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多元自回归序列中二次型的联合矩母函数AI 解读

Let { X t } follow a discrete Gaussian vector autoregression with deterministic components. We derive the exact finite-sample joint moment generating function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of functionals involving multivariate and univariate Ornstein–Uhlenbeck processes, drifts, and time trends. Such processes arise asymptotically from more general non-Gaussian processes and…

时间序列回归模型中条件异方差的一致检验AI 解读

We show that the standard consistent test for testing the null of conditional homoskedasticity (against conditional heteroskedasticity) can be generalized to a time-series regression model with weakly dependent data and with generated regressors. The test statistic is shown to have an asymptotic normal distribution under the null hypothesis of conditional homoskedastic error. We also discuss extension of our test to the case of testing the null of a parametrically specified…

近季节整合AI 解读

This paper presents asymptotic results for the seasonal unit root test proposed by Hylleberg, Engle, Granger and Yoo (1990, Journal of Econometrics 44, 215–238) in a near integration context. The findings are important in that they provide the asymptotic power functions of the Hylleberg et al. statistics when the characteristic roots of a seasonal process are local to unity. These conclusions extend the available asymptotic results for this test and serve as a framework for…

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不稳定自回归过程单位根检验的渐近分布AI 解读

UNIT ROOT TESTING has been developed through numerous papers since the work of Ž. Dickey and Fuller 1979 . The idea is to test the hypothesis that the differences of an observed time series do not depend on its levels, or in other words, the levels of the time series have a unit root that can be removed by differencing. While it is in general possible to have multiple unit roots, only the hypothesis of exactly one unit root is considered Ž. here. The available tests…

含单整时间序列的非线性回归AI 解读

An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable and asymptotically homogeneous functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. The rates of convergence depend on the properties of the nonlinear regression…

自回归模型的自助法后再自助法预测区间AI 解读

The use of the Bonferroni prediction interval based on the bootstrap-after-bootstrap is proposed for autoregressive (AR) models. Monte Carlo simulations are conducted using a number of AR models including stationary, unit-root, and near-unit-root processes. The major finding is that the bootstrap-after-bootstrap provides a superior small-sample alternative to asymptotic and standard bootstrap prediction intervals. The latter are often too narrow, substantially…

基于部分累计数据预测累计总量AI 解读

We present a Bayesian solution to forecasting a time series when few observations are available. The quantity to predict is the accumulated value of a positive, continuous variable when partially accumulated data are observed. These conditions appear naturally in predicting sales of style goods and coupon redemption. A simple model describes the relation between partial and total values, assuming stable seasonality. Exact analytic results are obtained for point forecasts and…

解释时间序列数据中的长期与短期相互作用AI 解读

In this article, I extend the concept of separate cointegration to include the common-feature trend-cycle decomposition approach. This combined approach operates a reduction of the parameter space and permits the identification of the time series long- and short-run constituent factors. A careful assessment of their reciprocal relations, in turn, allows for the answering of potentially interesting economic questions. To show the usefulness of the proposed methodology, I…

协整向量线性约束的 Bootstrap 检验AI 解读

We consider a computer-intensive method for inference on cointegrating vectors in maximum likelihood cointegration analysis. Simulation studies show that the size distortion for the asymptotic likelihood ratio test can be considerable for small samples. Itis demonstrated that a parametric bootstrap frequently results in a nearly exact α-level test. Furthermore, response surface regression is used to examine small-sample properties of the asymptotic test. In particular, using…

预测共识的检验AI 解读

A panel of forecasts may be defined to be in consensus when individual forecasters place identical weights on a common latent variable. We suggest this definition and formulate a dynamic latent-variable model to test for consensus. This method also tests whether it is valid to use the mean forecast as the consensus forecast. In applications to surveys of U.S. macroeconomic forecasters, there is greater consensus in forecasts for output growth than for inflation or…

生产中的准固定投入与长期均衡：协整分析AI 解读

Abstract This paper proposes a cointegration approach to testing the validity long‐run equilibrium in production, where capital and labour are taken as quasi‐fixed inputs. Previous studies consider only capital as the quasi‐fixed input and do not take account of the time series properties of the variables, assuming implicitly that they are stationary. The canonical cointegrating regressions (CCR) procedure is employed to test for cointegration in both the single‐equation and…

部分观测时间序列的非线性检验AI 解读

We have implemented a Lagrange multiplier test specifically for the alternative of a nonlinear continuous-time autoregressive model with the instantaneous mean having one degree of nonlinearity. The test is then extended to testing for the alternative of general nonlinear continuous-time autoregressive models with multiple degrees of nonlinearity. The performance of the test in the finite-sample case is compared with several existing tests for nonlinearity including Keenan's…

多窗多变量谱估计的统一视角AI 解读

The orthogonal multitaper framework for cross‐spectral estimators provides a simple unifying structure for determining the corresponding statistical properties. Here cross‐spectral estimators are represented by a weighted average of orthogonally‐tapered cross‐periodograms, with the weights corresponding to a set of rescaled eigenvalues. Such a structure not only encompasses the Thomson estimators, using Slepian and sine tapers, but also Welch's weighted overlapped segment…

局部平稳过程的似然近似AI 解读

A new approximation to the Gaussian likelihood of a multivariate locally stationary process is introduced. It is based on an approximation of the inverse of the covariance matrix of such processes. The new quasi likelihood is a generalization of the classical Whittle likelihood for stationary processes. Several approximation results are proved for the likelihood function. For parametric models, asymptotic normality and efficiency of the resulting estimator are derived for…

BIC 马尔可夫阶数估计量的一致性AI 解读

The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with finite alphabet $A$) from observation of a sample path $x_1, x_2,\dots, x_n$, as that value $k = \hat{k}$ that minimizes the sum of the negative logarithm of the $k$th order maximum likelihood and the penalty term $\frac{|A|^k(|A|-1)}{2}\log n$. We show that $\hat{k}$ equals the correct order of the chain, eventually almost surely as $n \rightarrow \infty$, thereby strengthening earlier…

In this paper we propose a sequential testing procedure to determine the order of differencing in seasonally observed time series processes, which builds upon existing approaches developed for nonseasonal series. We allow for the possible presence of multiple unit roots at both the zero and seasonal frequencies of the data. Multiple seasonal unit roots can be useful in circumstances where one does not wish to take logarithms of the data‐set at hand. Multiple unit roots at…

This paper proposes a residual-based Lagrange multiplier (LM) test for a null that the individual observed series are stationary around a deterministic level or around a deterministic trend against the alternative of a unit root in panel data. The tests which are asymptotically similar under the null, belong to the locally best invariant (LBI) test statistics. The asymptotic distributions of the statistics are derived under the null and are shown to be normally distributed.…

异方差下线性自回归动态的检验AI 解读

A puzzling characteristic of asset returns for various frequencies is the often observed positive autocorrelation at lag one. To some extent this can be explained by standard asset pricing models when assuming time-varying risk premia. However, one often finds better results when directly fitting an autoregressive model, for which there is little economic foundation. One may ask whether the underlying process does in fact contain an autoregressive component. It is therefore…

马尔可夫过程、双向自回归与平稳及非平稳自回归的有限样本推断AI 解读

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression…

条件异方差下鞅假设的谱检验AI 解读

We study the asymptotic distribution of the sample standardized spectral distribution function when the observed series is a conditionally heteroscedastic martingale difference. We show that the asymptotic distribution is no longer a Brownian bridge but another Gaussian process. Furthermore, this limiting process depends on the covariance structure of the second moments of the series. We show that this causes test statistics based on the sample spectral distribution, such as…

非平稳时间序列的 Whittle 伪极大似然估计AI 解读

Whittle pseudo-maximum likelihood estimates of parameters for stationary time series have been found to be consistent and asymptotically normal in the presence of long-range dependence. Generalizing the definition of the memory parameter d we extend these results to include possibly nonstationary (.5 ≤ d < 1) or antipersistent (-.5 < d < 0) observations. Using adequate data tapers, we can apply this estimation technique to any degree of nonstationarity d ≥ .5 without a…