#This is an R version of a toy simulation to illustrate the Hotelling-Secrist effect 

#described in Hotelling's 1933 review of H. Secrist's The Triumph of Mediocrity

#in Business.  See also:  M. Friedman, JEL, 1992, and Stigler, Stat. Sci,1996.

# For original s version see the directory projects/hotelling

n <- 500

s <- 100

m <- 100

g <- n/m

rho <- .9

X <- matrix(rnorm(n*s),s)

Y <- filter(X,rho,"rec")

Y <- Y[51:100,]



pdf("fig.1.pdf",width=6.5,height=6)

plot(1:50,apply(Y,1,"var"),xlab="time",ylab="variance",type="l")

dev.off()

Z <- Y[,order(Y[1,])]

Z <- array(Z,c(50,m,g))



pdf("fig.2.pdf",width=6.5,height=6)

matplot(1:50,apply(Z,c(1,3),"mean"),xlab="time",ylab="group means",type="n")

matlines(1:50,apply(Z,c(1,3),"mean"))

dev.off()



Z <- Y[,order(Y[50,])]

Z <- array(Z,c(50,m,g))

pdf("fig.3.pdf",width=6.5,height=6)

matplot(1:50,apply(Z,c(1,3),"mean"),xlab="time",ylab="group means",type="n")

matlines(1:50,apply(Z,c(1,3),"mean"))

dev.off()



#This is a second toy simulation to illustrate the Hotelling-Secrist effect 

#described in Hotelling's 1933 review of H. Secrist's The Triumph of Mediocrity

#in Business.  See also:  M. Friedman, JEL, 1992, and Stigler, Stat. Sci,1996.

# like the prior one but now there are different intercepts

n <- 500

s <- 100

m <- 100

g <- n/m

rho <- .9

X <- matrix(rnorm(n*s),s)

Y <- filter(X,rho,"rec")

Y <- Y[51:100,]+outer(rep(1,50),rnorm(500)*2)



pdf("fig.1.1.pdf",width=6.5,height=6)

plot(1:50,apply(Y,1,"var"),xlab="time",ylab="variance",type="l")

dev.off()



Z <- Y[,order(Y[1,])]

Z <- array(Z,c(50,m,g))

pdf("fig.1.2.pdf",width=6.5,height=6)

matplot(1:50,apply(Z,c(1,3),"mean"),xlab="time",ylab="group means",type="n")

matlines(1:50,apply(Z,c(1,3),"mean"))

dev.off()



Z <- Y[,order(Y[50,])]

Z <- array(Z,c(50,m,g))

pdf("fig.1.3.pdf",width=6.5,height=6)

matplot(1:50,apply(Z,c(1,3),"mean"),xlab="time",ylab="group means",type="n")

matlines(1:50,apply(Z,c(1,3),"mean"))

dev.off()