::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Standard Deviation-Mean Plot and the Range Mean Plot for any univariate timeseries. The SMP is often used to identify the quasi-optimal Box-Cox transformation parameter that induces stationarity of the variance.

Enter (or paste) your data delimited by hard returns.

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Source code of R module

par1 <- as.numeric(par1) (n <- length(x)) (np <- floor(n / par1)) arr <- array(NA,dim=c(par1,np)) j <- 0 k <- 1 for (i in 1:(np*par1)) { j = j + 1 arr[j,k] <- x[i] if (j == par1) { j = 0 k=k+1 } } arr arr.mean <- array(NA,dim=np) arr.sd <- array(NA,dim=np) arr.range <- array(NA,dim=np) for (j in 1:np) { arr.mean[j] <- mean(arr[,j],na.rm=TRUE) arr.sd[j] <- sd(arr[,j],na.rm=TRUE) arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE) } arr.mean arr.sd arr.range (lm1 <- lm(arr.sd~arr.mean)) (lnlm1 <- lm(log(arr.sd)~log(arr.mean))) (lm2 <- lm(arr.range~arr.mean)) bitmap(file="test1.png") plot(arr.mean,arr.sd,main="Standard Deviation-Mean Plot",xlab="mean",ylab="standard deviation") dev.off() bitmap(file="test2.png") plot(arr.mean,arr.range,main="Range-Mean Plot",xlab="mean",ylab="range") dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Standard Deviation-Mean Plot",4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Section",header=TRUE) a<-table.element(a,"Mean",header=TRUE) a<-table.element(a,"Standard Deviation",header=TRUE) a<-table.element(a,"Range",header=TRUE) a<-table.row.end(a) for (j in 1:np) { a<-table.row.start(a) a<-table.element(a,j,header=TRUE) a<-table.element(a,arr.mean[j]) a<-table.element(a,arr.sd[j] ) a<-table.element(a,arr.range[j] ) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Regression: S.E.(k) = alpha + beta * Mean(k)",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"alpha",header=TRUE) a<-table.element(a,lm1$coefficients[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"beta",header=TRUE) a<-table.element(a,lm1$coefficients[[2]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"S.D.",header=TRUE) a<-table.element(a,summary(lm1)$coefficients[2,2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"T-STAT",header=TRUE) a<-table.element(a,summary(lm1)$coefficients[2,3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,summary(lm1)$coefficients[2,4]) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable1.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Regression: ln S.E.(k) = alpha + beta * ln Mean(k)",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"alpha",header=TRUE) a<-table.element(a,lnlm1$coefficients[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"beta",header=TRUE) a<-table.element(a,lnlm1$coefficients[[2]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"S.D.",header=TRUE) a<-table.element(a,summary(lnlm1)$coefficients[2,2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"T-STAT",header=TRUE) a<-table.element(a,summary(lnlm1)$coefficients[2,3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,summary(lnlm1)$coefficients[2,4]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Lambda",header=TRUE) a<-table.element(a,1-lnlm1$coefficients[[2]]) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable2.tab")

Cite this software as:

Wessa P. (2017), Standard Deviation-Mean Plot (v1.0.7) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_smp.wasp/

The R code is based on :

Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
Server : www.wessa.net

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