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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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Asymptotic Inference on Cointegrating Rank in Partial Systems

部分系统中协整秩的渐近推断

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.

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Modeling Inflation in Australia

澳大利亚通胀建模

This article develops an empirically constant, data-coherent, error-correction model for inflation in Australia. The level of consumer prices is a markup over domestic and import costs, with adjustments for dynamics and relative aggregate demand. The authors address issues of cointegration, general to specific modeling, dynamic specification, model evaluation and testing, parameter constancy, forecasting, and exogeneity. They also test this model against existing models of…

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AN AUTOREGRESSIVE SPECTRAL DENSITY ESTIMATOR AT FREQUENCY ZERO FOR NONSTATIONARITY TESTS

用于非平稳性检验的零频自回归谱密度估计量

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant…

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Testing and Modeling Multivariate Threshold Models

多元门限模型的检验与建模

Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this article I use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The finite-sample performance of the…

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Tests for cointegration with infinite variance errors

无限方差误差下的协整检验

This paper develops the asymptotic theory for residual-based tests and quasi-likelihood ratio tests for cointegration under the assumption of infinite variance errors. This article extends the results of Phillips and Ouliaris (1990) and Johansen (1988, 1991) which are derived under the assumption of square-integrable errors. Here the limit laws are expressed in terms of functionals of symmetric stable laws rather than Brownian motion. Critical values of the residual-based…

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Adaptive estimation of cointegrating regressions with ARMA errors

具有 ARMA 误差的协整回归自适应估计

Adaptive maximum likelihood estimators are derived for the parameters of a cointegrating regression whose errors follow a stationary and invertible ARMA process with innovations of unknown distribution. It is shown how to use preliminary estimates of these innovations to nonparametrically estimate their density, which can in turn be used to construct an asymptotically efficient iterative estimator of the cointegrating vector. The asymptotic distribution of this estimator is…

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Maximum-Likelihood Estimation of Fractional Cointegration with an Application to U.S. and Canadian Bond Rates

分数协整的极大似然估计:美国与加拿大债券利率的应用

We estimate a multivariate ARFIMA model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series. Previous cointegration tests relied on a two-step testing procedure and maintained the assumption in the second step that the parent series were known to have a unit root. In our empirical example of fractional cointegration, we illustrate how uncertainty regarding the order…

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Analysis of cointegration vectors using the GMM approach

使用 GMM 方法分析协整向量

This paper generalizes Johansen's (1988) maximum likelihood approach of the analysis of cointegrating vectors to the generalized method of moments (GMM) approach. We derive the asymptotic distribution of the cointegration vectors estimated from the fully modified generalized method of moments (FM-GMM) estimation procedure. We also introduce the FM-GMM version of Johansen's (1988) likelihood ratio (LR) test for the rank of a cointegrating matrix. Unlike the LR test which has…

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A Locally Optimal Seasonal Unit-Root Test

局部最优的季节单位根检验

This article proposes a locally best invariant test of the null hypothesis of seasonal stationarity against the alternative of seasonal unit roots at all or individual seasonal frequencies. An asymptotic distribution theory is derived and the finite-sample properties of the test are examined in a Monte Carlo simulation. My test is also compared with the Canova and Hansen test. The proposed test is superior to the Canova and Hansen test in terms of both size and power.

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Unit-Root Tests and Asymmetric Adjustment With an Example Using the Term Structure of Interest Rates

单位根检验与非对称调整:利率期限结构示例

This article develops critical values to test the null hypothesis of a unit root against the alternative of stationarity with asymmetric adjustment. Specific attention is paid to threshold and momentum threshold autoregressive processes. The standard Dickey–Fuller tests emerge as a special case. Within a reasonable range of adjustment parameters, the power of the new tests is shown to be greater than that of the corresponding Dickey–Fuller test. The use of the tests is…

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Estimating the Kronecker indices of cointegrated echelon‐form VARMA models

协整阶梯形 VARMA 模型的 Kronecker 指数估计

VARMA models can be parameterized by using the echelon form, which is characterized by the Kronecker indices. Three different methods for estimating the Kronecker indices of echelon-form VARMA models are discussed and compared. The three methods are expected to work even for non-stationary processes with cointegrated variables. They have the common feature of estimating the individual equations of the system separately and using order selection criteria. The small sample…

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Fully Modified Vector Autoregressive Inference in Partially Nonstationary Models

部分非平稳模型中完全修正向量自回归的推断

The likelihood ratio (LR) test for ranks is commonly used to test for the number of cointegrating relationships among multivariate time series. The distribution of the LR test in partially nonstationary models is nonstandard and contains nuisance parameters in the presence of non-iid errors and misspecified lags. In contrast, I show that under less-restrictive assumptions on the errors, the fully modified (FM) vector autoregressive (VAR) rank test has a chi-squared…

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A Unified Approach to Identifying Multivariate Time Series Models

识别多元时间序列模型的统一方法

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

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A Unified Approach to Identifying Multivariate Time Series Models

多元时间序列模型识别的统一方法

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

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TIME-SERIES-BASED ECONOMETRICS

以时间序列为基础的计量经济学

Since the influential work by Nelson and Plosser (1982) and Engle and Granger (1987), many new and exciting developments have been made in the analysis of time series involving autoregressive unit roots. Hatanaka (1996; hereafter HT) reviewed the literature on unit roots and cointegration up to 1994 and provided new perspectives on this research area.

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EFFECT OF A SHIFT IN THE TREND FUNCTION ON DICKEY–FULLER UNIT ROOT TESTS

趋势函数突变对 Dickey–Fuller 单位根检验的影响

This article analyzes the asymptotic behavior of the Dickey–Fuller unit root tests when the variable is generated under the breaking trend hypothesis. Our results show that the asymptotic behavior of these statistics allows for the rejection of the unit root hypothesis. This asymptotic finding contrasts with the results that can be found in the literature devoted to the analysis of the integration order of a variable in the presence of a structural break. However, some Monte…

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ON ESTIMATING AN ARMA MODEL WITH AN MA UNIT ROOT

含 MA 单位根的 ARMA 模型估计

This paper investigates the behavior of the maximum likelihood estimator of a Gaussian autoregressive moving average model with a unit root in the moving average polynomial. The results are primarily of interest in testing hypotheses that involve moving average unit roots as, for example, when testing for stationarity of a series.

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On Seasonal Cycles, Unit Roots, and Mean Shifts

季节周期、单位根与均值变化

The interpretation of seasonality in terms of economic behavior depends on the form of the econometric time-series model that allows for a description of seasonality. Popular models often assume either approximate deterministic seasonality (cf. Miron (1996)) or stochastic trend seasonality (cf. Hylleberg (1994)). Inference from an inappropriate model can be shown to be invalid. Since much graphical evidence clearly suggests that seasonal fluctuations are not constant over…

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Small-sample Confidence Intervals for Impulse Response Functions

脉冲响应函数的小样本置信区间

Bias-corrected bootstrap confidence intervals explicitly account for the bias and skewness of the small-sample distribution of the impulse response estimator, while retaining asymptotic validity in stationary autoregressions. Monte Carlo simulations for a wide range of bivariate models show that in small samples bias-corrected bootstrap intervals tend to be more accurate than delta method intervals, standard bootstrap intervals, and Monte Carlo integration intervals. This…

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