归的研究，其中采用了完全参数化的方法。当远程依赖性程度未知并且必须在初始步骤中进行估计时，广义最小二乘估计是不可行的。在这种情况下，我们证明存在与不可行估计具有相同渐近性质的可行估计。通过蒙特卡罗模拟，我们评估了广义最小二乘估计和可行估计的有限样本性能。
Abstract. We consider semiparametric estimation in time‐series regression in the presence of long‐range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain‐weighted least squares estimates, which includes both narrow‐band ordinary least squares and narrow‐band generalized least squares as special cases. The estimates are semiparametric in the sense that focus is on the neighbourhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier studies on time‐series regression with long‐range dependence, where a fully parametric approach has been employed. The generalized least squares estimate is infeasible when the degree of long‐range dependence is unknown and must be estimated in an initial step. In that case, we show that a feasible estimate which has the same asymptotic properties as the infeasible estimate, exists. By Monte Carlo simulation, we evaluate the finite‐sample performance of the generalized least squares estimate and the feasible estimate.