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欠拟合回归与时间序列模型中修正 AIC 的偏差AI 解读

The Akaike Information Criterion, AIC (Akaike, 1973), and a bias-corrected version, AICC(Sugiura, 1978; Hurvich & Tsai, 1989) are two methods for selection of regression and autoregressive models. Both criteria may be viewed as estimators of the expected Kullback-Leibler information. The bias of AIC and AICC is studied in the underfitting case, where none of the candidate models includes the true model (Shibata, 1980, 1981; Parzen, 1978). Both normal linear regression and…

频率估计的一种快速高效方法AI 解读

A technique is presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is based on fitting ARMA (2, 2) models iteratively, in a special way. The estimator is shown to be strongly consistent and as efficient as the least squares estimator of the frequency, or the periodogram maximizer. A simple accelerated version of the technique is shown to converge in a small number of iterations, the number depending on the accuracy of the…

季节差分的若干拉格朗日乘子检验AI 解读

Determining whether a time series has a unit root is an important problem in many time series analyses. For seasonal time series the problem is more complicated as one has to decide whether both regular and seasonal differencing or just one of them would suffice to transform a series into stationarity. This important problem is addressed via the Lagrange multiplier test approach. The large sample representations of the test statistics in terms of integrals of Wiener…

若干时间序列 Markov 回归模型的适合性检验AI 解读

The asymptotic distribution of residual autocorrelations and a score statistic are derived for checking model adequacy for some Markov regression models for time series. These models are natural extensions of the popular generalized linear models to time series data. The score statistic appears to be somewhat easier to use in practice. Some empirical results are also obtained for the score statistic in some simple cases. A real example is given.

周期函数的频率估计AI 解读

The problem of estimating the frequency and other parameters of a cyclical oscillation is considered, where the data consists of a periodic function observed subject to stationary additive noise. An estimation procedure is proposed and the asymptotic properties of the estimators established. Tests for unknown frequencies to be harmonics of a fundamental frequency are also developed and their asymptotic properties investigated. The procedures are applied to observations on…

识别时间序列中过度影响结果的观测AI 解读

The purpose of this paper is to develop a tool for identifying over-influential observations in time series when they are viewed in the time domain. We present a method for obtaining various measures of influence for the autocorrelation function, as well as thresholds for declaring an observation over-influential. An example of the use of these thresholds is also presented.

季节性时间序列中周期自相关的检验AI 解读

This paper presents statistical procedures for deciding if periodicities exist in the autocorrelation function of a seasonal time series after removal of seasonal means and standard deviations. The procedures are based on asymptotic properties of a Fourier-transformed version of the estimated periodic autocorrelation function. Analyses of simulated and actual data sets illustrate the usefulness of the proposed methods.

基于曲线长度的拟合优度检验AI 解读

The length of the graph of an estimate of the distribution function is used as a measure of goodness of fit. The asymptotic theory of tests which are based on such a measure is studied and, in addition, tables of critical values for these tests are given. In the context of time series analysis, the proposed test rejects the null hypothesis of white noise whenever the length of the linearly interpolated cumulative periodogram, or of some smoothed version of it, is too large.

阈值自回归检验AI 解读

We consider the problem of determining whether a threshold autoregressive model fits a stationary time series significantly better than an autoregressive model does. A test statistic $\lambda$ which is equivalent to the (conditional) likelihood ratio test statistic when the noise is normally distributed is proposed. Essentially, $\lambda$ is the normalized reduction in sum of squares due to the piecewise linearity of the autoregressive function. It is shown that, under…

未知分布下变点的渐近有效估计AI 解读

Suppose $X_1,\cdots, X_n$ are distributed according to a probability measure under which $X_1,\cdots, X_n$ are independent, $X_1 \sim F_0$, for $i = 1,\cdots, \lbrack\theta_n n\rbrack$ and $X_i \sim F^{(n)}$ for $i = \lbrack\theta_nn\rbrack + 1, \cdots, n$ where $\lbrack x\rbrack$ denotes the integer part of $x$. In this paper we consider the asymptotic efficient estimation of $\theta_n$ when the distributions are not known. Our estimator is efficient in the sense that if $F^{(n)} = F_{\eta_n}, \eta_n \rightarrow 0$…

非高斯线性过程的最大标准化累积量反卷积AI 解读

A linear process is represented as a driving white noise convolved with a system response sequence. The concept of natural peakedness of a system response sequence is defined and its properties are investigated. Utilizing natural peakedness, the convergence theory of maximum standardized cumulant deconvolution is established and the uniqueness theorem of non-Gaussian linear process representations is proved. In addition, autoregressive models on a countable abelian group are…

基于 Hannan–Rissanen 方法的非平稳 ARMAX 模型估计AI 解读

We consider in this paper the estimation problems for both orders and coefficients of linear feedback control systems, described by ARMAX models. The estimation algorithms are inspired by the Hannan-Rissanen method used for the estimation of stationary ARMA models, while the convergence analyses are based on limit theorems for both double array martingales and nonnegative supermartingales, and on techniques of stochastic Lyapunov functions. Traditionally used assumptions,…

无限方差近单位根时间序列的统计推断AI 解读

An autoregressive time series is said to be near-integrated (nearly nonstationary) if some of its characteristic roots are close to the unit circle. Statistical inference for the least squares estimators of near-integrated AR(1) models has been under rigorous study recently both in the statistics and econometric literatures. Although classical asymptotics are no longer available, through the study of weak convergence of stochastic processes, one can establish the asymptotic…

自回归谱估计量的偏差AI 解读

Bias of the least squares estimator of the log of the spectral density of an autoregression attenuates the peaks of the estimator. Under the assumption of an autoregressive generating process of known finite order, we obtain an expression for the order 1/T bias, where T is the sample length of the observed series. This approximation is a sum of several simple functions of the unknown coefficients. When the spectral density has sharp peaks, one of these functions dominates…

自回归谱估计量的偏差AI 解读

Bias of the least squares estimator of the log of the spectral density of an autoregression attenuates the peaks of the estimator. Under the assumption of an autoregressive generating process of known finite order, we obtain an expression for the order 1/T bias, where T is the sample length of the observed series. This approximation is a sum of several simple functions of the unknown coefficients. When the spectral density has sharp peaks, one of these functions dominates…

时间序列存在时相关积分行为的一则注记AI 解读

The behaviour of the correlation integral is well known when applied to simple chaotic regimes and to pure random noise. The asymptotic behaviour of a chaotic system is represented by an infinite set of points called an attractor, the dimension of which can be estimated by the correlation integral. Essentially, the correlation integral of a time series is a normalized count of the number of close pairs of points of the series lying in phase space. We examine the expected…

不等间隔纵向数据中的序列相关AI 解读

Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed…

非线性时间序列识别：一阶刻画与阶数确定AI 解读

We study the possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance. It is shown that most nonlinear models satisfy the assumptions needed to apply nonparametric asymptotic theory. Sampling variations of the conditional quantities are studied by simulation and explained by asymptotic arguments for a number of first-order nonlinear autoregressive processes. The conditional mean and variance can be used…

摘要暂缺

移动平均单位根检验AI 解读

Testing for a unit root in the moving average model is discussed. First, for the stationary MA(1) model, we suggest a score type test which is locally best invariant and unbiased. Performance of the test for finite samples is compared with the most powerful test. The asymptotic behavior of the test is also considered by computing the limiting power under a sequence of local alternatives. We then extend the model to an infinite order MA and suggest a test for this extended…

非平稳与不可逆时间序列模型渐近推断的 Fredholm 方法AI 解读

A unified approach which I call the Fredholm approach is suggested for the study of asymptotic behavior of estimators and" test statistics arising from nonstationary and/or noninvertible time series models. Some limit theorems are given concerning the distribution of (the ratio of) quadratic (plus linear) forms in random variables generated by a linear process that is not necessarily stationary. Especially, the limiting characteristic function is derived explicitly via the…

The results of forecasting experiments based on an error correction mechanism (ECM) model and various types of vector autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models are presented. A Bayesian error correction mechanism (BECM) model is also tested. This model represents a hybrid of the BVAR and ECM models. The results from experiments using fifty industries and monthly Ohio labor market data demonstrate that the ECM model produces forecasts with much…

A simple one-period-ahead and multiperiod-ahead prediction procedure for multivariate time series is suggested, based on the canonical correlation technique. The prediction procedure is direct in the sense that no lag orders and parameters have to be estimated first, as in the usual ARMAX or VAR parameterizations of multivariate stationary stochastic processes. A best (in the mean squared error sense) predictor can be obtained directly using singular-value decompositions of…

阿根廷 1978—1987 年货币需求：奥斯特拉尔计划前后AI 解读

In this study, a monthly money-demand function for Argentina is estimated for a period that ends one month before the austral program (May 1985). The performance of the traditional econometric approach is compared with the new cointegration approach to time series econometrics. The comparison is carried out by a postsample forecast of the demand for money for a period of two years after the stabilization (until July 1987). The cointegration approach is found superior to the…