# FederalFundsRate package

Version 1.0.0 by Lawrence Murray

Ornstein--Uhlenbeck model for diffusion bridge sampling and parameter estimation with U.S. Federal Funds Rate data.

## Synopsis

./init.sh


This simulates a number of parameter sets from the prior for testing. GNU Octave is required. Running it is optional, as a number of parameter sets are already included.

./run.sh


This runs a particle filter as well as samples from the posterior distribution using a Federal Funds Rate data set.

./test.sh


This runs tests on the bootstrap and bridge particle filters on the simulated parameter sets. Alternatively, these tests may be run as an array job on a cluster:

qsub -t 0-15 qsub_test_bridge.sh
qsub -t 0-15 qsub_test_bootstrap.sh


Finally, results may be plot with:

octave --path oct/ --eval "plot_and_print"


GNU Octave and OctBi are required.

Note that, as of version 1.1.0 of LibBi, running any of these gives the warnings:

Warning (line 29): 'obs' variables should not appear on the right side of actions in the 'transition' block.
Warning (line 42): 'obs' variables should not appear on the right side of actions in the 'lookahead_transition' block.


This is normal.

## Description

This package includes an Ornstein–Uhlenbeck model that is observed directly. The task is to simulate diffusion bridges between the observed values. The form of the model is: $dx=(\theta_{1}-\theta_{2}x)\, dt+\theta_{3}\, dW,$ with parameters $\theta_1$, $\theta_2$ and $\theta_3$ to be estimated. It was used as a test case in Del Moral & Murray (2014). The package may be used to reproduce the results in that paper.

A U.S. Federal Funds Rate data set is included. The data set contains 25 years of data at a monthly time interval, beginning January 1989 and ending December

1. The observation for January 1989 defines the initial value of the system and is hardcoded in the model file. The remaining observations, beginning February 1989, are in the file data/obs.nc. The data set was obtained from http://www.federalreserve.gov/releases/h15/data.htm on 7 April 2014.

## References

Del Moral, P. & Murray, L. M. Sequential Monte Carlo with Highly Informative Observations, 2014. [arXiv]