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利用扩展函数型Delta方法检验未知时点的相关性变化AI 解读

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional delta method argument, provide a formula for its local power for particular types of structural changes, give some Monte Carlo evidence on its finite-sample behavior, and apply it to…

We consider the finite-sample power of various tests against serial correlation in the disturbances of a linear regression model when these disturbances follow certain stationary long-memory processes. It emerges that the power depends on the form of the regressor matrix and that, for the Durbin--Watson test and many other tests that can be written as ratios of quadratic forms in the disturbances, the power can drop to zero as the long-memory parameter approaches the…

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基于 OLS 残差的抗趋势结构变化检验AI 解读

We discuss the null distribution and local power of an OLS-based version of the CUSUM test and show that this, contrary to other tests for structural change like, e.g., the Ploberger-Kontrus-Krämer fluctuation test, can also be applied to trending data.

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误差的空间自相关与线性回归中 OLS 的相对效率AI 解读

The article considers the efficiency of ordinary least squares (OLS) coefficient estimates relative to generalized least squares (GLS) in a linear regression model where the disturbances follow a spatial autocorrelation pattern. The main result is that the limiting relative efficiency of OLS, as correlation among disturbances increases, tends to either zero or unity for most design matrices and correlation patterns encountered in practice. Which of these cases applies…

自变量服从 ARIMA 过程时的最小二乘回归AI 解读

In the regression model yt = α + βxt + ut where the disturbances ut may be autocorrelated and xt follows an ARIMA(p, 1, q) process, it is shown that the asymptotic distributions of the ordinary and generalized least squares estimates of β are identical.

自相关误差线性回归中普通最小二乘的有限样本效率AI 解读

In the standard linear regression model y = X β + u, with errors following a first-order stationary autoregressive process, it is shown that the relative efficiency of the ordinary least squares (OLS) as compared with the Gauss-Markov estimator depends to a great extent on the X matrix observed. In particular, it is seen that the relative efficiency of OLS increases with increasing correlation for certain cases important in practice. Since this seems to run contrary to what…