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线性过程自相关的序贯估计AI 解读

This paper considers sequential point estimation of the autocorrelations of stationary linear processes within the framework of the sequential procedure initiated by Robbins. The sequential estimator proposed here is based on the usual sample autocorrelations and is shown to be risk efficient in the sense of Starr as the cost per observation approaches zero. To achieve the asymptotic risk efficiency, we are led to study the uniform integrability and random central limit…

满足误报概率界的分布变化检测动态抽样策略AI 解读

We show that if dynamic sampling is feasible, then there exist surveillance schemes that satisfy a probability constraint on false alarm. Procedures are suggested for detecting a change of a normal mean from 0 to a (unknown) positive value. These procedures are optimal (up to a constant term) when the post-change mean is known, and almost optimal [up to an $o(\log(1/\alpha))$ term when the post-change mean is unknown.

离散线性系统的盲反卷积AI 解读

We study the blind deconvolution problem in the case where the input noise has a finite discrete support and the transfer linear system is not necessarily minimum phase. We propose a new family of estimators built using algebraic considerations. The estimates are consistent under very wide assumptions: The input signal need not be independently distributed; the cardinality of the finite support may be estimated simultaneously. We consider in particular AR systems: In this…

时间序列比值统计量的频域自助法AI 解读

The asymptotic properties of the bootstrap in the frequency domain based on Studentized periodogram ordinates are studied. It is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations. By using Edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation. The results carry over to Whittle estimates. In a simulation study the behavior of the bootstrap is studied for empirical correlations…

平稳观测下分块自助法的二阶正确性AI 解读

We show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second-order correct provided we choose an appropriate variance estimator. We also show how to adapt the $BC_a$ confidence interval of Efron to the a dependent case. For the proofs we extend the results of Götze and Hipp on the validity of the formal Edgeworth expansion for a sum to the studentized mean.

无限方差分数 ARIMA 模型的参数估计AI 解读

Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Klüppelberg and Adler for ARMA time series remain valid for fractional ARIMA with…

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经济时间序列能通过差分变得平稳吗？AI 解读

This paper considers a class of nonstationary varying coefficient autoregressive models which allow stochastic variability in the autoregressive root. It is argued that such models provide a better description of the behaviour of macroeconomic variables than fixed unit root autoregressive models as they allow more general forms of nonstationarity. We construct a test of the null hypothesis of a fixed unit root against the alternative of a fixed unit root against the…

通过整合多个模型预测转折点AI 解读

A new method for forming composite turning point (or other qualitative) forecasts is proposed. Rather than forming composite forecasts by the standard Bayesian approach with weights proportional to each model's posterior odds, weights are assigned to the individual models in proportion to the probability of each model's having the correct turning point prediction. These probabilities are generated by logit models estimated with data on the models' past turning point…

无需预先确定平稳化方式的股票价格建模：计算更正AI 解读

In “Modeling Stock Prices without Knowing How to Induce Stationarity” (1994, Econometric Theory 10, 701–719), we used posterior-odds calculations to evaluate restrictions imposed by a present-value model of stock prices across the equations of a VAR representation of stock prices and dividends. The results we reported are tainted by the omission of two factors: the Jacobians induced by the mapping of our priors over VAR parameters β into the restricted sample spaces relevant…

近观测等价与单位根检验的理论尺寸问题AI 解读

Said and Dickey (1984, Biometrika 71, 599–608) and Phillips and Perron (1988, Biometrika 75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is…

随机游走水平穿越次数的极限分布与简单单位根检验AI 解读

We derive the limit distribution of the number of crossings of a level by a random walk with continuously distributed increments, using a Brownian motion local time approximation. This complements the well-known result for the random walk on the integers. Use of the frequency of level crossings to test for a unit root is examined.

多变量自回归序列中二次型的联合矩母函数AI 解读

Let ( X 1 ) be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (m.g.f.) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of interest, including the m.g.f. of functional of multivariate Ornstein-Uhlenbeck processes that arise asymptotically from more general ( X 1 ) processes as well.

长记忆参数变化的检验AI 解读

Long-range dependence is often observed in long time series. Correlations decay approximately like |k|2H-2, with H ε (0.5, 1), as the lag k tends to infinity. The long-term features of the data are essentially characterised by the parameter H. Small changes of H have strong implications for the long-term behaviour of the process. In particular, rates of convergence of estimators for the mean, and for many other parameters of interest, differ for different values of H. For…

长序列向量一般线性过程的快速似然近似：分数差分应用AI 解读

The quadratic form appearing in the likelihood function of a Gaussian stationary and invertible vector general linear process is considered in this paper. A new expression for this quadratic form is developed, which allows repeated computations to be performed very efficiently by possibly using forecast and backcast values of the series. While the quadratic form itself involves the inverse of the covariance matrix, the new expression uses the autocovariances of the…

条件高斯状态空间模型中的马尔可夫链蒙特卡洛AI 解读

A Bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values. A sequence of indicator variables determines which components the errors belong to and the values of the coefficients. The computation is carried out using Markov chain Monte Carlo, with the indicator variables generated without conditioning on the states. Previous approaches use the Gibbs sampler to…

两个协方差平稳时间序列的独立性检验AI 解读

A one-sided asymptotically normal test for independence between two stationary time series is proposed by first prewhitening the two time series and then basing the test on the residual cross-correlation function. The test statistic is a properly standardised version of the sum of weighted squares of residual cross-correlations, with weights depending on a kernel function. Haugh's (1976) test can be viewed as a special case of our approach in the sense that it corresponds to…

针对 ARMA(1,1) 备择的序列相关检验AI 解读

This article is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against autoregressive moving average model ARMA(1, 1) alternatives is considered. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are shown to be asymptotically admissible for ARMA(1, 1) alternatives. In addition, they are shown to be consistent…

环境时间序列的非线性加性模型及地面臭氧应用AI 解读

Environmental time series usually vary systematically in response to meteorological conditions and thus often are not stationary. In this article a class of additive models are introduced for environmental time series, in which both mean levels and variances of the series are nonlinear functions of relevant meteorological variables. Backfitting algorithms in nonlinear regression are adopted to estimate the unknown functions in the model, and the maximum likelihood method is…

环境时间序列的非线性可加模型：地面臭氧数据应用AI 解读

Environmental time series usually vary systematically in response to meteorological conditions and thus often are not stationary. In this article a class of additive models are introduced for environmental time series, in which both mean levels and variances of the series are nonlinear functions of relevant meteorological variables. Backfitting algorithms in nonlinear regression are adopted to estimate the unknown functions in the model, and the maximum likelihood method is…

以ARMA(1,1)为备择的序列相关检验AI 解读

This paper is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against ARMA(1,1) alternatives is considered. Sup Lagrange multiplier (LM) and exponential average LM tests are introduced and are shown to be asymptotically admissible for ARMA(1,1) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white…

分数整合广义自回归条件异方差模型AI 解读

The new class of Fractionally Integrated Generalized AutoRegressive Conditionally Heteroskedastic (FIGARCH) processes is introduced. The conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations. Unlike I(d) processes for the mean, Maximum Likelihood Estimates (MLE) of the FIGARCH parameters are argued to be T^(1/2)-consistent. The small-sample behavior of an approximate MLE procedure is assessed through a…

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