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TESTING THE NULL OF NO COINTEGRATION WHEN COVARIATES ARE KNOWN TO HAVE A UNIT ROOT

协变量已知含单位根时的无协整原假设检验

A number of tests have been suggested for the test of the null of no cointegration. Under this null, correlations are spurious in the sense of Granger and Newbold (1974) and Phillips (1986). We examine a set of models local to the null of no cointegration and derive tests with optimality properties in order to examine the efficiency of available tests. We find that, for a sufficiently tight weighting over potential cointegrating vectors, commonly employed full system tests…

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TESTING FOR GENERAL FRACTIONAL INTEGRATION IN THE TIME DOMAIN

一般分数整合的时域检验

We propose a family of least-squares–based testing procedures that look to detect general forms of fractional integration at the long-run and/or the cyclical component of a time series, and that are asymptotically equivalent to Lagrange multiplier tests. Our setting extends Robinson’s (1994) results to allow for short memory in a regression framework and generalizes the procedures in Agiakloglou and Newbold (1994), Tanaka (1999), and Breitung and Hassler (2002) by allowing…

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HETEROSKEDASTICITY-ROBUST TESTING FOR A FRACTIONAL UNIT ROOT

分数单位根的异方差稳健检验

This paper shows how fractional unit root tests originally derived under stationarity can be made robust to heteroskedasticity. This is done by using existing tests nested in a regression framework and then implementing these tests using White’s heteroskedasticity consistent standard errors (White, 1980). We show this approach is effective both asymptotically and in finite samples. We also provide some evidence on the asymptotic local power of different implementations of…

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INFERENCE ON NONPARAMETRICALLY TRENDING TIME SERIES WITH FRACTIONAL ERRORS

分数误差下非参数趋势时间序列的推断

The central limit theorem for nonparametric kernel estimates of a smooth trend, with linearly generated errors, indicates asymptotic independence and homoskedasticity across fixed points, irrespective of whether disturbances have short memory, long memory, or antipersistence. However, the asymptotic variance depends on the kernel function in a way that varies across these three circumstances, and in the latter two it involves a double integral that cannot necessarily be…

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UNIT ROOT AND COINTEGRATING LIMIT THEORY WHEN INITIALIZATION IS IN THE INFINITE PAST

无限过去初始化下的单位根与协整极限理论

It is well known that unit root limit distributions are sensitive to initial conditions in the distant past. If the distant past initialization is extended to the infinite past, the initial condition dominates the limit theory, producing a faster rate of convergence, a limiting Cauchy distribution for the least squares coefficient, and a limit normal distribution for the t -ratio. This amounts to the tail of the unit root process wagging the dog of the unit root limit…

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ROBUST INFERENCE IN AUTOREGRESSIONS WITH MULTIPLE OUTLIERS

含多个异常值的自回归稳健推断

We consider robust methods for estimation and unit root (UR) testing in autoregressions with infrequent outliers whose number, size, and location can be random and unknown. We show that in this setting standard inference based on ordinary least squares estimation of an augumented Dickey–Fuller (ADF) regression may not be reliable, because (a) clusters of outliers may lead to inconsistent estimation of the autoregressive parameters and (b) large outliers induce a jump…

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TESTING FOR A UNIT ROOT IN THE PRESENCE OF A POSSIBLE BREAK IN TREND

可能存在趋势断点时的单位根检验

We consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at an unknown point in the series. We propose a new break fraction estimator which, where a break in trend occurs, is consistent for the true break fraction at rate O p ( T −1 ). Unlike other available estimators, however, when there is no trend break, our estimator converges to zero at rate O p ( T −1/2 ). Used in conjunction with a quasi…

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A NOTE ON THE POOLING OF INDIVIDUAL PANIC UNIT ROOT TESTS

关于个体 PANIC 单位根检验合并的说明

One of the most cited studies in recent years within the field of nonstationary panel data analysis is that of Bai and Ng (2004), in which the authors propose PANIC, a new framework for analyzing the nonstationarity of panels with idiosyncratic and common components. The problem is that the asymptotic validity of PANIC as a platform for constructing pooled panel unit root tests based on averaging is not fully proven. This paper provides the required results, whose usefulness…

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GLS-BASED UNIT ROOT TESTS WITH MULTIPLE STRUCTURAL BREAKS UNDER BOTH THE NULL AND THE ALTERNATIVE HYPOTHESES

原假设与备择假设下均允许多重结构断点的 GLS 单位根检验

Perron (1989, Econometrica 57, 1361–1401) introduced unit root tests valid when a break at a known date in the trend function of a time series is present. In particular, they allow a break under both the null and alternative hypotheses and are invariant to the magnitude of the shift in level and/or slope. The subsequent literature devised procedures valid in the case of an unknown break date. However, in doing so most research, in particular the commonly used test of Zivot…

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REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES

以分数过程为积分器的随机积分表示与弱收敛

This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process—possibly itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analyzed in a previous paper (Davidson and Hashimzade, 2008), and the construction derived from moving average representations in the time domain. Depending…

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AVERAGING ESTIMATORS FOR REGRESSIONS WITH A POSSIBLE STRUCTURAL BREAK

可能存在结构断点的回归平均估计量

This paper investigates selection and averaging of linear regressions with a possible structural break. Our main contribution is the construction of a Mallows criterion for the structural break model. We show that the correct penalty term is nonstandard and depends on unknown parameters, but it can be approximated by an average of limiting cases to yield a feasible penalty with good performance. Following Hansen (2007, Econometrica 75, 1175–1189) we recommend averaging the…

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THE PROPERTIES OF KULLBACK–LEIBLER DIVERGENCE FOR THE UNIT ROOT HYPOTHESIS

单位根假设下 Kullback–Leibler 散度的性质

The fundamental contributions made by Paul Newbold have highlighted how crucial it is to detect when economic time series have unit roots. This paper explores the effects that model specification has on our ability to do that. Asymptotic power, a natural choice to quantify these effects, does not accurately predict finite-sample power. Instead, here the Kullback–Leibler divergence between the unit root null and any alternative is used and its numeric and analytic properties…

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A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC

基于免调节参数统计量的高功效自回归单位根检验

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d , and containing the Breitung (2002, Journal of Econometrics 108, 342–363) test as the special case d = 1. It is shown that (a) each member of the family with d > 0 is consistent, (b) the asymptotic distribution depends on d and thus reflects the parameter chosen to implement the test, and (c) because the asymptotic distribution depends on d and the test remains consistent for…

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LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION

局部极限理论与非参数伪回归

A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnostics are suggested for forensic analysis of such regresssions, including a local R…

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Detecting Changes in the Mean of Functional Observations

函数型观测均值变化的检测

Summary Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t) = μ(t)+Σ1≤l<∞ηi, l+ vl(t), where μ is the common mean, vl are the eigenfunctions of the covariance operator and the ηi, l are the scores. Inferential procedures assume that the mean function μ(t) is the same for all values of i. If, in fact, the observations do not come from one population, but rather their mean changes at some point(s),…

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Testing for the cointegrating rank of a vector autoregressive process with uncertain deterministic trend term

确定性趋势项不确定时VAR过程的协整秩检验

When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to being orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second…

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Empirical likelihood-based inference for nonparametric recurrent diffusions

非参数常返扩散过程的经验似然推断

This paper provides a new approach to constructing confidence intervals for nonparametric drift and diffusion functions in the continuous-time diffusion model via empirical likelihood (EL). The log EL ratios are constructed through the estimating equations satisfied by the local linear estimators. Limit theories are developed by means of increasing time span and shrinking observational intervals. The results apply to both stationary and nonstationary recurrent diffusion…

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The political economy of financial reform: are Abiad and Mody right?

金融改革的政治经济学:Abiad 与 Mody 的结论是否成立?

Abstract Motivated by the questions ‘Financial Reform: What Shakes It? What Shapes It?’ raised by Abiad and Mody ( 2005 ), this paper studies the forces that induce governments to undertake financial sector reform. Rather than their ordered logit technique, it uses a within groups approach allowing for error dependence across countries and over time. This analysis shows that some of the AM findings are not robust to error dependence and the estimation method. It has shed new…

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Economic transition and growth

经济转型与增长

Abstract Some extensions of neoclassical growth models are discussed that allow for cross‐section heterogeneity among economies and evolution in rates of technological progress over time. The models offer a spectrum of transitional behavior among economies that includes convergence to a common steady‐state path as well as various forms of transitional divergence and convergence. Mechanisms for modeling such transitions, measuring them econometrically, assessing group…

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A State Space Approach to Extracting the Signal From Uncertain Data

不确定数据的信号提取:状态空间方法

Most macroeconomic data are uncertain—they are estimates rather than perfect measures of underlying economic variables. One symptom of that uncertainty is the propensity of statistical agencies to revise their estimates in the light of new information or methodological advances. This paper sets out an approach for extracting the signal from uncertain data. It describes a two-step estimation procedure in which the history of past revisions is first used to estimate the…

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Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes

多维因果时间过程准极大似然估计量的渐近正态性

Strong consistency and asymptotic normality of the quasi-maximum likelihood estimator are given for a general class of multidimensional causal processes. For particular cases already studied in the literature [for instance univariate or multivariate ARCH(∞) processes], the assumptions required for establishing these results are often weaker than existing conditions. The QMLE asymptotic behavior is also given for numerous new examples of univariate or multivariate processes…

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Local linear quantile estimation for nonstationary time series

非平稳时间序列的局部线性分位数估计

We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are applied to environmental data sets. In particular, our results can be used to address the problem of whether climate variability has changed, an important problem raised by IPCC (Intergovernmental Panel on Climate Change) in 2001.

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On maxima of periodograms of stationary processes

平稳过程周期图最大值的极限分布

Abstract. We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on m-dependent approximation for stationary processes and a moderate deviation result.

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Functional-coefficient cointegration models

函数系数协整模型

This paper studies estimation and inference of functional coefficient cointegration models. The proposed model offers a more flexible structure of cointegration where the value of cointegrating coefficients may be affected by informative covariates and thus may vary over time. The model may be viewed as a stochastic cointegration model and includes the conventional cointegration model as a special case. The proposed new model provides a useful complement to the conventional…

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