论文检索

时间序列分析在天文学和气象学中的应用AI 解读

Part 1 Time series - theory and methodology: A short history of time series, M.B. Priestley Frequency estimation, E.J. Hannan et al Asymptotic expansion of estimators for diffusions with small noises, N. Yoshida Spatial-temporal spectral analysis with random sampling, I-Shang Chow, Ken-Shin Lii Detection of periodicities, M.B. Priestley Spectral and multivariate probability density estimation of continuous time stationary processes from randomly sampled data, Elias Masry…

摘要暂缺

双变量非平稳过程的分析AI 解读

Summary In this paper, we propose a general definition of the evolutionary (time-dependent) cross-spectrum between two non-stationary processes and describe its physical interpretation. We also study the estimation of the evolutionary cross-spectrum at each time instant t from a single realization of a bivariate process. Further, we propose a definition (and a method of estimation) for the coherency (spectrum) between the two components of the bivariate process and show that…

非参数函数拟合AI 解读

Summary In this note we consider the problem of fitting a general functional relationship between two variables. We require only that the function to be fitted is, in some sense, “smooth”, and do not assume that it has a known mathematical form involving only a finite number of unknown parameters.

非平稳信号的滤波AI 解读

Summary We observe a record consisting of a “signal” plus “noise” up to the time instant t, and wish to extract the value of the signal at the time instant (t + m) by means of a linear filter. Here, m may be positive (corresponding to “prediction”) or negative (corresponding to “smoothing”). In this paper we consider the case where both the signal and noise processes are non-stationary and possess evolutionary spectral representations. Using this approach we obtain a close…

时间序列非平稳性的检验AI 解读

Summary We consider the problem of testing a given time-series for stationarity. The approach is based on evolutionary spectral analysis, and the proposed method consists essentially in testing the “homogeneity” of a set of evolutionary spectra evaluated at different instants of time. Using a logarithmic transformation, we show that the mechanics of the test are formally equivalent to a two-factor analysis of variance procedure when the residual variance is known, a priori.…

非平稳过程的预测AI 解读

Summary We consider the problem of linear least-squares prediction for a class of non-stationary processes which possess “evolutionary spectral representations”. It is shown that, under certain conditions, such processes admit moving-average representations in terms of time-dependent coefficients. This feature enables us to develop a close analogue of the Wiener–Kolmogorov approach to the corresponding problem for stationary processes.

非平稳过程谱估计的设计关系AI 解读

Summary Further developments in the theory of evolutionary spectra are discussed, and some asymptotic results are derived in the sampling theory of spectral estimates. Various forms of “design” criteria for spectral estimation are constructed in terms of resolvability conditions, and it is shown that by introducing the concepts of “frequency-domain” and “time-domain” bandwidths, estimates may be obtained which satisfy the required conditions.

演化谱与非平稳过程AI 解读

Summary We develop an approach to the spectral analysis of non-stationary processes which is based on the concept of “evolutionary spectra”; that is, spectral functions which are time dependent, and have a physical interpretation as local energy distributions over frequency. It is shown that the notion of evolutionary spectra generalizes the usual definition of spectra for stationary processes, and that, under certain conditions, the evolutionary spectrum at each instant of…

摘要暂缺

存在谐波分量时的谱密度函数估计AI 解读

Summary Consider a stationary process of the form Xt = Yt + Zt, where Yt is a linear process with a continuous spectrum, and Zt is a finite sum of harmonic components. We discuss two methods of estimating the spectral density function of Yt. In one method we first estimate the autocovariance function of Yt by “correcting” the sample autocovariance function of Xt, and then form the usual “smoothed” Fourier transform. In the other approach, we estimate the spectral density…

摘要暂缺

混合谱平稳过程分析（二）AI 解读

SUMMARY We investigate the asymptotic power functions of three types of tests for detecting the presence of harmonic components superimposed on a nonuniform spectral density function. These power functions are tabulated for a range of values of the signal to noise ratio of the process, and each test is applied to several artificial series of the “mixed ”type with known structure.

混合谱平稳过程的分析（一）AI 解读

SUMMARY We consider a normal stationary process whose spectrum may contain harmonic components superimposed on a non-uniform continuous spectral density function. The problem of separating the discrete and continuous spectral components is discussed, and it is shown that the bandwidth of the spectral density function must be restricted, in relation to the number of observations, in order to make the problem tractable. Assuming only that this bandwidth is known, the presence…

时间序列的谱分析AI 解读

Summary (i) A review has been made of spectral analysis and its relation with other branches of time-series analysis. A detailed account has been given of the methods available for estimating the spectral density, the band spectrum and the integrated spectrum; suggestions have also been made for confidence intervals for the latter two estimators. (ii) Emphasis has been laid throughout upon the difficulties which are met in practice and gaps in the theoretical structure have…