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量化初始值对非线性预测的影响AI 解读

SUMMARY Motivated by the m-step-ahead prediction problem in non-linear time series, a brief sketch of stochastic chaotic systems is provided. The accuracy of the prediction depends on the initial value, which is a typical feature of non-linear but not necessarily chaotic models. However, if the model is chaotic, small noise can be amplified very quickly through time evolution at some initial values, thereby decreasing dramatically the reliability of the prediction. Further,…

干扰参数仅在备择假设下存在时的最优检验AI 解读

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. For example, the results apply to tests of structural change with unknown changepoint. The testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier, Wald, and likelihood ratio do not apply. A weighted average power criterion is used here to generate…

加性异常值对单位根与协整检验的影响AI 解读

This paper discusses the properties of the univariate Dickey-Fuller test and the Johansen test for the cointegrating rank when there exist additive outlying observations in the time series. The authors provide analytical as well as numerical evidence that additive outliners may produce spurious stationarity. The results easily generalize to models with 'temporary change' outliers. Through an empirical example, the authors discuss how additive and temporary change outliers…

单位根检验准则的比较AI 解读

The ordinary least squares estimator has been widely used for testing the unit-root hypothesis in autoregressive processes. Recently, several new criteria, based on maximum likelihood and weighted symmetric estimators, have been proposed. In this article, the authors describe several different test criteria. Results from Monte Carlo studies that compare the power of the different test criteria indicate that the new tests are more powerful against the stationary alternative.…

基于数据预检验选模的时间序列单位根检验AI 解读

In this article we examine the impact of data-based lag-length estimation on the behavior of the augmented Dickey–Fuller (ADF) test for a unit root. We derive conditions under which the ADF test converges to the distribution tabulated by Dickey and Fuller and verify that these conditions are satisfied by several commonly employed lag-selection strategies. Simulation evidence indicates that the performance of the ADF test is considerably improved when the lag length is…

极值指数的估计AI 解读

SUMMARY The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the…

用时间序列交叉验证自动平滑依赖数据AI 解读

SUMMARY The problem of selecting the bandwidth of a kernel regression estimator when the observed data are serially correlated is considered. The bandwidth is selected by using a version of cross-validation that seeks a good one-step-ahead predictor of the data. This method, referred to as time series cross-validation (TSCV), simultaneously estimates an optimal bandwidth and, given a time series model for the errors, the autocorrelation function of the data. In addition,…

动态模型的最优递归估计AI 解读

This article checks, using both real and simulated data, the effectiveness of modern adaptive techniques to track the parameters of time-varying dynamic models. The real case studies concern a bone marrow transplant data set published by Tong, the gas furnace model of Box and Jenkins, and two series of West German interest rates. Simulation studies focus on ARX models with smoothly and suddenly changing parameters. The general approach is to compare the fitting-forecasting…

利用平方累积和回顾检测方差变化AI 解读

This article studies the problem of multiple change points in the variance of a sequence of independent observations. We propose a procedure to detect variance changes based on an iterated cumulative sums of squares (ICSS) algorithm. We study the properties of the centered cumulative sum of squares function and give an intuitive basis for the ICSS algorithm. For series of moderate size (i.e., 200 observations and beyond), the ICSS algorithm offers results comparable to those…

动态模型的最优递归估计AI 解读

This article checks, using both real and simulated data, the effectiveness of modern adaptive techniques to track the parameters of time-varying dynamic models. The real case studies concern a bone marrow transplant data set published by Tong, the gas furnace model of Box and Jenkins, and two series of West German interest rates. Simulation studies focus on ARX models with smoothly and suddenly changing parameters. The general approach is to compare the fitting-forecasting…

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扫描统计量检测伯努利序列变化区段的功效AI 解读

Fu & Curnow (1990) derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length, based on the scan statistic, the maximum number of successes within the specified length. Their method is computationally feasible for segment lengths of 20 or less. We present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for…

平稳与部分非平稳 VARMA 过程精确似然的快速算法AI 解读

An expression for the likelihood function of a stationary vector autoregressive-moving average process is developed. The expression is very efficient numerically and applies to any stationary but not necessarily invertible model. In particular, when the multivariate process is autoregressive, the exact likelihood can be evaluated with a small number of operations depending on the order of the autoregressive operator and the process dimension, but not on the size of the…

通过变量增广检验工具变量估计动态模型中的序列相关AI 解读

Instrumental variable tests for serial correlation can be carried out by adding lagged residuals from initial estimation to the regressors of the model under scrutiny and then checking their joint significance. It is shown that asymptotically valid tests are obtained if the lagged residuals are also added to the initial instrument set. Monte Carlo evidence suggests that useful improvements in finite sample behavior under null and alternative hypotheses can be produced when…

摘要暂缺

结合数据驱动模型选择的单位根后验赔率检验AI 解读

The Kalman filter is used to derive updating equations for the Bayesian data density in discrete time linear regression models with stochastic regressors. The implied “Bayes model” has time varying parameters and conditionally heterogeneous error variances. A σ-finite Bayes model measure is given and used to produce a new-model-selection criterion (PIC) and objective posterior odds tests for sharp null hypotheses like the presence of a unit root. This extends earlier work by…

可能含非平稳过程的时间序列模型中的贝叶斯渐近理论AI 解读

Asymptotic normality of the Bayesian posterior is a well-known result for stationary dynamic models or nondynamic models. This paper extends the analysis to a time series model with a possible nonstationary process. We spell out conditions under which asymptotic normality of the posterior is obtained even if the true data-generation process is a nonstationary process.

单位根假设的贝叶斯涵盖检验AI 解读

The object of this paper is to report, for a simple testing problem of a unit root hypothesis, some experience regarding the numerical problems involved by using a Bayesian encompassing test, i.e., a Bayesian procedure that treats the null and the alternative hypotheses as different models, the null one and the alternative one, that share a same sample space but with different parameter spaces. Numerical procedures and efficient simulations are discussed briefly, and the…

以平稳性为原假设的残差检验及美国宏观时间序列应用AI 解读

This paper proposes residual-based tests for the null of level- and trend-stationarity, which are analogs of the LM test for an MA unit root. Asymptotic distributions of the tests are nonstandard, but they are expressed in a unified manner by expressing stochastic integrals. In addition, the tests are shown to be consistent. By expressing the distributions expressed as a function of a chi-square variable with one degree of freedom, the exact limiting probability density and…

在未知平稳化方式下建模股票价格AI 解读

Bayesian procedures for evaluating linear restrictions imposed by economic theory on dynamic econometric models are applied to a simple class of presentvalue models of stock prices. The procedures generate inferences that are not conditional on ancillary assumptions regarding the nature of the nonstationarity that characterizes the data. Inferences are influenced by prior views concerning nonstationarity, but these views are formally incorporated into the analysis, and…

解释变量单整阶数未知时的时间序列回归推断AI 解读

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible…

宏观经济学家应了解的单位根问题：贝叶斯视角AI 解读

This paper summarizes recent Bayesian research on unit roots for the applied macroeconomist in the way Campbell and Perron [8] summarized the classical unit roots perspective. The appropriate choice of a prior is discussed. In recognizing a consensus distaste for explosive roots, I find the popular Normal-Wishart priors centered at the unit root to be reasonable provided they are modified by concentrating the prior mass for the time trend coefficient toward zero as the…

使用精确似然函数时的 Jeffreys 先验AI 解读

In this paper, we calculate Jeffreys prior for an AR(1) process with and without a constant and a time trend when using the exact likelihood function. We show how this prior can be calculated for the explosive region, even though the unconditional variance of the process is infinite. The calculations lend additional support to the Schotman-van Dijk [6] procedure for restricting the location and the variance of the time trend coefficient. The results show that flat priors are…

趋势平稳与差分平稳的贝叶斯推断AI 解读

This paper proposes a general Bayesian framework for distinguishing between trend- and difference-stationarity. Usually, in model selection, we assume that all of the data were generated by one of the models under consideration. In studying time series, however, we may be concerned that the process is changing over time, so that the preferred model changes over time as well. To handle this possibility, we compute the posterior probabilities of the competing models for each…