论文标题
与频域中的估计应用相结合
Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain
论文作者
论文摘要
在时间序列分析中，时间和频域方法之间存在明显的二分法。本文的目的是在频率和时域方法之间绘制连接。我们的重点将是调和高斯的可能性和值得。我们得出了二阶固定时间序列的高斯和晶体可能性之间的确切，可解释的束缚。该推导基于获得与时间序列离散的傅立叶变换为生物构成的转换。这样的转换为toeplitz矩阵的倒数产生了新的分解，并实现了频域内高斯可能性的表示。我们表明，高斯和惠特的可能性之间的差异是由于省略了与晶体可能性相关的期刊图中观察域之外的最佳线性预测。基于此结果，我们从最佳的拟合，有限的订单自回归参数方面获得了高斯和惠特可能性之间差异的近似值。这些近似值用于定义两个新的频域准可能性标准。我们表明，与高斯和惠特的可能性相比，这些新标准可以更好地近似光谱差异标准。在模拟中，我们表明所提出的估计器具有令人满意的有限样品特性。
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.
