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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2011 14:25:08 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t13244091323or24na8vui7mj4.htm/, Retrieved Mon, 06 May 2024 02:53:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158181, Retrieved Mon, 06 May 2024 02:53:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

132

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD  [Central Tendency] [] [2011-12-06 20:01:16] [b98453cac15ba1066b407e146608df68]
- RMP       [(Partial) Autocorrelation Function] [Autocorrelatie] [2011-12-20 19:25:08] [0f3e8e7e39f9d04dccdcd37cd9447b26] [Current]

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Dataseries X:

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Histogram

Boxplots

867.887509505211
-2250.28069676838
33618.3570412959
9954.34468238836
354.191730842355
18882.406400463
20229.4310915672
268402.416151187
-113346.926055862
-45016.394227939
35069.861367254
58531.0957290091
-77256.3771198791
-31473.594568955
-52391.0075132882
32854.9847569661
101107.732845397
-176275.960398033
79531.884415102
-176414.251561376
151290.579462589
167731.594163443
143237.122434691
80251.9665265577
118735.726273623
75035.8259037494
19198.3085437346
-36364.5639276314
-36170.5787440905
-109567.395064155
-100783.336097857
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38947.3510583149
58613.0600994635
16074.4602044407
-41563.0049150659
-15970.5964777959
-47563.9548420802
59595.3577179922
65897.8405390448
-166489.283203891
46312.3269884632
-15952.8722863516
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134744.172737777
75232.8122408289
24408.7558471514
-15406.1403381955
-3766.75348767364
27197.2239951006
-46777.2890031503
-82472.8212609495
-35154.7184801844
-46946.870011609
-43641.5364941684
-54920.7084991732
54905.4038222157
-10509.5840707596
-13706.8046976985
-42347.6087628011
-28990.4687708701

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158181&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158181&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.043129	-0.3019	0.382002
2	0.192019	1.3441	0.092548
3	0.0487	0.3409	0.367319
4	0.048239	0.3377	0.368527
5	0.039456	0.2762	0.39178
6	-0.091292	-0.639	0.262886
7	-0.167871	-1.1751	0.122818
8	-0.132945	-0.9306	0.178308
9	-0.145184	-1.0163	0.157242
10	-0.193882	-1.3572	0.090473
11	-0.064907	-0.4544	0.325791
12	-0.358096	-2.5067	0.007777
13	-0.029028	-0.2032	0.419913
14	-0.102545	-0.7178	0.238141
15	-0.046719	-0.327	0.372518
16	0.006727	0.0471	0.481318
17	0.113824	0.7968	0.214716

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.043129 & -0.3019 & 0.382002 \tabularnewline
2 & 0.192019 & 1.3441 & 0.092548 \tabularnewline
3 & 0.0487 & 0.3409 & 0.367319 \tabularnewline
4 & 0.048239 & 0.3377 & 0.368527 \tabularnewline
5 & 0.039456 & 0.2762 & 0.39178 \tabularnewline
6 & -0.091292 & -0.639 & 0.262886 \tabularnewline
7 & -0.167871 & -1.1751 & 0.122818 \tabularnewline
8 & -0.132945 & -0.9306 & 0.178308 \tabularnewline
9 & -0.145184 & -1.0163 & 0.157242 \tabularnewline
10 & -0.193882 & -1.3572 & 0.090473 \tabularnewline
11 & -0.064907 & -0.4544 & 0.325791 \tabularnewline
12 & -0.358096 & -2.5067 & 0.007777 \tabularnewline
13 & -0.029028 & -0.2032 & 0.419913 \tabularnewline
14 & -0.102545 & -0.7178 & 0.238141 \tabularnewline
15 & -0.046719 & -0.327 & 0.372518 \tabularnewline
16 & 0.006727 & 0.0471 & 0.481318 \tabularnewline
17 & 0.113824 & 0.7968 & 0.214716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158181&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]-0.043129[/C][C]-0.3019[/C][C]0.382002[/C][/ROW]
[ROW][C]2[/C][C]0.192019[/C][C]1.3441[/C][C]0.092548[/C][/ROW]
[ROW][C]3[/C][C]0.0487[/C][C]0.3409[/C][C]0.367319[/C][/ROW]
[ROW][C]4[/C][C]0.048239[/C][C]0.3377[/C][C]0.368527[/C][/ROW]
[ROW][C]5[/C][C]0.039456[/C][C]0.2762[/C][C]0.39178[/C][/ROW]
[ROW][C]6[/C][C]-0.091292[/C][C]-0.639[/C][C]0.262886[/C][/ROW]
[ROW][C]7[/C][C]-0.167871[/C][C]-1.1751[/C][C]0.122818[/C][/ROW]
[ROW][C]8[/C][C]-0.132945[/C][C]-0.9306[/C][C]0.178308[/C][/ROW]
[ROW][C]9[/C][C]-0.145184[/C][C]-1.0163[/C][C]0.157242[/C][/ROW]
[ROW][C]10[/C][C]-0.193882[/C][C]-1.3572[/C][C]0.090473[/C][/ROW]
[ROW][C]11[/C][C]-0.064907[/C][C]-0.4544[/C][C]0.325791[/C][/ROW]
[ROW][C]12[/C][C]-0.358096[/C][C]-2.5067[/C][C]0.007777[/C][/ROW]
[ROW][C]13[/C][C]-0.029028[/C][C]-0.2032[/C][C]0.419913[/C][/ROW]
[ROW][C]14[/C][C]-0.102545[/C][C]-0.7178[/C][C]0.238141[/C][/ROW]
[ROW][C]15[/C][C]-0.046719[/C][C]-0.327[/C][C]0.372518[/C][/ROW]
[ROW][C]16[/C][C]0.006727[/C][C]0.0471[/C][C]0.481318[/C][/ROW]
[ROW][C]17[/C][C]0.113824[/C][C]0.7968[/C][C]0.214716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158181&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 k	ACF(k)	T-STAT	P-value
1	-0.043129	-0.3019	0.382002
2	0.192019	1.3441	0.092548
3	0.0487	0.3409	0.367319
4	0.048239	0.3377	0.368527
5	0.039456	0.2762	0.39178
6	-0.091292	-0.639	0.262886
7	-0.167871	-1.1751	0.122818
8	-0.132945	-0.9306	0.178308
9	-0.145184	-1.0163	0.157242
10	-0.193882	-1.3572	0.090473
11	-0.064907	-0.4544	0.325791
12	-0.358096	-2.5067	0.007777
13	-0.029028	-0.2032	0.419913
14	-0.102545	-0.7178	0.238141
15	-0.046719	-0.327	0.372518
16	0.006727	0.0471	0.481318
17	0.113824	0.7968	0.214716

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.043129	-0.3019	0.382002
2	0.190514	1.3336	0.094252
3	0.066139	0.463	0.322716
4	0.017103	0.1197	0.452598
5	0.021364	0.1495	0.440867
6	-0.108734	-0.7611	0.225111
7	-0.203712	-1.426	0.080107
8	-0.133719	-0.936	0.176923
9	-0.096931	-0.6785	0.250317
10	-0.154203	-1.0794	0.142843
11	-0.016386	-0.1147	0.454574
12	-0.317122	-2.2199	0.015544
13	-0.107546	-0.7528	0.22758
14	-0.077752	-0.5443	0.294365
15	-0.120248	-0.8417	0.202012
16	-0.08962	-0.6273	0.266675
17	0.051782	0.3625	0.359277

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.043129 & -0.3019 & 0.382002 \tabularnewline
2 & 0.190514 & 1.3336 & 0.094252 \tabularnewline
3 & 0.066139 & 0.463 & 0.322716 \tabularnewline
4 & 0.017103 & 0.1197 & 0.452598 \tabularnewline
5 & 0.021364 & 0.1495 & 0.440867 \tabularnewline
6 & -0.108734 & -0.7611 & 0.225111 \tabularnewline
7 & -0.203712 & -1.426 & 0.080107 \tabularnewline
8 & -0.133719 & -0.936 & 0.176923 \tabularnewline
9 & -0.096931 & -0.6785 & 0.250317 \tabularnewline
10 & -0.154203 & -1.0794 & 0.142843 \tabularnewline
11 & -0.016386 & -0.1147 & 0.454574 \tabularnewline
12 & -0.317122 & -2.2199 & 0.015544 \tabularnewline
13 & -0.107546 & -0.7528 & 0.22758 \tabularnewline
14 & -0.077752 & -0.5443 & 0.294365 \tabularnewline
15 & -0.120248 & -0.8417 & 0.202012 \tabularnewline
16 & -0.08962 & -0.6273 & 0.266675 \tabularnewline
17 & 0.051782 & 0.3625 & 0.359277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158181&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]-0.043129[/C][C]-0.3019[/C][C]0.382002[/C][/ROW]
[ROW][C]2[/C][C]0.190514[/C][C]1.3336[/C][C]0.094252[/C][/ROW]
[ROW][C]3[/C][C]0.066139[/C][C]0.463[/C][C]0.322716[/C][/ROW]
[ROW][C]4[/C][C]0.017103[/C][C]0.1197[/C][C]0.452598[/C][/ROW]
[ROW][C]5[/C][C]0.021364[/C][C]0.1495[/C][C]0.440867[/C][/ROW]
[ROW][C]6[/C][C]-0.108734[/C][C]-0.7611[/C][C]0.225111[/C][/ROW]
[ROW][C]7[/C][C]-0.203712[/C][C]-1.426[/C][C]0.080107[/C][/ROW]
[ROW][C]8[/C][C]-0.133719[/C][C]-0.936[/C][C]0.176923[/C][/ROW]
[ROW][C]9[/C][C]-0.096931[/C][C]-0.6785[/C][C]0.250317[/C][/ROW]
[ROW][C]10[/C][C]-0.154203[/C][C]-1.0794[/C][C]0.142843[/C][/ROW]
[ROW][C]11[/C][C]-0.016386[/C][C]-0.1147[/C][C]0.454574[/C][/ROW]
[ROW][C]12[/C][C]-0.317122[/C][C]-2.2199[/C][C]0.015544[/C][/ROW]
[ROW][C]13[/C][C]-0.107546[/C][C]-0.7528[/C][C]0.22758[/C][/ROW]
[ROW][C]14[/C][C]-0.077752[/C][C]-0.5443[/C][C]0.294365[/C][/ROW]
[ROW][C]15[/C][C]-0.120248[/C][C]-0.8417[/C][C]0.202012[/C][/ROW]
[ROW][C]16[/C][C]-0.08962[/C][C]-0.6273[/C][C]0.266675[/C][/ROW]
[ROW][C]17[/C][C]0.051782[/C][C]0.3625[/C][C]0.359277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158181&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 k	PACF(k)	T-STAT	P-value
1	-0.043129	-0.3019	0.382002
2	0.190514	1.3336	0.094252
3	0.066139	0.463	0.322716
4	0.017103	0.1197	0.452598
5	0.021364	0.1495	0.440867
6	-0.108734	-0.7611	0.225111
7	-0.203712	-1.426	0.080107
8	-0.133719	-0.936	0.176923
9	-0.096931	-0.6785	0.250317
10	-0.154203	-1.0794	0.142843
11	-0.016386	-0.1147	0.454574
12	-0.317122	-2.2199	0.015544
13	-0.107546	-0.7528	0.22758
14	-0.077752	-0.5443	0.294365
15	-0.120248	-0.8417	0.202012
16	-0.08962	-0.6273	0.266675
17	0.051782	0.3625	0.359277

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code