Autocorrelated bivariate count data frequently arise in criminal, environmental and financial studies, where capturing both serial dependence and cross‐series interaction is essential for statistical modelling and inference. In many applications, such dynamics are further influenced by exogenous covariates such as policy interventions or environmental factors, leading to time‐varying dependence structures that are not adequately captured by standard models. Existing bivariate integer‐valued autoregressive (BINAR) models mainly rely on constant or observation‐driven coefficients and rarely incorporate covariate information, which restricts their ability to represent evolving dependence in multivariate count processes. To address this limitation, we propose a covariate‐driven doubly stochastic bivariate integer‐valued autoregressive process, in which the thinning mechanism evolves jointly with past observations and exogenous covariates. This formulation extends the classical BINAR framework by allowing the dependence structure to vary dynamically under both internal and external driving mechanisms. The basic statistical properties of the proposed process are derived, and two estimation methods are developed, including an EM‐based algorithm. Monte Carlo simulations and a real data application are conducted to assess finite‐sample performance and robustness under different settings.
Integer-valued time series are ubiquitous in fields such as finance, economics, and epidemiology. As spatiotemporal data structures in these domains grow increasingly complex and high-dimensional, the matrix integer-valued autoregressive (MINAR) model efficiently captures row-column cross-correlations to reduce dimensionality. However, it fundamentally fails to accommodate negative values, which is a critical flaw for analyzing real-world differenced data or financial tick fluctuations. To bridge this theoretical and practical gap, this paper introduces the Z-MINAR model, a novel matrix autoregressive framework defined on the full integer domain (Z). By pioneering a signed matrix thinning operator and utilizing an extended poisson distribution for the innovations, the Z-MINAR model elegantly handles both positive and negative integers while strictly preserving the crucial topological interactions inherent in matrix data. Furthermore, we employ a projection-based conditional least squares estimation procedure and rigorously establish the model's stationarity, causality, and asymptotic normality. Extensive simulations demonstrate the superior estimation accuracy, robustness, and adaptability of Z-MINAR over existing benchmark models. Finally, an empirical application focusing on crime count variations across different urban regions confirms the model's practical efficacy in uncovering dynamic spatiotemporal dependence structures in Z-valued matrix time series.
Identifying the autoregressive (AR) orders of a multivariate time series is a foundational step whose accuracy governs every downstream modelling and forecasting task. When the series exhibits two simultaneously operating seasonal periodicities, as is routinely observed in hourly electricity loads and intraday financial prices, no principled Bayesian identification framework currently exists. This paper addresses this gap by introducing a complete Bayesian order identification procedure for double-seasonal vector autoregressive (DSVAR) models. These DSVAR models are multivariate processes governed by a multiplicative triple autoregressive operator that jointly captures regular, first-seasonal, and second-seasonal dynamics. We treat the three order indices as unknown discrete parameters and derive closed-form expressions for the joint posterior probability mass function of the order triple. Two complementary prior specifications are considered: a conjugate matrix normal-Wishart prior and Jeffreys’ non-informative prior. The analysis is carried out under the assumption of symmetric, normally distributed errors, which ensures analytical tractability and allows for the posterior probabilities to be evaluated exactly for every admissible combination of orders. Specifically, under each prior, the posterior mass function reduces to explicit determinantal expressions that can be evaluated by a straightforward three-dimensional grid search. Monte Carlo experiments on various DSVAR processes confirm that the proposed technique achieves high identification accuracy even at moderate sample sizes across a range of parameter configurations and prior choices. The proposed Bayesian procedure is benchmarked against the standard Bayesian information criterion (BIC), consistently achieving higher correct identification rates across all cases. Empirical applications to hourly electricity load data from the Czech Republic and Germany, as well as to hourly solar radiation in Najran, Saudi Arabia, demonstrate the practical applicability of the Bayesian identification method.
Ayman A. Amin, F. Almuhayfith· Mathematics· 0 citations
A wide range of real-world multivariate time series encountered in practice exhibit two simultaneous and interacting seasonal cycles, for example hourly electricity demand, intraday financial prices, and sub-daily traffic volumes. Existing Bayesian frameworks for vector autoregressive (VAR) processes accommodate at most a single seasonal periodicity, leaving no established methodology for the double seasonal case commonly observed in high-frequency multivariate data. This paper bridges that gap by introducing the double seasonal VAR (DSVAR) models, which extend the univariate double seasonal literature to a coherent multivariate setting. These models are defined through a multiplicative triple autoregressive operator that naturally accommodates the second seasonal cycle. Under a Gaussian error assumption, we derive a comprehensive and analytically convenient Bayesian framework for both modeling and forecasting of DSVAR processes. We consider two prior families: a conjugate matrix normal-Wishart prior which yields exact closed-form inference, and a Jeffreys’ non-informative prior. Under each prior, we derive the marginal posterior distribution of the coefficient matrix as a matrix-t distribution and the marginal posterior of the precision matrix as a Wishart distribution. Moreover, we derive the predictive distribution of future observations as a multivariate-t with an exact analytic form, together with its highest predictive density regions. The methodology is validated through a Monte Carlo simulation experiment and applied to hourly electricity loads in Czech Republic and Germany, two physically interconnected markets with pronounced intraday and intraweek seasonal cycles. Benchmark comparisons against standard VAR, single-seasonal VAR, and univariate seasonal AR models confirm the substantial forecasting gains delivered by the proposed DSVAR framework at both short and long horizons.
Ayman A. Amin, F. Almuhayfith· Mathematics· 0 citations
Hierarchical Bayesian smooth transition autoregressive models provide accurate forecasts by accommodating nonlinear regime-switching dynamics while delivering robust uncertainty quantification, which makes them well suited for infectious disease surveillance and public health decision-making in resource-limited, high-uncertainty settings.
G. Singini, Samuel Manda· Frontiers in Applied Mathema...· 0 citations
Despite its conceptual appeal, the autoregressive inverse‐Wishart (AIW) multivariate stochastic volatility model has been hindered by inefficient sampling methods. The existing samplers for the latent covariance matrix severely suffer from the curse of dimensionality and only work when the dimension is very low. In this paper, we introduce a new proposal for the latent covariance matrix in the AIW model, which demonstrates far better scalability. We introduce different extensions to the basic AIW model that capture various stylized volatility features. We further fit the AIW model into a factor structure and provide an a posteriori identification procedure without introducing order dependence. When evaluated using real datasets ranging from 10 assets to 1000 assets, the new AIW‐based models, whether the standalone versions or the factor versions, are especially suited for multivariate volatility modeling in a wide range of dimensions.
Xin Jin· Journal of applied econometr...· 0 citations
The proposed additive ODE–SDE model produces a close fit with coherent uncertainty quantification and a flexible seasonal reconstruction, while keeping the mechanistic transmission model interpretable.
Miracle Amadi, J. García-Merino, H. Haario· Bulletin of Mathematical Bio...· 0 citations
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