Paper TSA MR Faillissementen Lags

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Title produced by software: Multiple Regression

Date of computation: Sat, 18 Dec 2010 19:33:04 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700878lj9ltw0jdklli1v.htm/, Retrieved Sat, 18 Dec 2010 20:34:48 +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/2010/Dec/18/t1292700878lj9ltw0jdklli1v.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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432 342 189 67 517 432 342 189 623 517 432 342 605 623 517 432 716 605 623 517 677 716 605 623 710 677 716 605 839 710 677 716 886 839 710 677 891 886 839 710 917 891 886 839 820 917 891 886 793 820 917 891 932 793 820 917 906 932 793 820 844 906 932 793 801 844 906 932 957 801 844 906 1159 957 801 844 1264 1159 957 801 1097 1264 1159 957 1240 1097 1264 1159 1411 1240 1097 1264 1535 1411 1240 1097 1862 1535 1411 1240 1894 1862 1535 1411 2239 1894 1862 1535 2465 2239 1894 1862 2423 2465 2239 1894 2692 2423 2465 2239 2856 2692 2423 2465 3450 2856 2692 2423 4162 3450 2856 2692 4260 4162 3450 2856 4225 4260 4162 3450 4092 4225 4260 4162 4160 4092 4225 4260 3896 4160 4092 4225 3628 3896 4160 4092 3754 3628 3896 4160 3749 3754 3628 3896 3907 3749 3754 3628 4449 3907 3749 3754 5272 4449 3907 3749 6197 5272 4449 3907 6446 6197 5272 4449 7157 6446 6197 5272 7559 7157 6446 6197 7674 7559 7157 6446 6929 7674 7559 7157 7156 6929 7674 7559 6805 7156 6929 7674 7095 6805 7 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Faillissementen[t] = -101.296914358582 + 1.19211826327857Y1[t] -0.0303519024107213Y2[t] -0.269812974917130Y3[t] + 17.1473915256253t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) -101.296914358582 79.372341 -1.2762 0.207658 0.103829 Y1 1.19211826327857 0.134173 8.8849 0 0 Y2 -0.0303519024107213 0.213986 -0.1418 0.887765 0.443882 Y3 -0.269812974917130 0.133225 -2.0252 0.048091 0.024046 t 17.1473915256253 6.247962 2.7445 0.008347 0.004173 Multiple Linear Regression - Regression Statistics Multiple R 0.99540113961845 R-squared 0.990823428753708 Adjusted R-squared 0.990103697675567 F-TEST (value) 1376.65783630393 F-TEST (DF numerator) 4 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 246.141268837931 Sum Squared Residuals 3089861.73548248 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 432 299.740944333240 132.259055666760 2 517 386.617955545198 130.382044454802 3 623 461.082343070225 161.917656929775 4 605 577.731191055927 27.2688089440734 5 716 547.269049319045 168.730950680955 6 677 668.687726970769 8.3122730292308 7 710 640.830078609448 69.1699213905517 8 839 668.551856801484 170.448143198516 9 886 849.003597532259 36.9964024677409 10 891 909.361323848729 -18.3613238487291 11 917 896.236893513134 20.7631064868662 12 820 931.546390550843 -111.546390550843 13 793 830.920096201182 -37.9200962011824 14 932 811.809291804281 120.190708195719 15 906 1021.65248185768 -115.652481857679 16 844 1010.87083442573 -166.870834425734 17 801 917.392039577285 -116.392039577285 18 957 892.175301079242 64.8246989207585 19 1159 1113.32667792485 45.6733220751523 20 1264 1378.14901977811 -114.149019778109 21 1097 1472.24692057395 -375.246920573946 22 1240 1232.62139144566 7.37860855433611 23 1411 1396.98009995642 14.0199000435826 24 1535 1658.69815926911 -123.698159269106 25 1862 1779.89478471589 82.1052152841083 26 1894 2136.96319372385 -242.963193723852 27 2239 2148.87648869636 90.1235113036381 28 2465 2488.10457737805 -23.1045773780508 29 2423 2755.56527487559 -332.565274875587 30 2692 2622.69869305228 69.3013069477208 31 2856 2900.82294496982 -44.8229449698199 32 3450 3116.64521487117 333.354785128833 33 4162 3764.3534525362 397.646547463801 34 4260 4568.01068959779 -308.010689597791 35 4225 4520.10620930751 -295.106209307508 36 4092 4300.44813704114 -208.448137041136 37 4160 4133.66444459321 26.3355554067921 38 3896 4245.3561351645 -349.356135164502 39 3628 3981.60550148463 -353.605501484632 40 3754 3668.93081839367 85.0691816063345 41 3749 3915.65004631659 -166.650046316587 42 3907 3995.32238409986 -88.3223840998592 43 4449 4166.97978589599 282.020214104006 44 5272 4826.8087404123 445.191259587702 45 6197 5765.98828147267 431.011718527327 46 6446 6714.62681844187 -268.626818441871 47 7157 6778.48006943715 378.519930562854 48 7559 7386.08892065522 172.911079344777 49 7674 7793.70422065045 -119.704220650447 50 6929 7743.90672251792 -814.90672251792 51 7156 6760.97072320709 395.029276792913 52 6805 7040.31263567747 -235.312635677467 53 7095 6833.14730125834 261.85269874166 54 7222 7145.41496157473 76.5850384252726 55 7593 7399.86367503353 193.136324966466 56 7910 7777.18648790338 132.813512096618 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.00244144408059051 0.00488288816118103 0.99755855591941 9 0.00435185609075723 0.00870371218151446 0.995648143909243 10 0.000822025895126926 0.00164405179025385 0.999177974104873 11 0.000179633514469794 0.000359267028939587 0.99982036648553 12 0.000433845244350814 0.000867690488701629 0.99956615475565 13 0.000164957394748326 0.000329914789496652 0.999835042605252 14 0.000100436975472271 0.000200873950944542 0.999899563024528 15 2.60751111216968e-05 5.21502222433937e-05 0.999973924888878 16 6.6663563279681e-06 1.33327126559362e-05 0.999993333643672 17 2.81431003754977e-06 5.62862007509953e-06 0.999997185689962 18 2.38175391977469e-06 4.76350783954937e-06 0.99999761824608 19 6.76932231245958e-06 1.35386446249192e-05 0.999993230677688 20 3.82931962035169e-06 7.65863924070338e-06 0.99999617068038 21 2.52464092740856e-06 5.04928185481711e-06 0.999997475359073 22 4.45892027304082e-06 8.91784054608164e-06 0.999995541079727 23 2.77937273998839e-06 5.55874547997679e-06 0.99999722062726 24 2.38005777129474e-06 4.76011554258948e-06 0.999997619942229 25 3.36362758694953e-05 6.72725517389905e-05 0.99996636372413 26 1.39383714254451e-05 2.78767428508902e-05 0.999986061628575 27 3.82654989000391e-05 7.65309978000781e-05 0.9999617345011 28 1.61559117697971e-05 3.23118235395942e-05 0.99998384408823 29 2.23394061559307e-05 4.46788123118614e-05 0.999977660593844 30 1.31779128579865e-05 2.63558257159730e-05 0.999986822087142 31 4.96696969893799e-06 9.93393939787597e-06 0.9999950330303 32 5.96556319420655e-05 0.000119311263884131 0.999940344368058 33 0.000824312233836671 0.00164862446767334 0.999175687766163 34 0.00164803697449291 0.00329607394898582 0.998351963025507 35 0.00192346426445346 0.00384692852890691 0.998076535735547 36 0.00251605243474725 0.0050321048694945 0.997483947565253 37 0.00252003407996341 0.00504006815992681 0.997479965920037 38 0.00313205005609548 0.00626410011219095 0.996867949943905 39 0.00303550618369456 0.00607101236738913 0.996964493816305 40 0.00201460564085960 0.00402921128171921 0.99798539435914 41 0.00146921522417916 0.00293843044835831 0.99853078477582 42 0.00408901412275406 0.00817802824550813 0.995910985877246 43 0.00955581368831517 0.0191116273766303 0.990444186311685 44 0.0148924708686042 0.0297849417372085 0.985107529131396 45 0.0116425823372904 0.0232851646745807 0.98835741766271 46 0.0873485386716586 0.174697077343317 0.912651461328341 47 0.144794987437148 0.289589974874295 0.855205012562853 48 0.103700534379981 0.207401068759961 0.89629946562002 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 35 0.853658536585366 NOK 5% type I error level 38 0.926829268292683 NOK 10% type I error level 38 0.926829268292683 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; par4 = 1 ;

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

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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