Reconciling the Gaussian and Whittle likelihood with an application to estimation in the frequency domain
Reconciling the Gaussian and Whittle likelihood with an application to estimation in the frequency domain
复制标题
协调高斯似然和惠特尔似然与频域估计的应用
作者：
S. Rao;Junho Yang
在时间序列分析中，时域方法和频域方法之间存在明显的二分法。本文的目的是建立频域方法和时域方法之间的联系。我们的重点是协调高斯似然和惠特尔似然。我们推导出二阶平稳时间序列的高斯似然和惠特尔似然之间的精确的、可解释的界限。该推导基于获得与时间序列的离散傅立叶变换双正交的变换。这种变换产生托普利茨矩阵的逆矩阵的新分解，并能够在频域内表示高斯似然。我们表明，高斯似然和惠特尔似然之间的差异是由于在与惠特尔似然相关的周期图中遗漏了观察域之外的最佳线性预测。基于此结果，我们根据最佳拟合、有限阶自回归参数获得高斯似然和惠特尔似然之间差异的近似值。这些近似用于定义两个新的频域准似然标准。我们证明，与高斯似然和惠特尔似然相比，这些新准则可以产生更好的谱散度准则近似值。在模拟中，我们表明所提出的估计量具有令人满意的有限样本属性。
In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussian likelihood and the Whittle likelihood. We derive an exact, interpretable, bound between the Gaussian and Whittle likelihood of a second order stationary time series. The derivation is based on obtaining the transformation which is biorthogonal to the discrete Fourier transform of the time series. Such a transformation yields a new decomposition for the inverse of a Toeplitz matrix and enables the representation of the Gaussian likelihood within the frequency domain. We show that the difference between the Gaussian and Whittle likelihood is due to the omission of the best linear predictions outside the domain of observation in the periodogram associated with the Whittle likelihood. Based on this result, we obtain an approximation for the difference between the Gaussian and Whittle likelihoods in terms of the best fitting, finite order autoregressive parameters. These approximations are used to define two new frequency domain quasi-likelihoods criteria. We show that these new criteria can yield a better approximation of the spectral divergence criterion, as compared to both the Gaussian and Whittle likelihoods. In simulations, we show that the proposed estimators have satisfactory finite sample properties.
影响因子：
2.7
作者：
A. Sykulski;S. Olhede;Arthur Guillaumin;J. Lilly;J. Early
通讯作者：
A. Sykulski;S. Olhede;Arthur Guillaumin;J. Lilly;J. Early
影响因子：
4.4
作者：
Kirch, Claudia;Edwards, Matthew C.;Meyer, Renate
通讯作者：
Meyer, Renate