Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Sun, 19 Dec 2010 13:35:17 +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/Dec/19/t1292765626yqbzz1irpsrm3g4.htm/, Retrieved Sun, 05 May 2024 01:27:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112370, Retrieved Sun, 05 May 2024 01:27:53 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

146

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]
F RMP   [(Partial) Autocorrelation Function] [WS 9] [2010-12-07 20:24:41] [9b13650c94c5192ca5135ec8a1fa39f7]
-    D      [(Partial) Autocorrelation Function] [ACF Paper] [2010-12-19 13:35:17] [5fd8c857995b7937a45335fd5ccccdde] [Current]
-   P         [(Partial) Autocorrelation Function] [] [2010-12-21 10:32:09] [74be16979710d4c4e7c6647856088456] 
-   P         [(Partial) Autocorrelation Function] [] [2010-12-21 10:32:09] [9b13650c94c5192ca5135ec8a1fa39f7] 
-               [(Partial) Autocorrelation Function] [] [2010-12-21 10:39:04] [9b13650c94c5192ca5135ec8a1fa39f7] 
-   P             [(Partial) Autocorrelation Function] [] [2010-12-21 10:40:43] [9b13650c94c5192ca5135ec8a1fa39f7] 
-   P               [(Partial) Autocorrelation Function] [] [2010-12-21 10:50:06] [9b13650c94c5192ca5135ec8a1fa39f7] 
- RMP                 [Spectral Analysis] [] [2010-12-21 11:01:31] [9b13650c94c5192ca5135ec8a1fa39f7] 
-   P                   [Spectral Analysis] [] [2010-12-21 11:12:16] [9b13650c94c5192ca5135ec8a1fa39f7] 
-   P                     [Spectral Analysis] [] [2010-12-21 11:21:27] [9b13650c94c5192ca5135ec8a1fa39f7] 
- RMP                       [Variance Reduction Matrix] [] [2010-12-21 11:45:42] [9b13650c94c5192ca5135ec8a1fa39f7] 
- RM                          [Standard Deviation-Mean Plot] [] [2010-12-21 12:07:57] [9b13650c94c5192ca5135ec8a1fa39f7] 
- RM                          [ARIMA Backward Selection] [] [2010-12-21 12:35:49] [9b13650c94c5192ca5135ec8a1fa39f7] 
- RMP                           [ARIMA Forecasting] [] [2010-12-22 19:05:16] [9b13650c94c5192ca5135ec8a1fa39f7] 
-   P                             [ARIMA Forecasting] [] [2010-12-22 19:15:24] [9b13650c94c5192ca5135ec8a1fa39f7] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112370&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112370&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.345963	3.3897	0.000508
2	0.154115	1.51	0.067162
3	-0.050831	-0.498	0.309799
4	-0.21735	-2.1296	0.017882
5	-0.266864	-2.6147	0.005185
6	-0.464787	-4.554	8e-06
7	-0.278496	-2.7287	0.003782
8	-0.208378	-2.0417	0.021963
9	-0.081268	-0.7963	0.213922
10	0.01331	0.1304	0.448256
11	0.237992	2.3318	0.0109
12	0.739408	7.2447	0
13	0.248541	2.4352	0.008365
14	0.096831	0.9487	0.172565
15	-0.076282	-0.7474	0.228322
16	-0.227116	-2.2253	0.014202
17	-0.254225	-2.4909	0.00723
18	-0.455775	-4.4657	1.1e-05
19	-0.257857	-2.5265	0.006578

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.345963 & 3.3897 & 0.000508 \tabularnewline
2 & 0.154115 & 1.51 & 0.067162 \tabularnewline
3 & -0.050831 & -0.498 & 0.309799 \tabularnewline
4 & -0.21735 & -2.1296 & 0.017882 \tabularnewline
5 & -0.266864 & -2.6147 & 0.005185 \tabularnewline
6 & -0.464787 & -4.554 & 8e-06 \tabularnewline
7 & -0.278496 & -2.7287 & 0.003782 \tabularnewline
8 & -0.208378 & -2.0417 & 0.021963 \tabularnewline
9 & -0.081268 & -0.7963 & 0.213922 \tabularnewline
10 & 0.01331 & 0.1304 & 0.448256 \tabularnewline
11 & 0.237992 & 2.3318 & 0.0109 \tabularnewline
12 & 0.739408 & 7.2447 & 0 \tabularnewline
13 & 0.248541 & 2.4352 & 0.008365 \tabularnewline
14 & 0.096831 & 0.9487 & 0.172565 \tabularnewline
15 & -0.076282 & -0.7474 & 0.228322 \tabularnewline
16 & -0.227116 & -2.2253 & 0.014202 \tabularnewline
17 & -0.254225 & -2.4909 & 0.00723 \tabularnewline
18 & -0.455775 & -4.4657 & 1.1e-05 \tabularnewline
19 & -0.257857 & -2.5265 & 0.006578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112370&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]0.345963[/C][C]3.3897[/C][C]0.000508[/C][/ROW]
[ROW][C]2[/C][C]0.154115[/C][C]1.51[/C][C]0.067162[/C][/ROW]
[ROW][C]3[/C][C]-0.050831[/C][C]-0.498[/C][C]0.309799[/C][/ROW]
[ROW][C]4[/C][C]-0.21735[/C][C]-2.1296[/C][C]0.017882[/C][/ROW]
[ROW][C]5[/C][C]-0.266864[/C][C]-2.6147[/C][C]0.005185[/C][/ROW]
[ROW][C]6[/C][C]-0.464787[/C][C]-4.554[/C][C]8e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.278496[/C][C]-2.7287[/C][C]0.003782[/C][/ROW]
[ROW][C]8[/C][C]-0.208378[/C][C]-2.0417[/C][C]0.021963[/C][/ROW]
[ROW][C]9[/C][C]-0.081268[/C][C]-0.7963[/C][C]0.213922[/C][/ROW]
[ROW][C]10[/C][C]0.01331[/C][C]0.1304[/C][C]0.448256[/C][/ROW]
[ROW][C]11[/C][C]0.237992[/C][C]2.3318[/C][C]0.0109[/C][/ROW]
[ROW][C]12[/C][C]0.739408[/C][C]7.2447[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.248541[/C][C]2.4352[/C][C]0.008365[/C][/ROW]
[ROW][C]14[/C][C]0.096831[/C][C]0.9487[/C][C]0.172565[/C][/ROW]
[ROW][C]15[/C][C]-0.076282[/C][C]-0.7474[/C][C]0.228322[/C][/ROW]
[ROW][C]16[/C][C]-0.227116[/C][C]-2.2253[/C][C]0.014202[/C][/ROW]
[ROW][C]17[/C][C]-0.254225[/C][C]-2.4909[/C][C]0.00723[/C][/ROW]
[ROW][C]18[/C][C]-0.455775[/C][C]-4.4657[/C][C]1.1e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.257857[/C][C]-2.5265[/C][C]0.006578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112370&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	0.345963	3.3897	0.000508
2	0.154115	1.51	0.067162
3	-0.050831	-0.498	0.309799
4	-0.21735	-2.1296	0.017882
5	-0.266864	-2.6147	0.005185
6	-0.464787	-4.554	8e-06
7	-0.278496	-2.7287	0.003782
8	-0.208378	-2.0417	0.021963
9	-0.081268	-0.7963	0.213922
10	0.01331	0.1304	0.448256
11	0.237992	2.3318	0.0109
12	0.739408	7.2447	0
13	0.248541	2.4352	0.008365
14	0.096831	0.9487	0.172565
15	-0.076282	-0.7474	0.228322
16	-0.227116	-2.2253	0.014202
17	-0.254225	-2.4909	0.00723
18	-0.455775	-4.4657	1.1e-05
19	-0.257857	-2.5265	0.006578

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.345963	3.3897	0.000508
2	0.039106	0.3832	0.351225
3	-0.13151	-1.2885	0.100329
4	-0.19387	-1.8995	0.030248
5	-0.140447	-1.3761	0.085996
6	-0.368432	-3.6099	0.000245
7	-0.070318	-0.689	0.246252
8	-0.152337	-1.4926	0.069412
9	-0.134516	-1.318	0.095322
10	-0.169645	-1.6622	0.04987
11	0.095669	0.9374	0.175462
12	0.641255	6.283	0
13	-0.361122	-3.5383	0.000311
14	-0.284206	-2.7846	0.003228
15	0.02001	0.1961	0.422489
16	-0.065997	-0.6466	0.259707
17	-0.126664	-1.2411	0.108806
18	-0.139807	-1.3698	0.086969
19	-0.052419	-0.5136	0.304358

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.345963 & 3.3897 & 0.000508 \tabularnewline
2 & 0.039106 & 0.3832 & 0.351225 \tabularnewline
3 & -0.13151 & -1.2885 & 0.100329 \tabularnewline
4 & -0.19387 & -1.8995 & 0.030248 \tabularnewline
5 & -0.140447 & -1.3761 & 0.085996 \tabularnewline
6 & -0.368432 & -3.6099 & 0.000245 \tabularnewline
7 & -0.070318 & -0.689 & 0.246252 \tabularnewline
8 & -0.152337 & -1.4926 & 0.069412 \tabularnewline
9 & -0.134516 & -1.318 & 0.095322 \tabularnewline
10 & -0.169645 & -1.6622 & 0.04987 \tabularnewline
11 & 0.095669 & 0.9374 & 0.175462 \tabularnewline
12 & 0.641255 & 6.283 & 0 \tabularnewline
13 & -0.361122 & -3.5383 & 0.000311 \tabularnewline
14 & -0.284206 & -2.7846 & 0.003228 \tabularnewline
15 & 0.02001 & 0.1961 & 0.422489 \tabularnewline
16 & -0.065997 & -0.6466 & 0.259707 \tabularnewline
17 & -0.126664 & -1.2411 & 0.108806 \tabularnewline
18 & -0.139807 & -1.3698 & 0.086969 \tabularnewline
19 & -0.052419 & -0.5136 & 0.304358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112370&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]0.345963[/C][C]3.3897[/C][C]0.000508[/C][/ROW]
[ROW][C]2[/C][C]0.039106[/C][C]0.3832[/C][C]0.351225[/C][/ROW]
[ROW][C]3[/C][C]-0.13151[/C][C]-1.2885[/C][C]0.100329[/C][/ROW]
[ROW][C]4[/C][C]-0.19387[/C][C]-1.8995[/C][C]0.030248[/C][/ROW]
[ROW][C]5[/C][C]-0.140447[/C][C]-1.3761[/C][C]0.085996[/C][/ROW]
[ROW][C]6[/C][C]-0.368432[/C][C]-3.6099[/C][C]0.000245[/C][/ROW]
[ROW][C]7[/C][C]-0.070318[/C][C]-0.689[/C][C]0.246252[/C][/ROW]
[ROW][C]8[/C][C]-0.152337[/C][C]-1.4926[/C][C]0.069412[/C][/ROW]
[ROW][C]9[/C][C]-0.134516[/C][C]-1.318[/C][C]0.095322[/C][/ROW]
[ROW][C]10[/C][C]-0.169645[/C][C]-1.6622[/C][C]0.04987[/C][/ROW]
[ROW][C]11[/C][C]0.095669[/C][C]0.9374[/C][C]0.175462[/C][/ROW]
[ROW][C]12[/C][C]0.641255[/C][C]6.283[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.361122[/C][C]-3.5383[/C][C]0.000311[/C][/ROW]
[ROW][C]14[/C][C]-0.284206[/C][C]-2.7846[/C][C]0.003228[/C][/ROW]
[ROW][C]15[/C][C]0.02001[/C][C]0.1961[/C][C]0.422489[/C][/ROW]
[ROW][C]16[/C][C]-0.065997[/C][C]-0.6466[/C][C]0.259707[/C][/ROW]
[ROW][C]17[/C][C]-0.126664[/C][C]-1.2411[/C][C]0.108806[/C][/ROW]
[ROW][C]18[/C][C]-0.139807[/C][C]-1.3698[/C][C]0.086969[/C][/ROW]
[ROW][C]19[/C][C]-0.052419[/C][C]-0.5136[/C][C]0.304358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112370&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	0.345963	3.3897	0.000508
2	0.039106	0.3832	0.351225
3	-0.13151	-1.2885	0.100329
4	-0.19387	-1.8995	0.030248
5	-0.140447	-1.3761	0.085996
6	-0.368432	-3.6099	0.000245
7	-0.070318	-0.689	0.246252
8	-0.152337	-1.4926	0.069412
9	-0.134516	-1.318	0.095322
10	-0.169645	-1.6622	0.04987
11	0.095669	0.9374	0.175462
12	0.641255	6.283	0
13	-0.361122	-3.5383	0.000311
14	-0.284206	-2.7846	0.003228
15	0.02001	0.1961	0.422489
16	-0.065997	-0.6466	0.259707
17	-0.126664	-1.2411	0.108806
18	-0.139807	-1.3698	0.086969
19	-0.052419	-0.5136	0.304358

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 ; 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 (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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code