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Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
Most of the stationary first-order autoregressive integer-valued (INAR(1)) models were developed for a given thinning operator using either the forward approach or the backward approach. In the forward approach the marginal distribution of…
This paper introduces a flexible time-varying network vector autoregressive model framework for large-scale time series. A latent group structure is imposed on the heterogeneous and node-specific time-varying momentum and network spillover…
In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is ``stationarity'', which reflects the underlying dynamic behavior and is crucial across various…
This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…
Time Series forecasting (univariate and multivariate) is a problem of high complexity due the different patterns that have to be detected in the input, ranging from high to low frequencies ones. In this paper we propose a new model for…
This work is the first part of a project dealing with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian…
For stationary time series, it is common to use the plots of partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of such processes. To our best knowledge, such analogs for non-stationary…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
The first-order autoregressive process, AR (1), has been widely used and implemented in time series analysis. Different estimation methods have been employed in order to estimate the autoregressive parameter. This article focuses on…
Under a high-dimensional vector autoregressive (VAR) model, we propose a way of efficiently estimating both the stationary graph structure between the nodal time series and their temporal dynamics. The framework is then used to make…
Conditions are obtained for a Gaussian vector autoregressive time series of order $k$, VAR($k$), to have univariate margins that are autoregressive of order $k$ or lower-dimensional margins that are also VAR($k$). This can lead to…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It…
Inspired by the remarkable success of autoregressive models in language modeling, this paradigm has been widely adopted in visual generation. However, the sequential token-by-token decoding mechanism inherent in traditional autoregressive…
Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
This article studies identification and estimation for the network vector autoregressive model with nonstationary regressors. In particular, network dependence is characterized by a nonstochastic adjacency matrix. The information set…
We propose a new approach to inference in tightly identified and large-scale structural vector autoregressions based on a reparameterization that enables imposing identifying inequality restrictions through continuously differentiable…
Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional…