In this note we consider the autoregressive moving average recurrent neural network ARMA-NN(1; 1) process. We show that in contrast to the pure autoregressive process simple ARMA-NN processes exist which are not irreducible. We prove that the controllability of the linear part of the process is sufficient for irreducibility. For the irreducible process essentially the shortcut weight correspond...

In the next example, the signal vector randomization method (SVR1) as given in (9), the deterministic SVR method (SVR2) as given in (11), the frequency estimation method (TK) outlined in Section III, and the spatial smoothing methods are compared. All three sources are perfectly correlated, i.e., they have a zero relative phase angle at each iteration, e.g., multipath propagation where the path...

In this letter, we study the modulo-limit modulator whose input signal is a causal stable ARMA process. We prove that for all the cases, the normalized quantization error can be taken as a uniformly distributed white noise.

Two distinct families of statistical processes are considered in the production of psychophysical time series data (Gilden, 1997, 2001; Gilden, Thornton, & Mallon, 1995). We inquire whether the spectral signatures of the underlying dynamics are better described in terms of short-range autoregressive moving-average (ARMA) processes or long-range fractal processes. A thorough presentation of both...

The needs of accuracy of machines are strictly increasing for the manufacturing processes. It is costly to use high precision machine to achieve the goal. Therefore, if the forecasting of errors can be obtained from the gathered past error values, it allows the control system to compensate the errors. In this paper, the simulations of manufacturing processes are using the ARMA and ARMAX models....

Discrete-time ARMA processes can be placed in a one-to-one correspondence with a set of continuous-time processes that are bounded in frequency by the Nyquist value of π radians per sample period. It is well known that, if data are sampled from a continuous process of which the maximum frequency exceeds the Nyquist value, then there will be a problem of aliasing. However, if the sampling is too...

The tail behaviour of stationary R-valued Markov-Switching ARMA processes driven by a regularly varying noise is analysed. It is shown that under appropriate summability conditions the MS-ARMA process is again regularly varying as a sequence. Moreover, the feasible stationarity condition given in Stelzer (2006) is extended to a criterion for regular variation. Our results complement in particul...

In our earlier work, we introduced a class of stochastic processes obeying a structure of the form, E [ X ( t ) X ( t X ) ] = R(X), t , X > 0, and outlined a mathematical framework for the modeling and analysis for these processes. We referred to this class of processes as scale stationary processes. We demonstrated that scale stationarity framework leads to engineering oriented mathematical to...

We analyze in this work the effect of the iterated application of the linear operator that maps a Wiener process onto an OrnsteinUhlenbeck process. The processes obtained after p iterations are called Ornstein-Uhlenbeck processes of order p (denoted OU(p)). Technically our composition of operators is easy to manipulate and its parameters can be computed efficiently because, as we show, in most ...