Reconciling the Gaussian and Whittle likelihood with an application to estimation in the frequency domain
协调高斯似然与 Whittle 似然：频域估计的应用AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究平稳时间序列、频域似然、谱散度与自回归近似，属于时间序列方法。
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协调高斯似然与 Whittle 似然：频域估计的应用
- 研究问题
- 二阶平稳时间序列的高斯似然与 Whittle 似然为何不同，能否解释这种差异并据此改进频域估计准则？
- 方法与思路
- 作者构造与离散傅里叶变换双正交的变换，得到 Toeplitz 矩阵逆的新分解，再用有限阶自回归参数近似似然差异。
- 材料陈述的贡献
- 摘要称推导了两种似然之间的精确界，将差异联系到遗漏的观测区间外线性预测，并提出两种新的频域拟似然准则。
- 阅读关注点
- 应核对界的成立条件、区间外预测的具体作用、自回归阶数选择，以及新准则逼近谱散度的条件与模拟比较指标。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；更好逼近和有限样本表现是作者陈述，摘要未提供具体条件与数值，不能推断普遍优势。
原文摘要
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-likelihood 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.