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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 13:17:25 -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/t1386181709kavmuzn17qcstwx.htm/, Retrieved Thu, 28 Mar 2024 08:36:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230746, Retrieved Thu, 28 Mar 2024 08:36:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [Spectrale analyse] [2013-12-04 17:49:56] [947cbe24e101527daf12b807d6a22f40]
- RMP     [(Partial) Autocorrelation Function] [Autocorrelatie] [2013-12-04 18:17:25] [46d3d8bfbaf7691f7408e38ca0da8f78] [Current]
- RM        [(Partial) Autocorrelation Function] [Autocorrelatie] [2013-12-04 18:28:43] [947cbe24e101527daf12b807d6a22f40]
- RMP       [Standard Deviation-Mean Plot] [Standard deviatio...] [2013-12-04 18:39:01] [947cbe24e101527daf12b807d6a22f40]
- RM          [Standard Deviation-Mean Plot] [Standard deviatio...] [2013-12-04 18:39:31] [947cbe24e101527daf12b807d6a22f40]
- RMP         [Histogram] [Histogram] [2013-12-04 19:32:37] [947cbe24e101527daf12b807d6a22f40]
- RM            [Histogram] [Histogram] [2013-12-04 19:33:05] [947cbe24e101527daf12b807d6a22f40]
- RMP           [Skewness and Kurtosis Test] [Skewness and Kurt...] [2013-12-04 19:40:53] [947cbe24e101527daf12b807d6a22f40]
- RM              [Skewness and Kurtosis Test] [Skewness and Kurt...] [2013-12-04 19:41:11] [947cbe24e101527daf12b807d6a22f40]
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Dataseries X:
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230746&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230746&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'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.3041962.41450.009337
20.2503881.98740.025615
30.2379061.88830.031795
40.2288141.81620.037052
50.3829063.03920.001726
60.250481.98810.025574
70.1092190.86690.194643
80.159991.26990.104398
90.2979132.36460.010571
100.0546040.43340.3331
110.0412470.32740.372229
12-0.003171-0.02520.49
130.010410.08260.467204
140.2451811.94610.028055
15-0.025139-0.19950.421244
160.0061450.04880.480626
170.0744050.59060.278461
180.0639460.50760.306769

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.304196 & 2.4145 & 0.009337 \tabularnewline
2 & 0.250388 & 1.9874 & 0.025615 \tabularnewline
3 & 0.237906 & 1.8883 & 0.031795 \tabularnewline
4 & 0.228814 & 1.8162 & 0.037052 \tabularnewline
5 & 0.382906 & 3.0392 & 0.001726 \tabularnewline
6 & 0.25048 & 1.9881 & 0.025574 \tabularnewline
7 & 0.109219 & 0.8669 & 0.194643 \tabularnewline
8 & 0.15999 & 1.2699 & 0.104398 \tabularnewline
9 & 0.297913 & 2.3646 & 0.010571 \tabularnewline
10 & 0.054604 & 0.4334 & 0.3331 \tabularnewline
11 & 0.041247 & 0.3274 & 0.372229 \tabularnewline
12 & -0.003171 & -0.0252 & 0.49 \tabularnewline
13 & 0.01041 & 0.0826 & 0.467204 \tabularnewline
14 & 0.245181 & 1.9461 & 0.028055 \tabularnewline
15 & -0.025139 & -0.1995 & 0.421244 \tabularnewline
16 & 0.006145 & 0.0488 & 0.480626 \tabularnewline
17 & 0.074405 & 0.5906 & 0.278461 \tabularnewline
18 & 0.063946 & 0.5076 & 0.306769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230746&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]0.304196[/C][C]2.4145[/C][C]0.009337[/C][/ROW]
[ROW][C]2[/C][C]0.250388[/C][C]1.9874[/C][C]0.025615[/C][/ROW]
[ROW][C]3[/C][C]0.237906[/C][C]1.8883[/C][C]0.031795[/C][/ROW]
[ROW][C]4[/C][C]0.228814[/C][C]1.8162[/C][C]0.037052[/C][/ROW]
[ROW][C]5[/C][C]0.382906[/C][C]3.0392[/C][C]0.001726[/C][/ROW]
[ROW][C]6[/C][C]0.25048[/C][C]1.9881[/C][C]0.025574[/C][/ROW]
[ROW][C]7[/C][C]0.109219[/C][C]0.8669[/C][C]0.194643[/C][/ROW]
[ROW][C]8[/C][C]0.15999[/C][C]1.2699[/C][C]0.104398[/C][/ROW]
[ROW][C]9[/C][C]0.297913[/C][C]2.3646[/C][C]0.010571[/C][/ROW]
[ROW][C]10[/C][C]0.054604[/C][C]0.4334[/C][C]0.3331[/C][/ROW]
[ROW][C]11[/C][C]0.041247[/C][C]0.3274[/C][C]0.372229[/C][/ROW]
[ROW][C]12[/C][C]-0.003171[/C][C]-0.0252[/C][C]0.49[/C][/ROW]
[ROW][C]13[/C][C]0.01041[/C][C]0.0826[/C][C]0.467204[/C][/ROW]
[ROW][C]14[/C][C]0.245181[/C][C]1.9461[/C][C]0.028055[/C][/ROW]
[ROW][C]15[/C][C]-0.025139[/C][C]-0.1995[/C][C]0.421244[/C][/ROW]
[ROW][C]16[/C][C]0.006145[/C][C]0.0488[/C][C]0.480626[/C][/ROW]
[ROW][C]17[/C][C]0.074405[/C][C]0.5906[/C][C]0.278461[/C][/ROW]
[ROW][C]18[/C][C]0.063946[/C][C]0.5076[/C][C]0.306769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230746&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
10.3041962.41450.009337
20.2503881.98740.025615
30.2379061.88830.031795
40.2288141.81620.037052
50.3829063.03920.001726
60.250481.98810.025574
70.1092190.86690.194643
80.159991.26990.104398
90.2979132.36460.010571
100.0546040.43340.3331
110.0412470.32740.372229
12-0.003171-0.02520.49
130.010410.08260.467204
140.2451811.94610.028055
15-0.025139-0.19950.421244
160.0061450.04880.480626
170.0744050.59060.278461
180.0639460.50760.306769







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.3041962.41450.009337
20.1739491.38070.086128
30.1387181.1010.137533
40.1132570.89890.186051
50.2845512.25860.013691
60.0544160.43190.333641
7-0.101531-0.80590.211673
80.0196590.1560.438251
90.2047881.62550.054529
10-0.225183-1.78730.039347
11-0.126322-1.00270.159932
12-0.033912-0.26920.394339
13-0.022314-0.17710.429995
140.1704231.35270.090495
15-0.117086-0.92930.17813
160.074310.58980.278711
170.1186640.94190.174929
180.0059450.04720.481255

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.304196 & 2.4145 & 0.009337 \tabularnewline
2 & 0.173949 & 1.3807 & 0.086128 \tabularnewline
3 & 0.138718 & 1.101 & 0.137533 \tabularnewline
4 & 0.113257 & 0.8989 & 0.186051 \tabularnewline
5 & 0.284551 & 2.2586 & 0.013691 \tabularnewline
6 & 0.054416 & 0.4319 & 0.333641 \tabularnewline
7 & -0.101531 & -0.8059 & 0.211673 \tabularnewline
8 & 0.019659 & 0.156 & 0.438251 \tabularnewline
9 & 0.204788 & 1.6255 & 0.054529 \tabularnewline
10 & -0.225183 & -1.7873 & 0.039347 \tabularnewline
11 & -0.126322 & -1.0027 & 0.159932 \tabularnewline
12 & -0.033912 & -0.2692 & 0.394339 \tabularnewline
13 & -0.022314 & -0.1771 & 0.429995 \tabularnewline
14 & 0.170423 & 1.3527 & 0.090495 \tabularnewline
15 & -0.117086 & -0.9293 & 0.17813 \tabularnewline
16 & 0.07431 & 0.5898 & 0.278711 \tabularnewline
17 & 0.118664 & 0.9419 & 0.174929 \tabularnewline
18 & 0.005945 & 0.0472 & 0.481255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230746&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]0.304196[/C][C]2.4145[/C][C]0.009337[/C][/ROW]
[ROW][C]2[/C][C]0.173949[/C][C]1.3807[/C][C]0.086128[/C][/ROW]
[ROW][C]3[/C][C]0.138718[/C][C]1.101[/C][C]0.137533[/C][/ROW]
[ROW][C]4[/C][C]0.113257[/C][C]0.8989[/C][C]0.186051[/C][/ROW]
[ROW][C]5[/C][C]0.284551[/C][C]2.2586[/C][C]0.013691[/C][/ROW]
[ROW][C]6[/C][C]0.054416[/C][C]0.4319[/C][C]0.333641[/C][/ROW]
[ROW][C]7[/C][C]-0.101531[/C][C]-0.8059[/C][C]0.211673[/C][/ROW]
[ROW][C]8[/C][C]0.019659[/C][C]0.156[/C][C]0.438251[/C][/ROW]
[ROW][C]9[/C][C]0.204788[/C][C]1.6255[/C][C]0.054529[/C][/ROW]
[ROW][C]10[/C][C]-0.225183[/C][C]-1.7873[/C][C]0.039347[/C][/ROW]
[ROW][C]11[/C][C]-0.126322[/C][C]-1.0027[/C][C]0.159932[/C][/ROW]
[ROW][C]12[/C][C]-0.033912[/C][C]-0.2692[/C][C]0.394339[/C][/ROW]
[ROW][C]13[/C][C]-0.022314[/C][C]-0.1771[/C][C]0.429995[/C][/ROW]
[ROW][C]14[/C][C]0.170423[/C][C]1.3527[/C][C]0.090495[/C][/ROW]
[ROW][C]15[/C][C]-0.117086[/C][C]-0.9293[/C][C]0.17813[/C][/ROW]
[ROW][C]16[/C][C]0.07431[/C][C]0.5898[/C][C]0.278711[/C][/ROW]
[ROW][C]17[/C][C]0.118664[/C][C]0.9419[/C][C]0.174929[/C][/ROW]
[ROW][C]18[/C][C]0.005945[/C][C]0.0472[/C][C]0.481255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230746&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
10.3041962.41450.009337
20.1739491.38070.086128
30.1387181.1010.137533
40.1132570.89890.186051
50.2845512.25860.013691
60.0544160.43190.333641
7-0.101531-0.80590.211673
80.0196590.1560.438251
90.2047881.62550.054529
10-0.225183-1.78730.039347
11-0.126322-1.00270.159932
12-0.033912-0.26920.394339
13-0.022314-0.17710.429995
140.1704231.35270.090495
15-0.117086-0.92930.17813
160.074310.58980.278711
170.1186640.94190.174929
180.0059450.04720.481255



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')