Related papers: Modeling of Stationary Periodic Time Series by ARM…
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
The rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite-dimensional positive-definite Toeplitz matrix…
Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task.…
In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complex-valued Ornstein-Uhlenbeck processes under some mild assumptions. The…
A new model for general cyclical long memory is introduced, by means of random modulation of certain bivariate long memory time series. This construction essentially decouples the two key features of cyclical long memory: quasi-periodicity…
Stationary reciprocal processes defined on a finite interval of the integer line can be seen as a special class of Markov random fields restricted to one dimension. Non stationary reciprocal processes have been extensively studied in the…
The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time…
This article develops a periodic version of a time varying parameter fractional process in the stationary region. It is a partial extension of Hosking (1981)'s article which dealt with the case where the coefficients are invariant in time.…
This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
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 series analysis, AR models have been extended to incorporate…
Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification…
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
The paper investigates the theoretical properties of zero-mean stationary time series with cyclical components, admitting the representation $y_t=\alpha_t \cos \lambda t + \beta_t \sin \lambda t$, with $\lambda \in (0,\pi]$ and…
The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the $\alpha$-stable locally stationary process by modifying the innovations…
In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling…
In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important…
This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of…
Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of…