arXiv subjects

Fanny Godet

Publications and source records attributed to Fanny Godet.

3 recordsLinked to original sources

arXiv2008

Prediction of long memory processes on same-realisation

For the class of stationary Gaussian long memory processes, we study some properties of the least-squares predictor of X_{n+1} based on (X_n, ..., X_1). The predictor is obtained by projecting X_{n+1} onto the finite past and the coefficients of the predictor are estimated on the same realisation. First we prove moment bounds for the inverse of the empirical covariance matrix. Then we deduce an asymptotic expression of the mean-squared error. In particular we give a relation between the number of terms used to estimate the coefficients and the number of past terms used for prediction, which ensures the L^2-sense convergence of the predictor. Finally we prove a central limit theorem when our predictor converges to the best linear predictor based on all the past.

math.ST↗

arXiv2007

Linear Prediction of Long-Memory Processes: Asymptotic Results on Mean-squared Errors

We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values in practice. We derive the asymptotic behaviour of the mean-squared error as $k$ tends to $ + \infty$. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long-memory time series and we study the error that arises in this misspecified model.

math.ST↗

arXiv2007

Linear Prediction of Long-Range Dependent Time Series

We present two approaches for next step linear prediction of long memory time series. The first is based on the truncation of the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values in practice. Part of the mean squared prediction error comes from the truncation, and another part comes from the parametric estimation of the parameters of the predictor. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long memory time series and we study the error made with this misspecified model.

math.ST↗