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CONSISTENT COVARIANCE MATRIX ESTIMATION FOR LINEAR PROCESSES

线性过程的协方差矩阵一致估计

Consistency of kernel estimators of the long-run covariance matrix of a linear process is established under weak moment and memory conditions. In addition, it is pointed out that some existing consistency proofs are in error as they stand.

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NON- AND SEMIPARAMETRIC IDENTIFICATION OF SEASONAL NONLINEAR AUTOREGRESSION MODELS

季节性非线性自回归模型的非参数与半参数识别

Non- or semiparametric estimation and lag selection methods are proposed for three seasonal nonlinear autoregressive models of varying seasonal flexibility. All procedures are based on either local constant or local linear estimation. For the semiparametric models, after preliminary estimation of the seasonal parameters, the function estimation and lag selection are the same as nonparametric estimation and lag selection for standard models. A Monte Carlo study demonstrates…

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ON THE PROPERTIES OF SOME TESTS FOR COMMON STOCHASTIC TRENDS

若干共同随机趋势检验的性质

We study the asymptotic properties of the tests suggested by Choi and Ahn (1995, Econometric Theory 11, 952–983) in the case of a (nearly) improper normalization of the cointegration vectors. To overcome the size problems in such situations we suggest a test statistic that is based on the eigenvalues of a canonical correlation analysis. Using Monte Carlo simulations, the small sample properties of our test are compared to various other test statistics recently suggested in…

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REGRESSION THEORY FOR NEARLY COINTEGRATED TIME SERIES

近协整时间序列的回归理论

This paper proposes a notion of near cointegration and generalizes several existing results from the cointegration literature to the case of near cointegration. In particular, the properties of conventional cointegration methods under near cointegration are characterized, thereby investigating the robustness of cointegration methods. In addition, we obtain local asymptotic power functions of five cointegration tests that take cointegration as the null hypothesis.

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TESTING FOR LONG MEMORY IN VOLATILITY

波动率长记忆检验

We consider the asymptotic behavior of log-periodogram regression estimators of the memory parameter in long-memory stochastic volatility models, under the null hypothesis of short memory in volatility. We show that in this situation, if the periodogram is computed from the log squared returns, then the estimator is asymptotically normal, with the same asymptotic mean and variance that would hold if the series were Gaussian. In particular, for the widely used GPH estimator…

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MINIMUM DISTANCE ESTIMATION OF NONSTATIONARY TIME SERIES MODELS

非平稳时间序列模型的最小距离估计

This paper analyzes the limit distribution of minimum distance (MD) estimators for nonstationary time series models that involve nonlinear parameter restrictions. A rotation for the restricted parameter space is constructed to separate the components of the MD estimator that converge at different rates. We derive regularity conditions for the restriction function that are easier to verify than the stochastic equicontinuity conditions that arise from direct estimation of the…

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Testing for reduction to random walk in autoregressive conditional heteroskedasticity models

自回归条件异方差模型退化为随机游走的检验

The autoregressive--ARCH (AR--ARCH) and autoregressive--GARCH (AR--GARCH) models, which allow for conditional heteroskedasticity and autoregression, reduce to random walk or white noise for some values of the parameters. We consider generalized versions of the AR--ARCH(1) and AR--GARCH(1,1) models, and, under mild assumptions, calculate the asymptotic distributions of pseudo-likelihood ratio statistics for testing hypotheses that reflect these reductions. These hypotheses…

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Distributions of error correction tests for cointegration

协整误差修正检验的分布

This paper provides densities and finite sample critical values for the single-equation error correction statistic for testing cointegration. Graphs and response surfaces summarize extensive Monte Carlo simulations and highlight simple dependencies of the statistic's quantiles on the number of variables in the error correction model, the choice of deterministic components, and the sample size. The response surfaces provide a convenient way for calculating finite sample…

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Particle Filtering for Partially Observed Gaussian State Space Models

部分观测高斯状态空间模型的粒子滤波

Summary Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been proposed to solve these problems. We propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions…

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Kernel density estimation for linear processes

线性过程的核密度估计

In this paper we provide a detailed characterization of the asymptotic behavior of kernel density estimators for one-sided linear processes. The conjecture that asymptotic normality for the kernel density estimator holds under short-range dependence is proved under minimal assumptions on bandwidths. We also depict the dichotomous and trichotomous phenomena for various choices of bandwidths when the process is long-range dependent.

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Properties of nonlinear transformations of fractionally integrated processes

分数单整过程非线性变换的性质

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0). For non-stationary I(d) processes,…

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Nonlinear minimization estimators in the presence of cointegrating relations

存在协整关系时的非线性最小化估计

In this paper, we consider estimation of a long-run and a short-run parameter jointly in the presence of nonlinearities. The theory developed establishes limit behavior of minimization estimators of the long-run and short-run parameters jointly. Typically, if the long-run parameter that is present in a cointegrating relationship is estimated, its estimator will be superconsistent. Therefore, we may conjecture that the joint minimization estimation of both parameters jointly…

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Generalized Method of Moments and Macroeconomics

广义矩方法与宏观经济学

We consider the contribution to the analysis of economic time series of the generalized method-of-moments estimator introduced by Hansen. We outline the theoretical contribution, conduct a small-scale literature survey, and discuss some ongoing theoretical research.

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ROBUST INFERENCE FOR THE MEAN IN THE PRESENCE OF SERIAL CORRELATION AND HEAVY-TAILED DISTRIBUTIONS

序列相关与厚尾分布下均值的稳健推断

The problem of statistical inference for the mean of a time series with possibly heavy tails is considered. We first show that the self-normalized sample mean has a well-defined asymptotic distribution. Subsampling theory is then used to develop asymptotically correct confidence intervals for the mean without knowledge (or explicit estimation) either of the dependence characteristics, or of the tail index. Using a symmetrization technique, we also construct a distribution…

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THE LIMITING PROPERTIES OF THE CANOVA AND HANSEN TEST UNDER LOCAL ALTERNATIVES

Canova–Hansen 检验在局部备择下的极限性质

This paper investigates the limiting properties of the Canova and Hansen test, testing for the null hypothesis of no unit root against seasonal unit roots, under a sequence of local alternatives with the model extended to have seasonal dummies and trends or no deterministic term and also only seasonal dummies. We derive the limiting distribution of the test statistic and its characteristic function under local alternatives. We find that the local limiting power is an inverse…

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ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS

不稳定解释变量回归中普通最小二乘估计量的渐近有效性

For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that…

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