Feiyu Zhu, Martin Lysy
realPSD provides Robust and Efficient cALibration of any parametric power spectral density (PSD) models, especially for dynamical processes with extremely large number (at least millions) of observations. Three built-in estimation methods are provided: maximum likelihood estimation (MLE) based on Whittle-type likelihood, log-periodogram estimation and nonlinear least squares estimation (NLS). The most effective of these combines the simplicity of nonlinear least-squares with the statistical efficiency of maximum likelihood. The technical details about these three estimation methods for high-throughput data (at extremely high sampling frequency and for extended durations) are extensively explained in this preprint. realPSD also provides a routine for removing most electronic noise in an automated pre-processing step, which is also discussed in this preprint. This feature would be very useful for spectral analysis based on recordings contaminated by various sources of instrumental noise in real-world applications.
realPSD relies upon TMB internally for automatic differentiation (AD) to enable efficient and accurate numerical gradient calculations. But users are not required to be familiar with TMB. realPSD itself can be used as a user-friendly platform that handles the TMB interface to R for users. All you need to do is to focus on writing your model and estimating it. That being said, there are some basic conventions required by realPSD to write your own model, see the quick tutorial. It would be easier for users to quickly grasp these steps if users are familiar with any object-oriented programming (OOP) language like C++ or Java. Understanding of the basic data types provided by the C++ Eigen library is preferred but not required.
realPSD relies on TMB. Please make sure that TMB is correctly installed on your machine. The installation of TMB can be found here.
Once you have installed TMB successfully, realPSD can be installed from GitHub via the command:
devtools::install_github("mlysy/realPSD")There are many built-in unit tests in realPSD. Once you have installed the package, run the following command to confirm that it can work properly on your machine.
require(realPSD)
require(testthat)
test_pacakge("realPSD")realPSD-quicktut: A quick tutorial teaches you how to use realPSD by showing you how to build and estimate an Ornstein-Uhlenbeck (OU) model step by step.realPSD-advancedtut: An Advanced tutorial explains the theoretical results behind estimation methods supplied by the package and also the design pattern of realPSD that handles the TMB interface to R effectively, which allows users to build any model without restrictions.