This paper addresses the issue of quantifying the frequency domain accuracy of ARMA spectral estimates as dictated by the Cramér–Rao Lower Bound (CRLB). Classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity, although they are commonly used in finite model order and finite data length settings as approximations. More...

For autoregressive and moving-average (ARMA) models with infinite variance innovations, quasi-likelihood based estimators (such as Whittle’s estimators ) suffer from complex asymptotic distributions depending on unknown tail indices. This makes the statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with hea...

4. Course Outline: (i) Review of Linear ARMA/ARIMA Time Series Models and their Properties. (ii) An Introduction to Spectral Analysis of Time Series. (iii) Fractional Differencing and Long Memory Time Series Modelling. (iv) Generalized Fractional Processes. Gegenbaur Processes. (v) Topics from Financial Time Series/Econometrics: ARCH and GARCH Models. (vi ) Time Series Modelling of Durations: A...

Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes....

Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set R are determined. Under these conditions the solution is shown to be unique and an explicit expression is given for the process as an integral with respect to the background driving Lévy process. The results gene...

The aim of this paper is the presentation of time-variant spectrograms of surface EMG signals to estimate fatigue processes in muscle and to consider recruitments of motor units. For this we used techniques on the base of ARMA and AR models. We illustrate our applications by three examples: influence of training to maximal and explosive isometric contraction, fatigue processes in an all-out cyc...

The space of rational matrices with xed size and degree is shown to have a manifold structure with bers over a Grassmannian. The bers are homeomorphic to a suitable space of strictly proper rational matrices. This structure is compatible with Willems' partition of external variables into inputs and outputs.

We consider the tting of latent Gaussian models to categorical time series of cow feeding data. We derive a spectral quasi-likelihood for the data, and compare it with least squares ts to autocorrelations and MCMC estimators of the parameters in thresholded ARMA processes. We show that the spectral method is more e cient than least squares and far faster than MCMC.

In order to predict unobserved values of a linear process with infinite variance, we introduce a linear predictor which minimizes the dispersion (suitably defined) of the error distribution. When the linear process is driven by symmetric stable white noise this predictor minimizes the scale parameter of the error distribution. In the more general case when the driving white noise process has re...