Estimating a Smooth Common Transfer Function with a Panel of Time Series - Inflow of Larvae Cod as an Example

Elizabeth Hansen, Kung-Sik Chan, Nils Chr. Stenseth

Abstract


The annual response variable in an ecological monitoring study often relates linearly to the weighted cumulative effect of some daily covariate, after adjusting for other annual covariates. Here we consider the problem of non-parametrically estimating the weights involved in computing the aforementioned cumulative effect, with a panel of short and contemporaneously correlated time series whose responses share the common cumulative effect of a daily covariate. The sequence of (unknown) daily weights constitutes the so-called transfer function. Specifically, we consider the problem of estimating a smooth common transfer function shared by a panel of short time series that are contemporaneously correlated. We propose an estimation scheme using a likelihood approach that penalizes the roughness of the common transfer function. We illustrate the proposed method with a simulation study and a biological example of indirectly estimating the spawning date distribution of North Sea cod.


Keywords


Cod-spawning-date distribution, (generalized) cross-validation, Seemingly unrelated regression, Multimodality.

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.537

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Title

Estimating a Smooth Common Transfer Function with a Panel of Time Series - Inflow of Larvae Cod as an Example

Keywords

Cod-spawning-date distribution, (generalized) cross-validation, Seemingly unrelated regression, Multimodality.

Description

The annual response variable in an ecological monitoring study often relates linearly to the weighted cumulative effect of some daily covariate, after adjusting for other annual covariates. Here we consider the problem of non-parametrically estimating the weights involved in computing the aforementioned cumulative effect, with a panel of short and contemporaneously correlated time series whose responses share the common cumulative effect of a daily covariate. The sequence of (unknown) daily weights constitutes the so-called transfer function. Specifically, we consider the problem of estimating a smooth common transfer function shared by a panel of short time series that are contemporaneously correlated. We propose an estimation scheme using a likelihood approach that penalizes the roughness of the common transfer function. We illustrate the proposed method with a simulation study and a biological example of indirectly estimating the spawning date distribution of North Sea cod.


Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810