Calculates the density of emissions observations

Usage

obs_density(data, xvals = NULL, up = Inf, low = 0, kernel = "gamma", bw = NULL)

Arguments

data: Emissions data from either the best source or top performers, must have a column named emissions.
xvals: Ordered sequence of emissions to define emission densities along. Default is NULL, in which case xvals is a 1024 length sequence. between 0 and 3*max(data$emissions).
up: Optional upper limit to bound density, default is Inf.
low: Optional lower limit to bound density, default is 0.
kernel: Kernel choice for density function, default is gamma defined on (0,Inf). Other options include: c('gaussian1','gaussian2','beta1','beta2','fb','fbl','fbu','rigaussian'). See np::npuniden.boundary() for more information on kernel options.
bw: Optional bandwidth, default is NULL in which case bw = sd(emissions)*n^(-2/5), where n is number of emissions. The bandwidth can also be provided manually, or searched for using least squares cross-validation by bw = "cv.ls" or likelihood cross-validation with bw = "cv.ml".

Value

A list containing two tibbles, Obs_onPoint with exact emission observations and densities, and obs_den_df with densities for every position given in xvals.

References

Bandwidth is set following Renault O. & O. Scaillet. On the way to recovery: A parametric bias free estimation of recovery rate densities. 2004. Journal of Banking and Finance. 28:12 p. 2915-2931.