5 papers
A spectral based coefficient of determination for the fit of an MA(q) model
Holger Dette, Sebastian Kühnert, Sebastian Kühnert
We develop a spectral based coefficient of determination to measure how well the spectral density of a stationary linear process is represented by the class of MA() models. Usin…
Pivotal inference for linear predictions in stationary processes
Holger Dette, Sebastian Kühnert
In this paper we develop pivotal inference for the final (FPE) and relative final prediction error (RFPE) of linear forecasts in stationary processes. Our approach is based on a se…
An operator-level ARCH Model
Alexander Aue, Sebastian Kühnert, Gregory Rice +1
AutoRegressive Conditional Heteroscedasticity (ARCH) models are standard for modeling time series exhibiting volatility, with a rich literature in univariate and multivariate setti…
Functional Periodic ARMA Processes
Sebastian Kühnert, Juhyun Park
Periodicity is a common feature of time series. For finite-dimensional data, periodic autoregressive moving average (ARMA) models have been extensively studied. In functional time…
Estimating invertible processes in Hilbert spaces, with applications to functional ARMA processes
Sebastian Kühnert, Gregory Rice, Alexander Aue
Invertible processes are central to functional time series analysis, making the estimation of their defining operators a key problem. While asymptotic error bounds have been establ…