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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationWed, 04 Dec 2013 06:11:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/04/t1386155513kwnjrvgjov044b2.htm/, Retrieved Thu, 28 Mar 2024 12:00:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230510, Retrieved Thu, 28 Mar 2024 12:00:33 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [kgjhg] [2013-12-04 11:11:28] [9c1e2bb2413149fa15098d3e18bf4ebf] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230510&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230510&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230510&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.316648-2.45270.008551
20.1903181.47420.072829
30.0874790.67760.250311
4-0.029326-0.22720.410538
50.07620.59020.278621
6-0.071919-0.55710.289772
7-0.176453-1.36680.088394
8-0.052345-0.40550.343289
9-0.043459-0.33660.368785
10-0.229343-1.77650.040361
110.1805671.39870.08353
12-0.426667-3.30490.000803
130.1128050.87380.192861
14-0.002853-0.02210.49122
15-0.010012-0.07760.469221
160.0126340.09790.461183
170.067570.52340.301313
180.1702231.31850.096167

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.316648 & -2.4527 & 0.008551 \tabularnewline
2 & 0.190318 & 1.4742 & 0.072829 \tabularnewline
3 & 0.087479 & 0.6776 & 0.250311 \tabularnewline
4 & -0.029326 & -0.2272 & 0.410538 \tabularnewline
5 & 0.0762 & 0.5902 & 0.278621 \tabularnewline
6 & -0.071919 & -0.5571 & 0.289772 \tabularnewline
7 & -0.176453 & -1.3668 & 0.088394 \tabularnewline
8 & -0.052345 & -0.4055 & 0.343289 \tabularnewline
9 & -0.043459 & -0.3366 & 0.368785 \tabularnewline
10 & -0.229343 & -1.7765 & 0.040361 \tabularnewline
11 & 0.180567 & 1.3987 & 0.08353 \tabularnewline
12 & -0.426667 & -3.3049 & 0.000803 \tabularnewline
13 & 0.112805 & 0.8738 & 0.192861 \tabularnewline
14 & -0.002853 & -0.0221 & 0.49122 \tabularnewline
15 & -0.010012 & -0.0776 & 0.469221 \tabularnewline
16 & 0.012634 & 0.0979 & 0.461183 \tabularnewline
17 & 0.06757 & 0.5234 & 0.301313 \tabularnewline
18 & 0.170223 & 1.3185 & 0.096167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230510&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]-0.316648[/C][C]-2.4527[/C][C]0.008551[/C][/ROW]
[ROW][C]2[/C][C]0.190318[/C][C]1.4742[/C][C]0.072829[/C][/ROW]
[ROW][C]3[/C][C]0.087479[/C][C]0.6776[/C][C]0.250311[/C][/ROW]
[ROW][C]4[/C][C]-0.029326[/C][C]-0.2272[/C][C]0.410538[/C][/ROW]
[ROW][C]5[/C][C]0.0762[/C][C]0.5902[/C][C]0.278621[/C][/ROW]
[ROW][C]6[/C][C]-0.071919[/C][C]-0.5571[/C][C]0.289772[/C][/ROW]
[ROW][C]7[/C][C]-0.176453[/C][C]-1.3668[/C][C]0.088394[/C][/ROW]
[ROW][C]8[/C][C]-0.052345[/C][C]-0.4055[/C][C]0.343289[/C][/ROW]
[ROW][C]9[/C][C]-0.043459[/C][C]-0.3366[/C][C]0.368785[/C][/ROW]
[ROW][C]10[/C][C]-0.229343[/C][C]-1.7765[/C][C]0.040361[/C][/ROW]
[ROW][C]11[/C][C]0.180567[/C][C]1.3987[/C][C]0.08353[/C][/ROW]
[ROW][C]12[/C][C]-0.426667[/C][C]-3.3049[/C][C]0.000803[/C][/ROW]
[ROW][C]13[/C][C]0.112805[/C][C]0.8738[/C][C]0.192861[/C][/ROW]
[ROW][C]14[/C][C]-0.002853[/C][C]-0.0221[/C][C]0.49122[/C][/ROW]
[ROW][C]15[/C][C]-0.010012[/C][C]-0.0776[/C][C]0.469221[/C][/ROW]
[ROW][C]16[/C][C]0.012634[/C][C]0.0979[/C][C]0.461183[/C][/ROW]
[ROW][C]17[/C][C]0.06757[/C][C]0.5234[/C][C]0.301313[/C][/ROW]
[ROW][C]18[/C][C]0.170223[/C][C]1.3185[/C][C]0.096167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230510&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230510&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
1-0.316648-2.45270.008551
20.1903181.47420.072829
30.0874790.67760.250311
4-0.029326-0.22720.410538
50.07620.59020.278621
6-0.071919-0.55710.289772
7-0.176453-1.36680.088394
8-0.052345-0.40550.343289
9-0.043459-0.33660.368785
10-0.229343-1.77650.040361
110.1805671.39870.08353
12-0.426667-3.30490.000803
130.1128050.87380.192861
14-0.002853-0.02210.49122
15-0.010012-0.07760.469221
160.0126340.09790.461183
170.067570.52340.301313
180.1702231.31850.096167







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.316648-2.45270.008551
20.1000870.77530.220613
30.1946781.5080.068405
40.0342430.26520.395865
50.0300750.2330.408293
6-0.07043-0.54550.293699
7-0.272883-2.11370.019352
8-0.22221-1.72120.045181
9-0.03703-0.28680.387614
10-0.184094-1.4260.079527
110.1509141.1690.123518
12-0.295596-2.28970.012786
13-0.176761-1.36920.088022
14-0.025235-0.19550.422844
150.0660280.51150.305455
16-0.051199-0.39660.346539
170.0248280.19230.424073
180.2066111.60040.057381

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.316648 & -2.4527 & 0.008551 \tabularnewline
2 & 0.100087 & 0.7753 & 0.220613 \tabularnewline
3 & 0.194678 & 1.508 & 0.068405 \tabularnewline
4 & 0.034243 & 0.2652 & 0.395865 \tabularnewline
5 & 0.030075 & 0.233 & 0.408293 \tabularnewline
6 & -0.07043 & -0.5455 & 0.293699 \tabularnewline
7 & -0.272883 & -2.1137 & 0.019352 \tabularnewline
8 & -0.22221 & -1.7212 & 0.045181 \tabularnewline
9 & -0.03703 & -0.2868 & 0.387614 \tabularnewline
10 & -0.184094 & -1.426 & 0.079527 \tabularnewline
11 & 0.150914 & 1.169 & 0.123518 \tabularnewline
12 & -0.295596 & -2.2897 & 0.012786 \tabularnewline
13 & -0.176761 & -1.3692 & 0.088022 \tabularnewline
14 & -0.025235 & -0.1955 & 0.422844 \tabularnewline
15 & 0.066028 & 0.5115 & 0.305455 \tabularnewline
16 & -0.051199 & -0.3966 & 0.346539 \tabularnewline
17 & 0.024828 & 0.1923 & 0.424073 \tabularnewline
18 & 0.206611 & 1.6004 & 0.057381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230510&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]-0.316648[/C][C]-2.4527[/C][C]0.008551[/C][/ROW]
[ROW][C]2[/C][C]0.100087[/C][C]0.7753[/C][C]0.220613[/C][/ROW]
[ROW][C]3[/C][C]0.194678[/C][C]1.508[/C][C]0.068405[/C][/ROW]
[ROW][C]4[/C][C]0.034243[/C][C]0.2652[/C][C]0.395865[/C][/ROW]
[ROW][C]5[/C][C]0.030075[/C][C]0.233[/C][C]0.408293[/C][/ROW]
[ROW][C]6[/C][C]-0.07043[/C][C]-0.5455[/C][C]0.293699[/C][/ROW]
[ROW][C]7[/C][C]-0.272883[/C][C]-2.1137[/C][C]0.019352[/C][/ROW]
[ROW][C]8[/C][C]-0.22221[/C][C]-1.7212[/C][C]0.045181[/C][/ROW]
[ROW][C]9[/C][C]-0.03703[/C][C]-0.2868[/C][C]0.387614[/C][/ROW]
[ROW][C]10[/C][C]-0.184094[/C][C]-1.426[/C][C]0.079527[/C][/ROW]
[ROW][C]11[/C][C]0.150914[/C][C]1.169[/C][C]0.123518[/C][/ROW]
[ROW][C]12[/C][C]-0.295596[/C][C]-2.2897[/C][C]0.012786[/C][/ROW]
[ROW][C]13[/C][C]-0.176761[/C][C]-1.3692[/C][C]0.088022[/C][/ROW]
[ROW][C]14[/C][C]-0.025235[/C][C]-0.1955[/C][C]0.422844[/C][/ROW]
[ROW][C]15[/C][C]0.066028[/C][C]0.5115[/C][C]0.305455[/C][/ROW]
[ROW][C]16[/C][C]-0.051199[/C][C]-0.3966[/C][C]0.346539[/C][/ROW]
[ROW][C]17[/C][C]0.024828[/C][C]0.1923[/C][C]0.424073[/C][/ROW]
[ROW][C]18[/C][C]0.206611[/C][C]1.6004[/C][C]0.057381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230510&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230510&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
1-0.316648-2.45270.008551
20.1000870.77530.220613
30.1946781.5080.068405
40.0342430.26520.395865
50.0300750.2330.408293
6-0.07043-0.54550.293699
7-0.272883-2.11370.019352
8-0.22221-1.72120.045181
9-0.03703-0.28680.387614
10-0.184094-1.4260.079527
110.1509141.1690.123518
12-0.295596-2.28970.012786
13-0.176761-1.36920.088022
14-0.025235-0.19550.422844
150.0660280.51150.305455
16-0.051199-0.39660.346539
170.0248280.19230.424073
180.2066111.60040.057381



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
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)
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')