Related papers: Forecasting time series of inhomogeneous Poisson p…

A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…

Today's call center managers face multiple operational decision-making tasks. One of the most common is determining the weekly staffing levels to ensure customer satisfaction and meeting their needs while minimizing service costs. An…

We introduce a new method for forecasting emergency call arrival rates that combines integer-valued time series models with a dynamic latent factor structure. Covariate information is captured via simple constraints on the factor loadings.…

Call centers' managers are interested in obtaining accurate point and distributional forecasts of call arrivals in order to achieve an optimal balance between service quality and operating costs. We present a strategy for selecting forecast…

Tensor time series data appears naturally in a lot of fields, including finance and economics. As a major dimension reduction tool, similar to its factor model counterpart, the idiosyncratic components of a tensor time series factor model…

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…

Arrival processes to service systems often display (i) larger than anticipated fluctuations, (ii) a time-varying rate, and (iii) temporal correlation. Motivated by this, we introduce a specific non-homogeneous Poisson process that…

In the context of time series forecasting, it is a common practice to evaluate multiple methods and choose one of these methods or an ensemble for producing the best forecasts. However, choosing among different ensembles over multiple…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating…

We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…

We introduce a general framework for monitoring, modelling, and predicting the recruitment to multi-centre clinical trials. The work is motivated by overly optimistic and narrow prediction intervals produced by existing time-homogeneous…

This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…

Forecasting recruitments is a key component of the monitoring phase of multicenter studies. One of the most popular techniques in this field is the Poisson-Gamma recruitment model, a Bayesian technique built on a doubly stochastic Poisson…

In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…

In a call center, staffing decisions must be made before the call arrival rate is known with certainty. Then, once the arrival rate becomes known, the call center may be over-staffed, in which case staff are being paid to be idle, or…

Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

Motivated by monitoring the arrival of incoming adverse events such as customer support calls or crash reports from users exposed to an experimental product change, we consider sequential hypothesis testing of continuous-time inhomogeneous…