On asymptotic normality of estimates of impulse response function for linear systems. I. (English. Russian original) Zbl 0927.62096

Buldygin, V. V.; Fu, Lee.

Theory Probab. Math. Stat. 54, 17-24 (1997); translation from Teor. Jmovirn. Mat. Stat. 54, 16-24 (1996).

The authors study the causal linear systems \[ Y_{\Delta}(t)=\int_0^{\infty}H(\tau)X_{\Delta}(t-\tau)d\tau,\quad H(\tau)=0,\quad \tau\leq 0. \] They consider systems for \(X_{\Delta},\) which is not a white noise. Properties of the estimates \[ \widehat H_{T,\Delta}(\tau)=(cT)^{-1} \int_0^T X_{\Delta}(t)Y_{\Delta}(t+\tau)dt \] of the impulse response function \(H\) for stationary Gaussian \(X_{\Delta}\) are obtained. Asymptotic properties of the correlation function of \[ Z_{T,\Delta}(\tau)=\sqrt{T}[ \widehat H_{T,\Delta}(\tau)-E \widehat H_{T,\Delta}(\tau)] \] are considered.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

62M20	Inference from stochastic processes and prediction
62G20	Asymptotic properties of nonparametric inference
60G35	Signal detection and filtering (aspects of stochastic processes)

Keywords:

asymptotic normality; linear systems; impulse response functions; stationary Gaussian processes

Citations:

Zbl 0927.62097