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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 25 Nov 2010 16:31:47 +0000

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/2010/Nov/25/t12907027442149m0hp1ehqgs7.htm/, Retrieved Thu, 25 Apr 2024 22:48:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101173, Retrieved Thu, 25 Apr 2024 22:48:11 +0000

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User-defined keywords

Estimated Impact

172

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

-     [Hierarchical Clustering] [paper] [2007-12-05 22:51:14] [8d3192ea84fef628e5e980e3df2ac42d]
- RMPD  [(Partial) Autocorrelation Function] [] [2008-01-16 17:22:33] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [WS8 1] [2010-11-25 16:31:47] [c1f1b5e209adb4577289f490325e36f2] [Current]

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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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101173&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101173&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101173&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.921322	7.1365	0
2	0.83412	6.4611	0
3	0.751629	5.8221	0
4	0.645053	4.9966	3e-06
5	0.548626	4.2496	3.8e-05
6	0.430327	3.3333	0.000737
7	0.309325	2.396	0.009855
8	0.23676	1.8339	0.035812
9	0.188267	1.4583	0.074985
10	0.148581	1.1509	0.127169
11	0.127098	0.9845	0.164412
12	0.102454	0.7936	0.215277
13	0.097993	0.7591	0.225396
14	0.127889	0.9906	0.162924
15	0.140616	1.0892	0.140209
16	0.124451	0.964	0.169458
17	0.097974	0.7589	0.22544

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921322 & 7.1365 & 0 \tabularnewline
2 & 0.83412 & 6.4611 & 0 \tabularnewline
3 & 0.751629 & 5.8221 & 0 \tabularnewline
4 & 0.645053 & 4.9966 & 3e-06 \tabularnewline
5 & 0.548626 & 4.2496 & 3.8e-05 \tabularnewline
6 & 0.430327 & 3.3333 & 0.000737 \tabularnewline
7 & 0.309325 & 2.396 & 0.009855 \tabularnewline
8 & 0.23676 & 1.8339 & 0.035812 \tabularnewline
9 & 0.188267 & 1.4583 & 0.074985 \tabularnewline
10 & 0.148581 & 1.1509 & 0.127169 \tabularnewline
11 & 0.127098 & 0.9845 & 0.164412 \tabularnewline
12 & 0.102454 & 0.7936 & 0.215277 \tabularnewline
13 & 0.097993 & 0.7591 & 0.225396 \tabularnewline
14 & 0.127889 & 0.9906 & 0.162924 \tabularnewline
15 & 0.140616 & 1.0892 & 0.140209 \tabularnewline
16 & 0.124451 & 0.964 & 0.169458 \tabularnewline
17 & 0.097974 & 0.7589 & 0.22544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101173&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]0.921322[/C][C]7.1365[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.83412[/C][C]6.4611[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.751629[/C][C]5.8221[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.645053[/C][C]4.9966[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.548626[/C][C]4.2496[/C][C]3.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.430327[/C][C]3.3333[/C][C]0.000737[/C][/ROW]
[ROW][C]7[/C][C]0.309325[/C][C]2.396[/C][C]0.009855[/C][/ROW]
[ROW][C]8[/C][C]0.23676[/C][C]1.8339[/C][C]0.035812[/C][/ROW]
[ROW][C]9[/C][C]0.188267[/C][C]1.4583[/C][C]0.074985[/C][/ROW]
[ROW][C]10[/C][C]0.148581[/C][C]1.1509[/C][C]0.127169[/C][/ROW]
[ROW][C]11[/C][C]0.127098[/C][C]0.9845[/C][C]0.164412[/C][/ROW]
[ROW][C]12[/C][C]0.102454[/C][C]0.7936[/C][C]0.215277[/C][/ROW]
[ROW][C]13[/C][C]0.097993[/C][C]0.7591[/C][C]0.225396[/C][/ROW]
[ROW][C]14[/C][C]0.127889[/C][C]0.9906[/C][C]0.162924[/C][/ROW]
[ROW][C]15[/C][C]0.140616[/C][C]1.0892[/C][C]0.140209[/C][/ROW]
[ROW][C]16[/C][C]0.124451[/C][C]0.964[/C][C]0.169458[/C][/ROW]
[ROW][C]17[/C][C]0.097974[/C][C]0.7589[/C][C]0.22544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101173&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101173&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	0.921322	7.1365	0
2	0.83412	6.4611	0
3	0.751629	5.8221	0
4	0.645053	4.9966	3e-06
5	0.548626	4.2496	3.8e-05
6	0.430327	3.3333	0.000737
7	0.309325	2.396	0.009855
8	0.23676	1.8339	0.035812
9	0.188267	1.4583	0.074985
10	0.148581	1.1509	0.127169
11	0.127098	0.9845	0.164412
12	0.102454	0.7936	0.215277
13	0.097993	0.7591	0.225396
14	0.127889	0.9906	0.162924
15	0.140616	1.0892	0.140209
16	0.124451	0.964	0.169458
17	0.097974	0.7589	0.22544

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.921322	7.1365	0
2	-0.097342	-0.754	0.226898
3	-0.01327	-0.1028	0.459238
4	-0.211392	-1.6374	0.053387
5	0.023234	0.18	0.42889
6	-0.237881	-1.8426	0.035163
7	-0.049847	-0.3861	0.35039
8	0.214649	1.6627	0.050798
9	0.137977	1.0688	0.144729
10	0.008471	0.0656	0.473951
11	0.028	0.2169	0.414515
12	-0.084195	-0.6522	0.25839
13	0.022973	0.178	0.429681
14	0.13376	1.0361	0.152156
15	-0.059505	-0.4609	0.323259
16	-0.192832	-1.4937	0.070251
17	-0.104273	-0.8077	0.211227

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921322 & 7.1365 & 0 \tabularnewline
2 & -0.097342 & -0.754 & 0.226898 \tabularnewline
3 & -0.01327 & -0.1028 & 0.459238 \tabularnewline
4 & -0.211392 & -1.6374 & 0.053387 \tabularnewline
5 & 0.023234 & 0.18 & 0.42889 \tabularnewline
6 & -0.237881 & -1.8426 & 0.035163 \tabularnewline
7 & -0.049847 & -0.3861 & 0.35039 \tabularnewline
8 & 0.214649 & 1.6627 & 0.050798 \tabularnewline
9 & 0.137977 & 1.0688 & 0.144729 \tabularnewline
10 & 0.008471 & 0.0656 & 0.473951 \tabularnewline
11 & 0.028 & 0.2169 & 0.414515 \tabularnewline
12 & -0.084195 & -0.6522 & 0.25839 \tabularnewline
13 & 0.022973 & 0.178 & 0.429681 \tabularnewline
14 & 0.13376 & 1.0361 & 0.152156 \tabularnewline
15 & -0.059505 & -0.4609 & 0.323259 \tabularnewline
16 & -0.192832 & -1.4937 & 0.070251 \tabularnewline
17 & -0.104273 & -0.8077 & 0.211227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101173&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]0.921322[/C][C]7.1365[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.097342[/C][C]-0.754[/C][C]0.226898[/C][/ROW]
[ROW][C]3[/C][C]-0.01327[/C][C]-0.1028[/C][C]0.459238[/C][/ROW]
[ROW][C]4[/C][C]-0.211392[/C][C]-1.6374[/C][C]0.053387[/C][/ROW]
[ROW][C]5[/C][C]0.023234[/C][C]0.18[/C][C]0.42889[/C][/ROW]
[ROW][C]6[/C][C]-0.237881[/C][C]-1.8426[/C][C]0.035163[/C][/ROW]
[ROW][C]7[/C][C]-0.049847[/C][C]-0.3861[/C][C]0.35039[/C][/ROW]
[ROW][C]8[/C][C]0.214649[/C][C]1.6627[/C][C]0.050798[/C][/ROW]
[ROW][C]9[/C][C]0.137977[/C][C]1.0688[/C][C]0.144729[/C][/ROW]
[ROW][C]10[/C][C]0.008471[/C][C]0.0656[/C][C]0.473951[/C][/ROW]
[ROW][C]11[/C][C]0.028[/C][C]0.2169[/C][C]0.414515[/C][/ROW]
[ROW][C]12[/C][C]-0.084195[/C][C]-0.6522[/C][C]0.25839[/C][/ROW]
[ROW][C]13[/C][C]0.022973[/C][C]0.178[/C][C]0.429681[/C][/ROW]
[ROW][C]14[/C][C]0.13376[/C][C]1.0361[/C][C]0.152156[/C][/ROW]
[ROW][C]15[/C][C]-0.059505[/C][C]-0.4609[/C][C]0.323259[/C][/ROW]
[ROW][C]16[/C][C]-0.192832[/C][C]-1.4937[/C][C]0.070251[/C][/ROW]
[ROW][C]17[/C][C]-0.104273[/C][C]-0.8077[/C][C]0.211227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101173&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101173&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	0.921322	7.1365	0
2	-0.097342	-0.754	0.226898
3	-0.01327	-0.1028	0.459238
4	-0.211392	-1.6374	0.053387
5	0.023234	0.18	0.42889
6	-0.237881	-1.8426	0.035163
7	-0.049847	-0.3861	0.35039
8	0.214649	1.6627	0.050798
9	0.137977	1.0688	0.144729
10	0.008471	0.0656	0.473951
11	0.028	0.2169	0.414515
12	-0.084195	-0.6522	0.25839
13	0.022973	0.178	0.429681
14	0.13376	1.0361	0.152156
15	-0.059505	-0.4609	0.323259
16	-0.192832	-1.4937	0.070251
17	-0.104273	-0.8077	0.211227

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code