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单位根检验准则的比较AI 解读

The ordinary least squares estimator has been widely used for testing the unit-root hypothesis in autoregressive processes. Recently, several new criteria, based on maximum likelihood and weighted symmetric estimators, have been proposed. In this article, the authors describe several different test criteria. Results from Monte Carlo studies that compare the power of the different test criteria indicate that the new tests are more powerful against the stationary alternative.…

二阶自回归多项式根的大样本分布AI 解读

The roots of the characteristic polynomial of an autoregressive process are sometimes of interest. In this paper, we show that the estimated roots of a second order autoregressive polynomial have different asymptotic distributions depending upon whether the true roots are equal or unequal.

摘要暂缺

Several test criteria are available for testing the hypothesis that the autoregressive polynomial of an autoregressive moving average process has a single unit root. Schwert (1989), using a Monte Carlo study, investigated the performance of some of the available test criteria. He concluded that the actual levels of the test criteria considered in his study are far from the specified levels when the moving average polynomial also has a root close to 1. This article studies…

时间序列数据中的单位根检验AI 解读

Let Y t satisfy the stochastic difference equation for t = 1,2,…, where e t are independent and identically distributed random variables with mean zero and variance σ 2 and the initial conditions ( Y −p+1 ,…, Y 0 ) are fixed constants. It is assumed that the process is invertible and that the true, but unknown, roots m 1 , m 2 ,…, m p of satisfy the hypothesis H d : m 1 = … = m d = 1 and | m j | < 1 for j = d + 1,…, p . We present a reparameterization of the model for Y t…

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…