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Description of Statistical Computation

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 computationThu, 02 Dec 2010 16:58:57 +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/2010/Dec/02/t12913090255af3tlpzwrcpx6f.htm/, Retrieved Sun, 05 May 2024 13:38:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104353, Retrieved Sun, 05 May 2024 13:38:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [autocorrelation f...] [2010-12-02 16:35:19] [717f3d787904f94c39256c5c1fc72d4c]
-    D        [(Partial) Autocorrelation Function] [autocorrelation f...] [2010-12-02 16:58:57] [c1f1b5e209adb4577289f490325e36f2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.6923
0.6886
0.6855
0.6745
0.6769
0.6758
0.6896
0.6843
0.6818
0.6774
0.6821
0.6885
0.6829
0.6796
0.6976
0.6924
0.6849
0.6921
0.6839
0.6727
0.6776
0.6692
0.6738
0.6740
0.6635
0.6737
0.6788
0.6828
0.6795
0.6740
0.6744
0.6764
0.6987
0.6967
0.7116
0.7357
0.7455
0.7639
0.7958
0.7864
0.7853
0.7903
0.7866
0.8039
0.7916
0.7903
0.8242
0.9567
0.8850
0.8865
0.9258
0.8948
0.8762
0.8527
0.8536
0.8805
0.9155
0.8961
0.9127
0.8857

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104353&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104353&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9377467.26380
20.8787366.80670
30.8351096.46870
40.7726085.98460
50.7210385.58510
60.6830665.2911e-06
70.647345.01433e-06
80.6118774.73967e-06
90.5656834.38182.4e-05
100.4840373.74930.000201
110.421183.26240.000912
120.3507252.71670.004302
130.2545991.97210.026606
140.1984081.53690.064792
150.1595481.23590.110665
160.1115780.86430.195438
170.0657390.50920.306235

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.937746 & 7.2638 & 0 \tabularnewline
2 & 0.878736 & 6.8067 & 0 \tabularnewline
3 & 0.835109 & 6.4687 & 0 \tabularnewline
4 & 0.772608 & 5.9846 & 0 \tabularnewline
5 & 0.721038 & 5.5851 & 0 \tabularnewline
6 & 0.683066 & 5.291 & 1e-06 \tabularnewline
7 & 0.64734 & 5.0143 & 3e-06 \tabularnewline
8 & 0.611877 & 4.7396 & 7e-06 \tabularnewline
9 & 0.565683 & 4.3818 & 2.4e-05 \tabularnewline
10 & 0.484037 & 3.7493 & 0.000201 \tabularnewline
11 & 0.42118 & 3.2624 & 0.000912 \tabularnewline
12 & 0.350725 & 2.7167 & 0.004302 \tabularnewline
13 & 0.254599 & 1.9721 & 0.026606 \tabularnewline
14 & 0.198408 & 1.5369 & 0.064792 \tabularnewline
15 & 0.159548 & 1.2359 & 0.110665 \tabularnewline
16 & 0.111578 & 0.8643 & 0.195438 \tabularnewline
17 & 0.065739 & 0.5092 & 0.306235 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104353&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]0.937746[/C][C]7.2638[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.878736[/C][C]6.8067[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.835109[/C][C]6.4687[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.772608[/C][C]5.9846[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.721038[/C][C]5.5851[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.683066[/C][C]5.291[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.64734[/C][C]5.0143[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.611877[/C][C]4.7396[/C][C]7e-06[/C][/ROW]
[ROW][C]9[/C][C]0.565683[/C][C]4.3818[/C][C]2.4e-05[/C][/ROW]
[ROW][C]10[/C][C]0.484037[/C][C]3.7493[/C][C]0.000201[/C][/ROW]
[ROW][C]11[/C][C]0.42118[/C][C]3.2624[/C][C]0.000912[/C][/ROW]
[ROW][C]12[/C][C]0.350725[/C][C]2.7167[/C][C]0.004302[/C][/ROW]
[ROW][C]13[/C][C]0.254599[/C][C]1.9721[/C][C]0.026606[/C][/ROW]
[ROW][C]14[/C][C]0.198408[/C][C]1.5369[/C][C]0.064792[/C][/ROW]
[ROW][C]15[/C][C]0.159548[/C][C]1.2359[/C][C]0.110665[/C][/ROW]
[ROW][C]16[/C][C]0.111578[/C][C]0.8643[/C][C]0.195438[/C][/ROW]
[ROW][C]17[/C][C]0.065739[/C][C]0.5092[/C][C]0.306235[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104353&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9377467.26380
20.8787366.80670
30.8351096.46870
40.7726085.98460
50.7210385.58510
60.6830665.2911e-06
70.647345.01433e-06
80.6118774.73967e-06
90.5656834.38182.4e-05
100.4840373.74930.000201
110.421183.26240.000912
120.3507252.71670.004302
130.2545991.97210.026606
140.1984081.53690.064792
150.1595481.23590.110665
160.1115780.86430.195438
170.0657390.50920.306235






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9377467.26380
2-0.005241-0.04060.483878
30.0967730.74960.228213
4-0.175916-1.36260.089044
50.0694690.53810.296248
60.0499560.3870.350077
70.0435990.33770.368378
8-0.024906-0.19290.423837
9-0.125265-0.97030.167897
10-0.339255-2.62790.005447
110.1050930.81410.209418
12-0.156979-1.2160.114382
13-0.179902-1.39350.084303
140.1733941.34310.092148
150.058550.45350.325902
16-0.032899-0.25480.39986
17-0.074733-0.57890.28242

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.937746 & 7.2638 & 0 \tabularnewline
2 & -0.005241 & -0.0406 & 0.483878 \tabularnewline
3 & 0.096773 & 0.7496 & 0.228213 \tabularnewline
4 & -0.175916 & -1.3626 & 0.089044 \tabularnewline
5 & 0.069469 & 0.5381 & 0.296248 \tabularnewline
6 & 0.049956 & 0.387 & 0.350077 \tabularnewline
7 & 0.043599 & 0.3377 & 0.368378 \tabularnewline
8 & -0.024906 & -0.1929 & 0.423837 \tabularnewline
9 & -0.125265 & -0.9703 & 0.167897 \tabularnewline
10 & -0.339255 & -2.6279 & 0.005447 \tabularnewline
11 & 0.105093 & 0.8141 & 0.209418 \tabularnewline
12 & -0.156979 & -1.216 & 0.114382 \tabularnewline
13 & -0.179902 & -1.3935 & 0.084303 \tabularnewline
14 & 0.173394 & 1.3431 & 0.092148 \tabularnewline
15 & 0.05855 & 0.4535 & 0.325902 \tabularnewline
16 & -0.032899 & -0.2548 & 0.39986 \tabularnewline
17 & -0.074733 & -0.5789 & 0.28242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104353&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]0.937746[/C][C]7.2638[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.005241[/C][C]-0.0406[/C][C]0.483878[/C][/ROW]
[ROW][C]3[/C][C]0.096773[/C][C]0.7496[/C][C]0.228213[/C][/ROW]
[ROW][C]4[/C][C]-0.175916[/C][C]-1.3626[/C][C]0.089044[/C][/ROW]
[ROW][C]5[/C][C]0.069469[/C][C]0.5381[/C][C]0.296248[/C][/ROW]
[ROW][C]6[/C][C]0.049956[/C][C]0.387[/C][C]0.350077[/C][/ROW]
[ROW][C]7[/C][C]0.043599[/C][C]0.3377[/C][C]0.368378[/C][/ROW]
[ROW][C]8[/C][C]-0.024906[/C][C]-0.1929[/C][C]0.423837[/C][/ROW]
[ROW][C]9[/C][C]-0.125265[/C][C]-0.9703[/C][C]0.167897[/C][/ROW]
[ROW][C]10[/C][C]-0.339255[/C][C]-2.6279[/C][C]0.005447[/C][/ROW]
[ROW][C]11[/C][C]0.105093[/C][C]0.8141[/C][C]0.209418[/C][/ROW]
[ROW][C]12[/C][C]-0.156979[/C][C]-1.216[/C][C]0.114382[/C][/ROW]
[ROW][C]13[/C][C]-0.179902[/C][C]-1.3935[/C][C]0.084303[/C][/ROW]
[ROW][C]14[/C][C]0.173394[/C][C]1.3431[/C][C]0.092148[/C][/ROW]
[ROW][C]15[/C][C]0.05855[/C][C]0.4535[/C][C]0.325902[/C][/ROW]
[ROW][C]16[/C][C]-0.032899[/C][C]-0.2548[/C][C]0.39986[/C][/ROW]
[ROW][C]17[/C][C]-0.074733[/C][C]-0.5789[/C][C]0.28242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104353&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104353&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9377467.26380
2-0.005241-0.04060.483878
30.0967730.74960.228213
4-0.175916-1.36260.089044
50.0694690.53810.296248
60.0499560.3870.350077
70.0435990.33770.368378
8-0.024906-0.19290.423837
9-0.125265-0.97030.167897
10-0.339255-2.62790.005447
110.1050930.81410.209418
12-0.156979-1.2160.114382
13-0.179902-1.39350.084303
140.1733941.34310.092148
150.058550.45350.325902
16-0.032899-0.25480.39986
17-0.074733-0.57890.28242


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')