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Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 11 Mar 2016 10:24:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/11/t14576918854erz6ey4gvtjwpx.htm/, Retrieved Sat, 18 May 2024 14:20:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293848, Retrieved Sat, 18 May 2024 14:20:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2016-03-11 10:24:05] [4c0c83f68a39c2484f611b00ec7d20d3] [Current]
- R P     [(Partial) Autocorrelation Function] [] [2016-05-26 13:40:46] [84e9be1ea6a4331c0a0a4a157e2ec517]
- R P     [(Partial) Autocorrelation Function] [] [2016-05-26 13:43:12] [84e9be1ea6a4331c0a0a4a157e2ec517]
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Dataseries X:
214320
212588
205816
202196
195722
198563
229139
229527
211868
203555
195770
199834
203089
198480
192684
187827
182414
182510
211524
211451
200140
191568
186424
191987
203583
201920
195978
191395
188222
189422
214419
224325
216222
210506
207221
210027
215191
215177
211701
210176
205491
206996
235980
241292
236675
229127
225436
229570
239973
236168
230703
224790
217811
219576
245472
248511
242084
235572
229827
229697
239567
237201
233164
227755
220189
221270
245413
247826
237736
230079
225939
228987




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293848&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293848&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2279021.92030.029416
2-0.398714-3.35960.000629
3-0.419412-3.5340.000362
4-0.274795-2.31550.011741
50.154951.30560.097946
60.4976014.19293.9e-05
70.1525311.28520.101441
8-0.223906-1.88670.031648
9-0.354222-2.98470.001945
10-0.349137-2.94190.002201
110.1658231.39720.083345
120.7751526.53150
130.2103751.77270.040288
14-0.29957-2.52420.006917
15-0.35024-2.95120.002143
16-0.2539-2.13940.017921
170.1076140.90680.183796
180.3974043.34860.000651

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.227902 & 1.9203 & 0.029416 \tabularnewline
2 & -0.398714 & -3.3596 & 0.000629 \tabularnewline
3 & -0.419412 & -3.534 & 0.000362 \tabularnewline
4 & -0.274795 & -2.3155 & 0.011741 \tabularnewline
5 & 0.15495 & 1.3056 & 0.097946 \tabularnewline
6 & 0.497601 & 4.1929 & 3.9e-05 \tabularnewline
7 & 0.152531 & 1.2852 & 0.101441 \tabularnewline
8 & -0.223906 & -1.8867 & 0.031648 \tabularnewline
9 & -0.354222 & -2.9847 & 0.001945 \tabularnewline
10 & -0.349137 & -2.9419 & 0.002201 \tabularnewline
11 & 0.165823 & 1.3972 & 0.083345 \tabularnewline
12 & 0.775152 & 6.5315 & 0 \tabularnewline
13 & 0.210375 & 1.7727 & 0.040288 \tabularnewline
14 & -0.29957 & -2.5242 & 0.006917 \tabularnewline
15 & -0.35024 & -2.9512 & 0.002143 \tabularnewline
16 & -0.2539 & -2.1394 & 0.017921 \tabularnewline
17 & 0.107614 & 0.9068 & 0.183796 \tabularnewline
18 & 0.397404 & 3.3486 & 0.000651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293848&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.227902[/C][C]1.9203[/C][C]0.029416[/C][/ROW]
[ROW][C]2[/C][C]-0.398714[/C][C]-3.3596[/C][C]0.000629[/C][/ROW]
[ROW][C]3[/C][C]-0.419412[/C][C]-3.534[/C][C]0.000362[/C][/ROW]
[ROW][C]4[/C][C]-0.274795[/C][C]-2.3155[/C][C]0.011741[/C][/ROW]
[ROW][C]5[/C][C]0.15495[/C][C]1.3056[/C][C]0.097946[/C][/ROW]
[ROW][C]6[/C][C]0.497601[/C][C]4.1929[/C][C]3.9e-05[/C][/ROW]
[ROW][C]7[/C][C]0.152531[/C][C]1.2852[/C][C]0.101441[/C][/ROW]
[ROW][C]8[/C][C]-0.223906[/C][C]-1.8867[/C][C]0.031648[/C][/ROW]
[ROW][C]9[/C][C]-0.354222[/C][C]-2.9847[/C][C]0.001945[/C][/ROW]
[ROW][C]10[/C][C]-0.349137[/C][C]-2.9419[/C][C]0.002201[/C][/ROW]
[ROW][C]11[/C][C]0.165823[/C][C]1.3972[/C][C]0.083345[/C][/ROW]
[ROW][C]12[/C][C]0.775152[/C][C]6.5315[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.210375[/C][C]1.7727[/C][C]0.040288[/C][/ROW]
[ROW][C]14[/C][C]-0.29957[/C][C]-2.5242[/C][C]0.006917[/C][/ROW]
[ROW][C]15[/C][C]-0.35024[/C][C]-2.9512[/C][C]0.002143[/C][/ROW]
[ROW][C]16[/C][C]-0.2539[/C][C]-2.1394[/C][C]0.017921[/C][/ROW]
[ROW][C]17[/C][C]0.107614[/C][C]0.9068[/C][C]0.183796[/C][/ROW]
[ROW][C]18[/C][C]0.397404[/C][C]3.3486[/C][C]0.000651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293848&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2279021.92030.029416
2-0.398714-3.35960.000629
3-0.419412-3.5340.000362
4-0.274795-2.31550.011741
50.154951.30560.097946
60.4976014.19293.9e-05
70.1525311.28520.101441
8-0.223906-1.88670.031648
9-0.354222-2.98470.001945
10-0.349137-2.94190.002201
110.1658231.39720.083345
120.7751526.53150
130.2103751.77270.040288
14-0.29957-2.52420.006917
15-0.35024-2.95120.002143
16-0.2539-2.13940.017921
170.1076140.90680.183796
180.3974043.34860.000651







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2279021.92030.029416
2-0.475343-4.00537.5e-05
3-0.241221-2.03260.022919
4-0.411026-3.46340.000454
5-0.018995-0.16010.436646
60.1744491.46990.072999
7-0.094896-0.79960.213303
8-0.006866-0.05790.477015
9-0.183377-1.54520.063376
10-0.355896-2.99880.001867
110.0025290.02130.491529
120.5633384.74685e-06
13-0.131666-1.10940.135493
140.2127891.7930.038617
150.1141390.96180.169718
160.1340281.12930.131278
17-0.022431-0.1890.425313
18-0.073252-0.61720.269527

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.227902 & 1.9203 & 0.029416 \tabularnewline
2 & -0.475343 & -4.0053 & 7.5e-05 \tabularnewline
3 & -0.241221 & -2.0326 & 0.022919 \tabularnewline
4 & -0.411026 & -3.4634 & 0.000454 \tabularnewline
5 & -0.018995 & -0.1601 & 0.436646 \tabularnewline
6 & 0.174449 & 1.4699 & 0.072999 \tabularnewline
7 & -0.094896 & -0.7996 & 0.213303 \tabularnewline
8 & -0.006866 & -0.0579 & 0.477015 \tabularnewline
9 & -0.183377 & -1.5452 & 0.063376 \tabularnewline
10 & -0.355896 & -2.9988 & 0.001867 \tabularnewline
11 & 0.002529 & 0.0213 & 0.491529 \tabularnewline
12 & 0.563338 & 4.7468 & 5e-06 \tabularnewline
13 & -0.131666 & -1.1094 & 0.135493 \tabularnewline
14 & 0.212789 & 1.793 & 0.038617 \tabularnewline
15 & 0.114139 & 0.9618 & 0.169718 \tabularnewline
16 & 0.134028 & 1.1293 & 0.131278 \tabularnewline
17 & -0.022431 & -0.189 & 0.425313 \tabularnewline
18 & -0.073252 & -0.6172 & 0.269527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293848&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.227902[/C][C]1.9203[/C][C]0.029416[/C][/ROW]
[ROW][C]2[/C][C]-0.475343[/C][C]-4.0053[/C][C]7.5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.241221[/C][C]-2.0326[/C][C]0.022919[/C][/ROW]
[ROW][C]4[/C][C]-0.411026[/C][C]-3.4634[/C][C]0.000454[/C][/ROW]
[ROW][C]5[/C][C]-0.018995[/C][C]-0.1601[/C][C]0.436646[/C][/ROW]
[ROW][C]6[/C][C]0.174449[/C][C]1.4699[/C][C]0.072999[/C][/ROW]
[ROW][C]7[/C][C]-0.094896[/C][C]-0.7996[/C][C]0.213303[/C][/ROW]
[ROW][C]8[/C][C]-0.006866[/C][C]-0.0579[/C][C]0.477015[/C][/ROW]
[ROW][C]9[/C][C]-0.183377[/C][C]-1.5452[/C][C]0.063376[/C][/ROW]
[ROW][C]10[/C][C]-0.355896[/C][C]-2.9988[/C][C]0.001867[/C][/ROW]
[ROW][C]11[/C][C]0.002529[/C][C]0.0213[/C][C]0.491529[/C][/ROW]
[ROW][C]12[/C][C]0.563338[/C][C]4.7468[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.131666[/C][C]-1.1094[/C][C]0.135493[/C][/ROW]
[ROW][C]14[/C][C]0.212789[/C][C]1.793[/C][C]0.038617[/C][/ROW]
[ROW][C]15[/C][C]0.114139[/C][C]0.9618[/C][C]0.169718[/C][/ROW]
[ROW][C]16[/C][C]0.134028[/C][C]1.1293[/C][C]0.131278[/C][/ROW]
[ROW][C]17[/C][C]-0.022431[/C][C]-0.189[/C][C]0.425313[/C][/ROW]
[ROW][C]18[/C][C]-0.073252[/C][C]-0.6172[/C][C]0.269527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293848&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293848&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2279021.92030.029416
2-0.475343-4.00537.5e-05
3-0.241221-2.03260.022919
4-0.411026-3.46340.000454
5-0.018995-0.16010.436646
60.1744491.46990.072999
7-0.094896-0.79960.213303
8-0.006866-0.05790.477015
9-0.183377-1.54520.063376
10-0.355896-2.99880.001867
110.0025290.02130.491529
120.5633384.74685e-06
13-0.131666-1.10940.135493
140.2127891.7930.038617
150.1141390.96180.169718
160.1340281.12930.131278
17-0.022431-0.1890.425313
18-0.073252-0.61720.269527



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
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,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')