meboot (version 1.4-6)

checkConv: Check Convergence

Description

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.

Usage

checkConv (y, bigx, trueb = 1, n999 = 999, nover = 5,  seed1 = 294, key = 0, trace = FALSE)

Arguments

y

vector of data containing the dependent variable.

bigx

vector of data for all regressor variables in a regression or ts object. bigx should not include column of ones for the intercept.

trueb

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.

n999

number of replicates to generate in a simulation.

nover

number of values of n over which convergence calculated.

seed1

seed for the random number generator.

key

the subset of key regression coefficient whose convergence is studied if key=0 all coefficients are studied for convergence.

trace

logical. If TRUE, tracing information on the process is printed.

Value

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.

Details

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.

References

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.

See Also

meboot, criterion.

Examples

## Not run: 
library("ConvergenceConcepts")
library("strucchange")
data("PhillipsCurve")
## Not run: 
# uk <- window(PhillipsCurve, start = 1948)
# attach(data.frame(uk))
# y <- uk[,5]
# bigx <- cbind(dp1,du,u1) # collect all regressors
# reg1 <- lm(y ~ bigx)
# coef(reg1)
# nover <- 16 # choose range allowing n=25, 26, ..., 40
# 
# # the following step will take some time to run
# 
# sC <- checkConv(y, bigx, trueb=0, n999=999, nover=nover, seed1=294)
# 
# dim(sC) # n999 x nover x length(key)
# j <- 3  # choose key coefficient no. 3 for lagged income
# epsilon <- 0.1  #needed for p.as.plot command below
# nb.sp <- 10 # needed for p.as.plot command below 
# mode <- "p"  # needed for p.as.plot command below
# 
# # criterion function in ConvergenceConcepts package wants 999 rows
# dat <- sC[,,j] # 999 sample paths for diff inflation n=25,26,..40
# critp <- criterion(data = dat, epsilon = epsilon, mode = "p")$crit
# critas <- criterion(data = dat, epsilon = epsilon, mode = "as")$crit
# 
# p.as.plot(dat, critp, critas, epsilon, nb.sp, mode = mode)  
# nstart <- length(y) - nover + 1
# nn <- seq(nstart, length(y))  # choose the range of n the sample size
# 
# opar <- par(mfrow = c(2,1)) #plot 2 plots in one
# plot(nn,critp, typ="l", 
#   main="Convergence in probability: Diff(Inflation) Coefficient",
#   xlab="Sample size", ylab="Criterion using 999 sample paths")
# plot(nn,critas, typ="l", 
#   main="Almost sure convergence:  Diff(Inflation) Coefficient",
#   xlab="Sample size", ylab="Criterion using 999 sample paths")
# par(opar)
# 
# regp <- lm(critp ~ nn) # OLS of conv. in prob. criterion
# sup <- summary(regp) # regressed on sample size
# sup$coef
# # slope coeff. should be negative in sign for convergence
# # the t statistic on the slope coefficient should be large
# regas <- lm(critas ~ nn) #OLS of almost sure conv criterion
# suas <- summary(regas)#regressed on sample size
# suas$coef
# # slope coeff. should be negative in sign for convergence
# # the t statistic on the slope coefficient should be large
# ## End(Not run)
## End(Not run)