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时间序列回归中的单位根检验AI 解读

This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The…

自回归过程差分阶数的确定AI 解读

One way of handling nonstationarity in time series is to compute first differences and fit a model to the differenced series unless the differenced series also looks nonstationary. In that case, second- or higher-order differencing is done. To decide if the current degree of differencing is sufficient, one can look at the autocorrelation function for slow decay. A formal statistical test for the need to difference further is available if one is willing to assume that at most…

单变量时间序列二阶差分的对称检验AI 解读

A test for the null hypothesis that a time series has characteristic equations with two unit roots is presented. The test, based on a standard regression computation, is shown to have good power properties when compared to previously existing tests.

迈向自回归模型的统一渐近理论AI 解读

This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these alternatives and helps to unify earlier theory in which the…

协整向量最小二乘估计量的渐近性质AI 解读

Time series variables that stochastically trend together form a cointegrated system. OLS and NLS estimators of the parameters of a cointegrating vector are shown to converge in probability to the true parameter value at the rate T11d for any positive d. These estim mators can be written asymptotically in terms of relatively simple nonnormal random matrices which do not depend on the parameters of th e system. These asymptotic representations form the basis for simple and…

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含单位根的时间序列回归AI 解读

This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the…

协整与误差修正：表示、估计与检验AI 解读

The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a…

迈向统一的自回归渐近理论AI 解读

This paper develops an asymptotic theory for a first-order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these possibilities and helps to unify earlier theory in which the…

理解计量经济学中的伪回归AI 解读

This paper provides an analytical study of linear regressions involving the levels of economic time series. An asymptotic theory is developed for regressions that relate quite general integrated random processes. This includes the spurious regressions of Granger and Newbold (1974) and the recent cointegrating regressions of Granger and Engle (1985). An asymptotic theory is developed for the regression coefficients and for conventional significance tests. It is shown that the…

含一阶单整过程的多元时间序列回归AI 解读

This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems such as those advanced recently by Granger and Engle and quite general linear simultaneous equations systems with…

观测时间序列单位根检验的理论AI 解读

This paper provides a framework for testing for a unit root in an observed time series against some alternatives considered previously by Anderson (1948). Some new tests for the unit root null hypothesis for the errors affecting a classical regression model against the non-stationary (including explosive) alternative hypothesis are developed. The previous results of Sargan and Bhargava (1983) and the new test statistics are then applied to test the simple random walk and the…

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近非平稳一阶自回归模型的参数推断AI 解读

The finite sample behaviour of the score function in a first-order autoregression is investigated. An object is to interpret the transition of the distribution of the score when the model approaches a nonstationary situation with a unit root. A framework is presented wherein the nonnormality of the score is clearly seen. Also, a simple interpretation for the behaviour of the distribution in terms of two chi-squared variables is given. Approximate finite sample distributions…

季节性时间序列的单位根检验AI 解读

Regression estimators of coefficients in seasonal autoregressive models are described. The percentiles of the distributions for time series that have unit roots at the seasonal lag are computed by Monte Carlo integration for finite samples and by analytic techniques and Monte Carlo integration for the limit case. The tabled distributions may be used to test the hypothesis that a time series has a seasonal unit root.

未知阶数 ARMA 模型的单位根检验AI 解读

Recently, methods for detecting unit roots in autoregressive and autoregressive-moving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an…

近非平稳一阶自回归模型的参数推断AI 解读

The finite sample behaviour of the score function in a first-order autoregression is investigated. An object is to interpret the transition of the distribution of the score when the model approaches a nonstationary situation with a unit root. A framework is presented wherein the nonnormality of the score is clearly seen. Also, a simple interpretation for the behaviour of the distribution in terms of two chi-squared variables is given. Approximate finite sample distributions…

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含单位根的自回归过程估计AI 解读

Let $Y_t$ satisfy the stochastic difference equation $Y_t = \sum^p_{j = 1}\eta_jY_{t - j} + e_t$ for $t = 1, 2, \cdots$, where the $e_t$ are independent identically distributed $(0, \sigma^2)$ random variables and the initial conditions $(Y_{-p + 1}, Y_{-p + 2}, \cdots, Y_0)$ are fixed constants. It is assumed the true, but unknown, roots $m_1, m_2, \cdots, m_p$ of $m^p - \sum^p_{j = 1}\eta_jm^{p - j} = 0$ satisfy $m_1 = m_2 = 1$ and $|m_j| < 1$ for $j = 3, 4, \cdots, p$.…

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具有单位根的自回归时间序列估计量分布AI 解读

Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of…