CIR bridge for modeling of fish migration on sub-hourly scale

TL;DR

This paper introduces a novel CIR bridge model for accurately representing fish migration patterns within a day, enabling efficient parameter estimation and application to real migration data.

Contribution

The paper develops the first CIR bridge model with closed-form moments for modeling intraday fish migration, including a new numerical method for computation.

Findings

Successfully modeled fish migration counts with the CIR bridge.

Achieved efficient parameter estimation using closed-form moments.

Applied the model to real fish migration data in Japan.

Abstract

Bridges, which are stochastic processes with pinned initial and terminal conditions, have recently been applied to various problems. We show that a bridge based on the Cox-Ingersoll-Ross process, called a CIR bridge in this paper, reasonably models the intraday number of migrating fish at an observation point in a river. The studied fish migrates between sunrise and sunset each day, which are considered the initial and terminal times, respectively. The CIR bridge is well-defined as a unique pathwise continuous solution to a stochastic differential equation with unbounded drift and diffusion coefficients and potentially represents the on-off intermittency of the fish count data. Our bridge is theoretically novel in that it admits closed-form time-dependent averages and variances, with which the model parameters can be identified efficiently, and is computable by a recently-developed one-step numerical method. The CIR bridge is applied to the sub-hourly migration data of the diadromous fish Plecoglossus altivelis altivelis in the Nagara River, Japan, from February to June.