%%% README for epsilonExpansion SDE Matlab code %%%
% Readme for the code to accompany the paper
% Approximate Maximum Likelihood Estimation for 1D Diffusions for a Fine
% Grid (Lu, Paine, Preston, Wood (2020))
% Authors: Phillip J. Paine (University of Nottingham), Kevin Lu
% (Australian National University)
% Contact : phillip.paine@nottingham.ac.uk \ pmxpp88@gmail.com, 
% kevin.lu@anu.edu.au
%
% This zip file contains the code to calculate the (log) transition density
% approximation for a selected number of SDEs and reproduce the three plots
% contained within the paper. Examples are contained within each piece of
% code.
%
% PPWdensity - calculate transition density approximations for Ito-Taylor 
% expansions using the epsilon-expansion method from the epsilon-expansion
% paper.
%
% generatePlots - script to reproduce figures in the epsilon-expansion
% paper by calling "generatePlotFunc".
%
% densityAS - code to calculate the transition density appoximation using
% the infinite Hermite polynomial expansions (see, Ait-Sahalia (2002)
% Maximum Likelihood Estimation of Discretely-Sampled Diffusions). Code was
% taken from https://www.princeton.edu/~yacine/closedformmle.htm
%
% densityExact - calculates the transition density of a small number of
% SDEs where it is known explicitly.
%
% densityKesser - computes the density using the Kessler (1997) method.
%
% densityShojiOzaki - calculate the transition density approximation 
% suggested by Shoji and Ozaki (1998) Estimation for non-linear sdes using
% a local-linearisation method
%
% absErrorOfLogDensity - calculate the absolute difference betweenthe log
% of two densities, used as a measure of error in generatePlots
%
% estimate - function that simulates and estimates the parameters for the
% exact and approximate methods
% 
% errorSummary - called by the "estimate" function take the parameter
% estimates to produce a table of the errors between the estimates and the
% MLE and true theta.
% 
% estimationTable - calls the "estimate" function to produce the tables in
% the epsilon-expansion paper over various models and values of the
% sampling interval and number of observations.
