This function generates a 3D array giving (Xn-X) in the notation of
the ConvergenceConcepts package by Lafaye de Micheaux and Liquet for sample paths
with dimensions \(=\) n999 as first dimension, nover \(=\) range of n
values as second dimension and number of items in key as the third
dimension. It is intended to be used for checking convergence of meboot in the context
of a specific real world time series regression problem.
checkConv (y, bigx, trueb = 1, n999 = 999, nover = 5,
seed1 = 294, key = 0, trace = FALSE)A 3 dimensional array giving (Xn-X) for sample paths with dimensions \(=\)
n999
as first dimension, nover
\(=\) range of n values as second dimension
and number of items in key as the third dimension ready for use in
ConvergenceConcepts package.
vector of data containing the dependent variable.
vector of data for all regressor variables in a regression or ts object.
bigx should not include column of ones for the intercept.
true values of regressor coefficients for simulation. If trueb=0 then use OLS
coefficient values rounded to 2 digits as true values of beta for simulation purposes, to be close
to but not exactly equal to OLS.
number of replicates to generate in a simulation.
number of values of n over which convergence calculated.
seed for the random number generator.
the subset of key regression coefficient whose convergence is studied
if key=0 all coefficients are studied for convergence.
logical. If TRUE, tracing information on the process is printed.
Use this only when lagged dependent variable is absent.
Warning: key=0 might use up too much memory for large regression problems.
The algorithm first creates data on the dependent variable for a simulation using known
true values denoted by trueb. It proceeds to create n999 regression problems using the
seven-step algorithm in meboot creating n999 time series for all variable
in the simulated regression. It then creates sample paths over a range of n values for
coefficients of interest denoted as key (usually a subset of original coefficients).
For each key coefficient there are n999 paths as n increases. If meboot algorithm
is converging to true values, the value of (Xn-X) based criteria for
"convergence in probability" and "almost sure convergence" in the notation of the
ConvergenceConcepts package should decline.
The decline can be plotted and/or tested to check if it is statistically significant
as sample size increases. This function permits the user of meboot working with a short
time series to see if the meboot algorithm is working in his or her particular situation.
Lafaye de Micheaux, P. and Liquet, B. (2009), Understanding Convergence Concepts: a Visual-Minded and Graphical Simulation-Based Approach, The American Statistician, 63(2) pp. 173-178.
Vinod, H.D. (2006), Maximum Entropy Ensembles for Time Series Inference in Economics, Journal of Asian Economics, 17(6), pp. 955-978
Vinod, H.D. (2004), Ranking mutual funds using unconventional utility theory and stochastic dominance, Journal of Empirical Finance, 11(3), pp. 353-377.
meboot, criterion.