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单位根与协整:单位根检验、协整、误差修正与长期关系。
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Forecasting autoregressive time series in the presence of deterministic components

This paper studies the error in forecasting an autoregressive process with a deterministic component. We show that when the data are strongly serially correlated, forecasts based on a model that detrends the data using OLS before estimating the autoregressive parameters are much less precise than those based on an autoregression that includes the deterministic components, and the asymptotic distribution of the forecast errors under the two‐step procedure exhibits bimodality.…

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On LM type tests for seasonal unit roots in quarterly data

In this paper the application of the score principle to test for unit roots in seasonal processes is analysed. In particular, tests based on the procedure proposed by Hylleberg et al.(1990, Journal of Econometrics, 44, 215–38) (HEGY) are introduced and the respective limit distributions derived in a local‐to‐unity context. It is shown that these statistics converge to distributions already tabulated in the literature. A Monte Carlo investigation contrasting the conventional…

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ASYMPTOTIC INFERENCE ON THE MOVING AVERAGE IMPACT MATRIX IN COINTEGRATED I (2) VAR SYSTEMS

协整 I(2) VAR 系统中移动平均影响矩阵的渐近推断

This paper provides asymptotic standard errors for the moving average (MA) impact matrix for the second differences of a vector autoregressive (VAR) process integrated of order 2, I (2). Standard errors of the row space of the MA impact matrix are also provided; bases of this row space define the common I (2) trends linear combinations. These standard errors are then used to formulate Wald-type tests. The MA impact matrix is shown to be linked to impact factors that measure…

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INSTRUMENTAL VARIABLE INTERPRETATION OF COINTEGRATION WITH INFERENCE RESULTS FOR FRACTIONAL COINTEGRATION

协整的工具变量解释与分数协整推断

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated…

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SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR MODELS FOR DEPENDENT DATA WITH GENERATED REGRESSORS

含生成解释变量的依赖数据部分线性模型半参数估计

In this paper we consider the problem of estimating a semiparametric partially linear model for dependent data with generated regressors. This type of model comes naturally from various econometric models such as a semiparametric rational expectation model when the surprise term enters the model nonparametrically, or a semiparametric type-3 Tobit model when the error distributions are of unknown forms, or a semiparametric error correction model. Using the nonparametric…

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On Monte Carlo estimation of relative power

相对检验功效的蒙特卡洛估计

This paper derives standard errors for Monte Carlo (MC) estimators of (relative) power of tests when the critical values under the null have also been estimated. This situation is common, for example, in unit root and cointegration (CI) tests. The associated issue of MC design is discussed. The results are illustrated on likelihood-based tests for CI rank determination. Copyright Royal Economic Society 2002

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Unit root tests in panel data: asymptotic and finite-sample properties

面板数据单位根检验:渐近与有限样本性质

We consider pooling cross-section time series data for testing the unit root hypothesis. The degree of persistence in individual regression error, the intercept and trend coefficient are allowed to vary freely across individuals. As both the cross-section and time series dimensions of the panel grow large, the pooled t-statistic has a limiting normal distribution that depends on the regression specification but is free from nuisance parameters. Monte Carlo simulations…

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Band Spectral Regression with Trending Data

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both semiparametric and nonparametric regression formulations are considered, the latter including general systems of two-sided distributed lags such as those arising in lead and lag regressions. The…

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Lower Risk Bounds and Properties of Confidence Sets for Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots, and Estimation of Long Memory Parameters

病态估计问题的风险下界与置信集合:谱密度、持续性、单位根及长记忆参数的应用

Important estimation problems in econometrics like estimating the value of a spectral density at frequency zero, which appears in the econometrics literature in the guises of heteroskedasticity and autocorrelation consistent variance estimation and long run variance estimation, are shown to be “ill-posed” estimation problems. A prototypical result obtained in the paper is that the minimax risk for estimating the value of the spectral density at frequency zero is infinite…

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Regression-Based Unit Root Tests With Recursive Mean Adjustment for Seasonal and Nonseasonal Time Series

季节与非季节时间序列中基于递归均值调整的回归单位根检验

This article considers tests for (seasonal) unit roots in a univariate time-series process that are similar with respect to both the initial values of the process and the possibility of (differential seasonal) drift under the (seasonal) unit root null. In contrast to existing approaches, the technique of recursive (seasonal) de-meaning and (seasonal) de-trending of the process is adopted. Representations are derived for the limiting distributions of the proposed statistics…

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Threshold Autoregressions for Strongly Autocorrelated Time Series

强自相关时间序列的阈值自回归模型

In some cases the unit root or near unit root behavior of linear autoregressive models fitted to economic time series is not in accordance with the underlying economic theory. To accommodate this feature we consider a threshold autoregressive (TAR) process with the threshold effect only in the intercept term. Although these processes are stationary, their realizations switch between different regimes and can therefore closely resemble those of (near) integrated processes for…

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AN INVARIANCE PRINCIPLE FOR SIEVE BOOTSTRAP IN TIME SERIES

时间序列筛自助法的不变原理

This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form…

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TESTING FOR A UNIT ROOT IN A TIME SERIES WITH A LEVEL SHIFT AT UNKNOWN TIME

未知时点水平变化下的时间序列单位根检验

Unit root tests for time series with level shifts of general form are considered when the timing of the shift is unknown. It is proposed to estimate the nuisance parameters of the data generation process including the shift date in a first step and apply standard unit root tests to the residuals. The estimation of the nuisance parameters is done in such a way that the unit root tests on the residuals have the same limiting distributions as for the case of a known break date.…

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ON A PARTITIONED INVERSION FORMULA HAVING USEFUL APPLICATIONS IN ECONOMETRICS

一种在计量经济学中具有应用价值的分块求逆公式

In this paper a novel partitioned inversion formula is obtained in terms of the orthogonal complements of off-diagonal blocks, with the emblematic matrix of unit-root econometrics emerging as the leading diagonal block of the inverse. The result paves the way to a straightforward derivation of a key result of vector autoregressive econometrics.

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TESTING LINEAR RESTRICTIONS ON COINTEGRATING VECTORS: SIZES AND POWERS OF WALD AND LIKELIHOOD RATIO TESTS IN FINITE SAMPLES

协整向量线性约束检验:Wald 与似然比检验的有限样本大小和功效

The Wald test for linear restrictions on cointegrating vectors is compared in finite samples using the Monte Carlo method. The Wald test is calculated within the vector error-correction based estimation methods of Bewley, Orden, Yang, and Fisher (1994, Journal of Econometrics 64, 3–27) and of Johansen (1991, Econometrica 59, 1551–1580), the canonical cointegration method of Park (1992, Econometrica 60, 119–143), the dynamic ordinary least squares method of Phillips and…

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Determination of cointegrating rank in fractional systems

分数阶系统中的协整秩确定

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a neighbourhood of frequency zero. We first discuss the definition of fractional cointegration. The initial step of cointegration analysis entails partitioning the vector series into subsets with…

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THE INVARIANCE PRINCIPLE FOR LINEAR PROCESSES WITH APPLICATIONS

线性过程的不变性原理及其应用

Let X t be a linear process defined by X t = [sum ] k=0 ∞ ψ k ε t − k , where {ψ k , k ≥ 0} is a sequence of real numbers and {ε k , k = 0,±1,±2,...} is a sequence of random variables. Two basic results, on the invariance principle of the partial sum process of the X t converging to a standard Wiener process on [0,1], are presented in this paper. In the first result, we assume that the innovations ε k are independent and identically distributed random variables but do not…

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The Message in Daily Exchange Rates

日度汇率传递的信息

Formal testing procedures confirm the presence of a unit root in the autoregressive ploynomial of the univariate time series representation of daily exchange-rate data. the first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and…

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Tests for Parameter Instability in Regressions With I(1) Processes

含 I(1) 过程的回归中的参数不稳定检验

This article derives the large-sample distributions of Lagrange multiplier (LM) tests for parameter instability against several alternatives of interest in the context of cointegrated regression models. The fully modified estimator of Phillips and Hansen is extended to cover general models with stochastic and deterministic trends. The test statistics considered include the SupF test of Quandt, as well as the LM tests of Nyblom and of Nabeya and Tanaka. It is found that the…

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