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非平稳时间序列与经济周期分析的新方法AI 解读

This paper models occasional, discrete shifts in the growth rate of a nonstationary series. Algorithms for inferring these unobserved shifts are presented, a byproduct of which permits estimation of parameters by maximum likelihood. An empirical application of this technique suggests that the periodic shift from a positive growth rate to a negative growth rate is a recurrent feature of the U.S. business cycle, and indeed could be used as an objective criterion for defining…

白高斯时间序列中周期成分的检测AI 解读

SUMMARY A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to a trimmed mean of the periodograms. The asymptotic distributions of the statistics are obtained. It is shown that the proposed test and Fisher's test have the same asymptotic powers against the alternative of a sinusoidal wave at a non-zero Fourier frequency. The simulation results suggest…

自回归模型的递归估计AI 解读

SUMMARY This paper is concerned with the recursive estimation of autoregressive models, in particular the realtime determination of the order of such a specification. A model selection criterion based on the minimum description length principle due to Rissanen is discussed and strong consistency in the stationary situation is shown. Alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the…

多元时间序列的模型设定AI 解读

SUMMARY We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models.…

共同根检验AI 解读

In this paper, the authors propose a simple procedure for testing the existence of common roots in lag polynomials. They first show, by using a generalized Bezout property, that this hypothesis can be put under a "mixed" form that is linear with respect to the auxiliary parameters and with respect to the initial parameters. It follows that the test procedures can be implemented only by using regressions packages. Copyright 1989 by The Econometric Society.

自回归条件异方差的非参数检验：马尔可夫链方法AI 解读

In this article we propose a nonparametric test for autoregressive conditional heteroscedasticity based on finite-state Markov chains. A simple Monte Carlo experiment suggests that in finite samples it performs comparably to the Lagrange multiplier test under conditional normality and is superior for the t, lognormal, and exponential distributions. As an illustration, we apply both tests to Canadian/U.S. forward foreign exchange data.

多元时间序列结构稳定性的预测检验AI 解读

Comparing forecasts with actually observed values is one possible way to check the structural stability of time series. In this study, prediction tests based on this principle are investigated in the context of multiple time series analysis. It is found that the power of tests based on univariate series may exceed that of tests based on multivariate series and vice versa. Therefore, it is proposed to use both kinds of tests in practice. The tests are used to investigate the…

时间序列模型适切性检验的蒙特卡洛研究AI 解读

In this article, we conduct a Monte Carlo experiment of several computationally attractive tests of model adequacy in time series analysis. The experiment is designed to examine the small-sample properties of tests of fitted autoregressive and moving average models, to compare the performances of asymptotically equivalent procedures, to consider the effects on estimated significance levels and powers of testing against both appropriate and inappropriate alternatives, to…

周期自回归模型预测英国季节性消费的表现AI 解读

The parameters of a periodic model are allowed to vary according to the time at which observations are made. Periodic autoregressive models are fitted to the quarterly values of seasonally unadjusted real nondurable consumers' expenditure for the United Kingdom and its components. The periodic model offers no improvement over conventional specifications if the aggregate is modeled directly. On the other hand, periodic models generally perform well for the components, which…

缺失观测与 Durbin–Watson 统计量的使用AI 解读

This paper recommends the use of the usual Durbin–Watson test for the serial independence of errors on a classical regression equation in the presence of occasional gaps in the data.

时间序列配对比较中差值的序列相关AI 解读

If observations are taken at the same set of time points on each of two time series whose nonnegative trends are proportional, the F statistic based on the differences of the two series at the time points may be used to test equality of trends against inequality of trends provided the paired differences are independently and identically distributed normal random variables. The present paper investigates the effect on the F test when the paired differences follow a stationary…

多变量时间序列中序列相关的渐近协方差结构AI 解读

A simple proof of the asymptotic joint normality of any finite set of serial correlations of a general multivariate second-order stationary time series is presented and an explicit formula for the asymptotic covariance between two serial correlations is derived. The latter extends Bartlett's formula for the asymptotic covariance between two sample cross-correlations.

白噪声的自适应检验AI 解读

Since conventional tests for white noise are completely insensitive to certain alternatives, it is difficult in a particular application to decide which test to use if one has no a priori information about the kind of departure from whiteness. Therefore, an alternative test is proposed which may be applied in case of arbitrary stationary alternatives. This test procedure is adaptive in that first the real part of the finite Fourier transform of the data is used to choose…

自回归频率估计AI 解读

Presume that an autoregressive model of given order is fitted to data obtained from a realization of a sinusoidal signal embedded in white noise. This paper investigates the statistical properties of the estimate of the frequency of the signal obtained by minimizing the transfer function of the autoregression. Strong consistency and convergence in distribution of the estimate are established when the order of the autoregression is allowed to increase with sample size at an…

简单线性回归变点的似然比检验AI 解读

We consider likelihood ratio tests to detect a change-point in simple linear regression (a) when the alternative specifies that only the intercept changes and (b) when the alternative permits the intercept and the slope to change. Approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable. The approximations are compared with simulations in order to assess their accuracy. For the…

多元时间序列的稳健建模AI 解读

A robust estimation procedure for multiple time series is proposed based on robustifying the residual autocovariances in the estimating equation. The asymptotic distribution of these estimators is derived. A robustified multivariate portmanteau statistic is also obtained which can be useful in model diagnostic checking. An illustrative example based on the mink-muskrat data is presented.

自相关误差回归模型的大样本推断AI 解读

SUMMARY Based on intermittent observations from several independent regression models with autocorrelated errors, we derive tests of homogeneity, and the maximum likelihood estimate of the common regression parameter. The estimate for the regression parameter is based on aggregated data in the form of sample means at each time point. The limit distributions of the test statistics, and the estimate are considered. Basawa, Billard & Srinivasan (1984) discussed testing the…

序列相关缓慢衰减数据的位置参数检验AI 解读

Slowly decaying serial correlations have, if ignored, disastrous effects on classical tests and confidence intervals. We propose a modified t test for the location parameter which takes into account such correlations. An approximate distribution function of the test statistic is given under the assumption of fractional Gaussian noise. The results are generalized to prediction intervals for a future average. An example is given to illustrate the methods.

近似条件似然的一个时间序列示例AI 解读

We consider the calculation of confidence intervals for the correlation parameter, based on observations of a large number of short Gaussian first-order autoregressive processes with different means but common correlation and variance. Ordinary profile likelihood gives very misleading answers. The approximate conditional likelihood of Cox & Reid (1987) is calculated and shown to lead to consistent estimation of the correlation. Simulations verify that the usual asymptotic…

小样本中的回归与时间序列模型选择AI 解读

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better…

状态空间模型中信号提取、影响诊断与交叉验证的快速算法AI 解读

A fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model. The resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector. The ideas of studentized residuals and leverage from regression analysis are generalized to state space models, and the new algorithm is used to compute the various measures. The results are also…

偏群时延的估计AI 解读

The partial group delay between two channels of a multiple time series has an interpretation as the time lag between frequency components of the two channels after adjustments have been made for the influence of the remaining channels. A procedure for estimating partial group delay is proposed, and conditions for consistency and asymptotic normality of the estimating sequence are obtained.

平稳时间序列上叠加单调趋势的一致检测AI 解读

Consider a time series made up of a signal and a stationary autocorrelated error series. A statistic is proposed for examining the hypothesis that the signal term is constant versus the hypothesis that it is monotonic in time. The statistic is the ratio of a linear combination of the time series values, with coefficients introduced by Abelson & Tukey (1963), to an estimate of the standard error of the linear combination. The statistic has asymptotic power 1 for a broad class…

移动平均误差下的单位根检验AI 解读

In this paper we propose a new approach to testing for unit roots in a time series {yt} with moving average innovations based on an instrumental variable estimator. If {yt} is a random walk with moving average innovations, we derive the limiting distribution of the instrumental variable estimator when the estimated model is either (i) the true model, (ii) a random walk with shift in mean, or (iii) a random walk with shift in mean and a linear time trend. These distributions…