A new class of asymmetric exponential power densities with applications to economics and finance
A new class of asymmetric exponential power densities with applications to economics and finance
复制标题
新型非对称指数功率密度及其在经济和金融领域的应用
DOI：
10.1093/icc/dtr036
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发表时间：
2011
影响因子：
2.5
通讯作者：
A. Secchi
中科院分区：
文献类型：
--
作者：
G. Bottazzi;A. Secchi
我们引入了一个新的 5 美元参数分布族，即非对称指数幂 (AEP)，它能够应对不对称性和尖峰态，同时允许从非正态到正态的连续变化。我们证明了 AEP 参数的最大似然（ML）估计在整个参数空间上是一致的，并且当考虑足够大的形状参数值时，它们也是渐近有效和正态的。我们推导了 AEP 的 Fisher 信息矩阵，并证明它也可以连续扩展到小形状参数的区域。通过数值模拟，我们发现此扩展可用于获取与 ML 估计相关的误差的可靠值，也适用于相对较小规模的样本（100 美元的观测值）。此外，我们表明，在这个样本量附近，与 ML 估计相关的偏差虽然存在，但可以忽略不计。最后，我们使用来自经济和金融的不同数据进行了一些实证研究，将 AEP 的性能与其他常用的分布系列进行比较。
We introduce a new $5$-parameter family of distributions, the Asymmetric Exponential Power (AEP), able to cope with asymmetries and leptokurtosis and, at the same time, allowing for a continuous variation from non-normality to normality. We prove that the Maximum Likelihood (ML) estimates of the AEP parameters are consistent on the whole parameter space, and when sufficiently large values of the shape parameters are considered, they are also asymptotically efficient and normal. We derive the Fisher information matrix for the AEP and we show that it can be continuously extended also to the region of small shape parameters. Through numerical simulations, we find that this extension can be used to obtain a reliable value for the errors associated to ML estimates also for samples of relatively small size ($100$ observations). Moreover we show that around this sample size, the bias associated with ML estimates, although present, becomes negligible. Finally, we present a few empirical investigations, using diverse data from economics and finance, to compare the performance of AEP with respect to other, commonly used, families of distributions.