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复数 ARMA 过程的实部AI 解读

In what follows all processes referred to are weakly stationary. Let us call the real part of a complex ARMA(p,q) process a Re CARMA(p,q) process. Every real ARMA(p,q) process can trivially be written as a Re CARMA(p,q) process. Provided the moment properties of complex linear processes are appropriately specified, the following inverse result is available: every Re CARMA(p,q) process is spectrally equivalent to a real ARMA(2p,p + q) process or some simpler process. Thus the…

非正交不可观测成分模型中针对随机游走成分的最优检验AI 解读

In this paper we consider the problem of testing the null hypothesis that a series has a constant level (possibly as part of a more general deterministic mean) against the alternative that the level follows a random walk. This problem has previously been studied by, inter alia, Nyblom and Makelainen (1983) in the context of the orthogonal Gaussian random walk plus noise model. This model postulates that the noise component and the innovations to the random walk are…

C([0,1]) 上的积分不等式与近单整下 OLS 的离散程度AI 解读

We obtain an inequality for the sample variance of a vector Brownian motion on [0,1] and an associated Ornstein–Uhlenbeck process. The result is applied to a regression involving near-integrated regressors, and establishes that in the limit the dispersion of the least squares estimator is greater in the near-integrated than in the integrated case. Our proof uses a quite general integral inequality, which appears to be new.