Paper: Central Tendendy: Residu's van ARIMA Backward Selection

*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Fri, 11 Dec 2009 06:42:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t12605390034suct2ic651s3lt.htm/, Retrieved Fri, 11 Dec 2009 14:43:25 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t12605390034suct2ic651s3lt.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

Residu's van ARIMA Backward Selection

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0.000746099568952258 0.0292111461738571 -0.00280267596084322 -0.00184368563002967 0.0107457257770334 -0.0175566443253344 0.0131165820445929 -0.0324353168918367 0.0224382020922924 -0.0196217959970839 0.00495492412026389 0.00168574453846993 -0.00506586405101019 -0.0116484658020629 -0.00266112877646428 0.0179412217929573 -0.0168120805195169 -0.0147697069296257 0.035665172596409 0.00293868331101443 -0.0145835439671676 0.0184871974956284 -0.00672423964360273 -0.00834464807562108 0.0169769773776811 0.0141585136611232 0.00520840412118636 -0.0225065086691335 0.0221256937859677 0.008638135296458 0.0259853418092942 -0.014962664383958 0.0336773377780083 -0.00849413990510539 -0.0229882773676451 0.0569000711376357 0.025309869239244 -0.029512999542613 -0.00750220761300227 0.00584857420117411 0.061296189365771 -0.0463306298649301 0.0380278085379684 -0.00825029078426785 0.0306190401585776 -0.04367173164859 -0.0556117529677963 -0.064 etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.00122627985686043 0.00395419867440867 0.310120951887632 Geometric Mean NaN Harmonic Mean 0.0252703654080890 Quadratic Mean 0.0301392371730883 Winsorized Mean ( 1 / 19 ) 0.0019532702209461 0.00360631186789072 0.541625431327030 Winsorized Mean ( 2 / 19 ) 0.00222413750672860 0.00350580529780868 0.634415581526678 Winsorized Mean ( 3 / 19 ) 0.00178912353953442 0.00316567613756403 0.565163163187987 Winsorized Mean ( 4 / 19 ) 0.00196585148833127 0.00311860476773866 0.630362496930552 Winsorized Mean ( 5 / 19 ) 0.00283147969483460 0.00287967579064828 0.983263360420575 Winsorized Mean ( 6 / 19 ) 0.00279174210761788 0.00283180239797685 0.985853430173097 Winsorized Mean ( 7 / 19 ) 0.00278991516103642 0.00273700529290356 1.01933129916484 Winsorized Mean ( 8 / 19 ) 0.00325993882958384 0.00248628963624615 1.31116615781971 Winsorized Mean ( 9 / 19 ) 0.00311866548084010 0.00243269137889601 1.28198155668040 Winsorized Mean ( 10 / 19 ) 0.00306085332956666 0.00224692915047756 1.36223847063274 Winsorized Mean ( 11 / 19 ) 0.00331994604344280 0.00215916728208679 1.53760483080039 Winsorized Mean ( 12 / 19 ) 0.00288731485541553 0.00203414324550115 1.41942553052806 Winsorized Mean ( 13 / 19 ) 0.00323087643007062 0.00195680953665843 1.65109397186804 Winsorized Mean ( 14 / 19 ) 0.00327136354994546 0.00194860155025461 1.67882630983128 Winsorized Mean ( 15 / 19 ) 0.00263018018985191 0.00182898324677817 1.43805592231918 Winsorized Mean ( 16 / 19 ) 0.00317383652076936 0.00166310014228685 1.90838569492585 Winsorized Mean ( 17 / 19 ) 0.00392539505132647 0.00150315193540061 2.61144263522523 Winsorized Mean ( 18 / 19 ) 0.00367682646583063 0.00144972413014029 2.53622491989206 Winsorized Mean ( 19 / 19 ) 0.00357121685536915 0.00142393119332630 2.50799818987516 Trimmed Mean ( 1 / 19 ) 0.00215664760760748 0.00340719155198688 0.632969287080396 Trimmed Mean ( 2 / 19 ) 0.00237481607693515 0.00315704200162202 0.752228217336044 Trimmed Mean ( 3 / 19 ) 0.00245868433771049 0.00291212759201097 0.844291419254966 Trimmed Mean ( 4 / 19 ) 0.00271688098537316 0.00278085537711394 0.976994707359727 Trimmed Mean ( 5 / 19 ) 0.00294295619111536 0.00263401674798470 1.11728833666947 Trimmed Mean ( 6 / 19 ) 0.00297094390720287 0.00253617155449764 1.17142860542466 Trimmed Mean ( 7 / 19 ) 0.00301010281896403 0.00242567490637508 1.24093414622585 Trimmed Mean ( 8 / 19 ) 0.00305326252599968 0.00231177446693409 1.32074411655258 Trimmed Mean ( 9 / 19 ) 0.0030160859957818 0.00223793750041705 1.3477078762118 Trimmed Mean ( 10 / 19 ) 0.00299884329031616 0.00215400981384122 1.39221431167407 Trimmed Mean ( 11 / 19 ) 0.00298895520297621 0.0020931831505271 1.42794728794924 Trimmed Mean ( 12 / 19 ) 0.00293823193132029 0.00203242844384904 1.44567546287427 Trimmed Mean ( 13 / 19 ) 0.00294581806131621 0.00198127723768024 1.48682779234131 Trimmed Mean ( 14 / 19 ) 0.00290408495025787 0.00192766856318549 1.50652711037567 Trimmed Mean ( 15 / 19 ) 0.0028507119517811 0.00184827068887325 1.54236712671073 Trimmed Mean ( 16 / 19 ) 0.00288283880104980 0.00176844606803106 1.63015364345233 Trimmed Mean ( 17 / 19 ) 0.00283991663739116 0.00170329825550528 1.66730437738205 Trimmed Mean ( 18 / 19 ) 0.00267612321943161 0.00165360288323112 1.61835906708296 Trimmed Mean ( 19 / 19 ) 0.00251992879737462 0.00158649321464431 1.58836405609184 Median 0.00168574453846993 Midrange -0.0252892010394305 Midmean - Weighted Average at Xnp 0.00226336465573421 Midmean - Weighted Average at X(n+1)p 0.00290408495025787 Midmean - Empirical Distribution Function 0.00290408495025787 Midmean - Empirical Distribution Function - Averaging 0.00290408495025787 Midmean - Empirical Distribution Function - Interpolation 0.0028507119517811 Midmean - Closest Observation 0.00226336465573421 Midmean - True Basic - Statistics Graphics Toolkit 0.00290408495025787 Midmean - MS Excel (old versions) 0.00290408495025787 Number of observations 59

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605390034suct2ic651s3lt/18xj91260538932.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605390034suct2ic651s3lt/18xj91260538932.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605390034suct2ic651s3lt/2ufg91260538932.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605390034suct2ic651s3lt/2ufg91260538932.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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