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非平稳性与水平突变：购买力平价应用AI 解读

The authors consider testing for a unit root in a time series with a structural change in mean occurring at an unknown date. They derive and tabulate the asymptotic distributions of the minimal t-statistic over all possible break points (and other related statistics) in the appropriate regressions. However, emphasis is given to the tabulation of finite sample critical values with particular attention given to the effect of various procedures to select the order of the…

采样频率变化下的检验一致性AI 解读

This paper considers the consistency property of some test statistics based on a time series of data. While the usual consistency criterion is based on keeping the sampling interval fixed, we let the sampling interval take any equispaced path as the sample size increases to infinity. We consider tests of the null hypotheses of the random walk and randomness against positive autocorrelation (stationary or explosive). We show that tests of the unit root hypothesis based on the…

平稳一阶自回归模型的连续时间近似AI 解读

We consider the least-squares estimator in a strictly stationary first-order autoregression without an estimated intercept. We study its continuous time asymptotic distribution based on an asymptotic framework where the sampling interval converges to zero as the sample size increases. We derive a momentgenerating function which permits the calculation of percentage points and moments of this asymptotic distribution and assess the adequacy of the approximation to the finite…

不含截距的不稳定一阶自回归过程的连续时间近似AI 解读

We consider a first-order autoregression with i.i.d. errors and a fixed initial condition. The asymptotic distribution of the normalized least-squares estimator as the sampling interval converges to zero is shown to be the same as the exact distribution of the continuous-time estimator in an Ornstein-Uhlenbeck process. This asymptotic distribution permits explicit consideration of the effect of the initial condition. The appropriate moment-generating function is derived and…

均值发生变化的时间序列单位根检验AI 解读

This study considers testing for a unit root in a time series characterized by a structural change in its mean level. My approach follows the “intervention analysis” of Box and Tiao (1975) in the sense that I consider the change as being exogenous and as occurring at a known date. Standard unit-root tests are shown to be biased toward nonrejection of the hypothesis of a unit root when the full sample is used. Since tests using split sample regressions usually have low power,…

大崩盘、石油价格冲击与单位根假说AI 解读

The unit root hypothesis is examined allowing a possible one-time change in the level or in the slope of the trend function. When fluctuations are stationary around a breaking trend function, standard tests cannot reject the unit root, even asymptotically. Consistent tests are derived and applied to the Nelson-Plosser data set (allowing a change in level for the 1929 crash) and to the postwar quarterly real GNP series (allowing a change in slope after 1973). The unit root…

近单位根模型中最小二乘估计量极限分布的计算AI 解读

We tabulate the limiting cumulative distribution and probability density functions of the least-squares estimator in a first-order autoregressive regression when the true model is near-integrated in the sense of Phillips. The results are obtained using an exact numerical method which integrates the appropriate limiting moment generating function. The adequacy of the approximation is examined for various first-order autoregressive processes with a root close to unity.

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…