Related papers: On model fitting and estimation of strictly statio…
We propose an $L^2$ norm for stationary Autoregressive Moving Average (ARMA) models. We look at ARMA models within the Hilbert space of the past with present of a true purely linearly non-deterministic stationary process $X_t$, and compute…
Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential…
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…
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…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…
We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those…
Linear processes on functional spaces were born about fifteen years ago. And this original topic went through the same fast development as the other areas of functional data modeling such as PCA or regression. They aim at generalizing to…
Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for…
Predicting future probable values of model parameters, is an essential pre-requisite for assessing model decision reliability in an uncertain environment. Scenario Analysis is a methodology for modelling uncertainty in water resources…
In this paper, we give a AR$(1)$ type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, we derive continuous time algebraic Riccati equations for the parameter matrix…
This paper studies system identification of high-dimensional ARMA models with binary-valued observations. The existing paper can only deal with the case where the regression term is only one-dimensional. In this paper, the ARMA model with…
Nonstationarity of real-life time series requires model adaptation. In classical approaches like ARMA-ARCH there is assumed some arbitrarily chosen dependence type. To avoid their bias, we will focus on novel more agnostic approach: moving…
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…
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…
We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two…
Generally, anomaly detection has a great importance particularly in applied statistical signal processing. Here we provide a general framework in order to detect anomaly through the statistical modeling. In this paper, it is assumed that a…
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…