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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 09 Dec 2008 07:13:19 -0700

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/2008/Dec/09/t1228832057zf9svnt5ya4lpzg.htm/, Retrieved Sun, 19 May 2024 12:02:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31434, Retrieved Sun, 19 May 2024 12:02:45 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-     [Standard Deviation-Mean Plot] [] [2008-12-02 16:33:43] [339926f84f7378398edd9a77d1fc8e74]
F    D  [Standard Deviation-Mean Plot] [] [2008-12-09 13:32:16] [339926f84f7378398edd9a77d1fc8e74]
- RMPD      [(Partial) Autocorrelation Function] [] [2008-12-09 14:13:19] [76e580e81b2082744334eb1f6d9ccc3e] [Current]
F   P         [(Partial) Autocorrelation Function] [] [2008-12-10 06:27:37] [74be16979710d4c4e7c6647856088456] 
F RMP         [Spectral Analysis] [] [2008-12-10 06:31:19] [339926f84f7378398edd9a77d1fc8e74] 
F RMP         [Spectral Analysis] [] [2008-12-10 06:33:27] [339926f84f7378398edd9a77d1fc8e74] 

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Dataseries X:

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Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31434&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31434&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.557901	-10.556	0
2	0.092868	1.7571	0.039874
3	0.022927	0.4338	0.332347
4	-0.105651	-1.999	0.023182
5	0.11199	2.1189	0.017391
6	-0.025147	-0.4758	0.31725
7	-0.060192	-1.1389	0.127757
8	0.079633	1.5067	0.06638
9	-0.027544	-0.5212	0.301291
10	-0.109239	-2.0669	0.019731
11	0.325985	6.1679	0
12	-0.407363	-7.7077	0
13	0.147642	2.7935	0.002747
14	0.017248	0.3263	0.372179
15	-0.02045	-0.3869	0.34952
16	0.01384	0.2619	0.396785
17	-0.012435	-0.2353	0.407063
18	-0.051047	-0.9659	0.167384
19	0.061271	1.1593	0.123552
20	0.028657	0.5422	0.294003
21	-0.03866	-0.7315	0.232481
22	0.039899	0.7549	0.225397
23	-0.047901	-0.9063	0.182683
24	-0.05842	-1.1054	0.134873
25	0.126789	2.399	0.008476

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.557901 & -10.556 & 0 \tabularnewline
2 & 0.092868 & 1.7571 & 0.039874 \tabularnewline
3 & 0.022927 & 0.4338 & 0.332347 \tabularnewline
4 & -0.105651 & -1.999 & 0.023182 \tabularnewline
5 & 0.11199 & 2.1189 & 0.017391 \tabularnewline
6 & -0.025147 & -0.4758 & 0.31725 \tabularnewline
7 & -0.060192 & -1.1389 & 0.127757 \tabularnewline
8 & 0.079633 & 1.5067 & 0.06638 \tabularnewline
9 & -0.027544 & -0.5212 & 0.301291 \tabularnewline
10 & -0.109239 & -2.0669 & 0.019731 \tabularnewline
11 & 0.325985 & 6.1679 & 0 \tabularnewline
12 & -0.407363 & -7.7077 & 0 \tabularnewline
13 & 0.147642 & 2.7935 & 0.002747 \tabularnewline
14 & 0.017248 & 0.3263 & 0.372179 \tabularnewline
15 & -0.02045 & -0.3869 & 0.34952 \tabularnewline
16 & 0.01384 & 0.2619 & 0.396785 \tabularnewline
17 & -0.012435 & -0.2353 & 0.407063 \tabularnewline
18 & -0.051047 & -0.9659 & 0.167384 \tabularnewline
19 & 0.061271 & 1.1593 & 0.123552 \tabularnewline
20 & 0.028657 & 0.5422 & 0.294003 \tabularnewline
21 & -0.03866 & -0.7315 & 0.232481 \tabularnewline
22 & 0.039899 & 0.7549 & 0.225397 \tabularnewline
23 & -0.047901 & -0.9063 & 0.182683 \tabularnewline
24 & -0.05842 & -1.1054 & 0.134873 \tabularnewline
25 & 0.126789 & 2.399 & 0.008476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31434&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]-0.557901[/C][C]-10.556[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.092868[/C][C]1.7571[/C][C]0.039874[/C][/ROW]
[ROW][C]3[/C][C]0.022927[/C][C]0.4338[/C][C]0.332347[/C][/ROW]
[ROW][C]4[/C][C]-0.105651[/C][C]-1.999[/C][C]0.023182[/C][/ROW]
[ROW][C]5[/C][C]0.11199[/C][C]2.1189[/C][C]0.017391[/C][/ROW]
[ROW][C]6[/C][C]-0.025147[/C][C]-0.4758[/C][C]0.31725[/C][/ROW]
[ROW][C]7[/C][C]-0.060192[/C][C]-1.1389[/C][C]0.127757[/C][/ROW]
[ROW][C]8[/C][C]0.079633[/C][C]1.5067[/C][C]0.06638[/C][/ROW]
[ROW][C]9[/C][C]-0.027544[/C][C]-0.5212[/C][C]0.301291[/C][/ROW]
[ROW][C]10[/C][C]-0.109239[/C][C]-2.0669[/C][C]0.019731[/C][/ROW]
[ROW][C]11[/C][C]0.325985[/C][C]6.1679[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]-0.407363[/C][C]-7.7077[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.147642[/C][C]2.7935[/C][C]0.002747[/C][/ROW]
[ROW][C]14[/C][C]0.017248[/C][C]0.3263[/C][C]0.372179[/C][/ROW]
[ROW][C]15[/C][C]-0.02045[/C][C]-0.3869[/C][C]0.34952[/C][/ROW]
[ROW][C]16[/C][C]0.01384[/C][C]0.2619[/C][C]0.396785[/C][/ROW]
[ROW][C]17[/C][C]-0.012435[/C][C]-0.2353[/C][C]0.407063[/C][/ROW]
[ROW][C]18[/C][C]-0.051047[/C][C]-0.9659[/C][C]0.167384[/C][/ROW]
[ROW][C]19[/C][C]0.061271[/C][C]1.1593[/C][C]0.123552[/C][/ROW]
[ROW][C]20[/C][C]0.028657[/C][C]0.5422[/C][C]0.294003[/C][/ROW]
[ROW][C]21[/C][C]-0.03866[/C][C]-0.7315[/C][C]0.232481[/C][/ROW]
[ROW][C]22[/C][C]0.039899[/C][C]0.7549[/C][C]0.225397[/C][/ROW]
[ROW][C]23[/C][C]-0.047901[/C][C]-0.9063[/C][C]0.182683[/C][/ROW]
[ROW][C]24[/C][C]-0.05842[/C][C]-1.1054[/C][C]0.134873[/C][/ROW]
[ROW][C]25[/C][C]0.126789[/C][C]2.399[/C][C]0.008476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31434&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	-0.557901	-10.556	0
2	0.092868	1.7571	0.039874
3	0.022927	0.4338	0.332347
4	-0.105651	-1.999	0.023182
5	0.11199	2.1189	0.017391
6	-0.025147	-0.4758	0.31725
7	-0.060192	-1.1389	0.127757
8	0.079633	1.5067	0.06638
9	-0.027544	-0.5212	0.301291
10	-0.109239	-2.0669	0.019731
11	0.325985	6.1679	0
12	-0.407363	-7.7077	0
13	0.147642	2.7935	0.002747
14	0.017248	0.3263	0.372179
15	-0.02045	-0.3869	0.34952
16	0.01384	0.2619	0.396785
17	-0.012435	-0.2353	0.407063
18	-0.051047	-0.9659	0.167384
19	0.061271	1.1593	0.123552
20	0.028657	0.5422	0.294003
21	-0.03866	-0.7315	0.232481
22	0.039899	0.7549	0.225397
23	-0.047901	-0.9063	0.182683
24	-0.05842	-1.1054	0.134873
25	0.126789	2.399	0.008476

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.557901	-10.556	0
2	-0.317078	-5.9994	0
3	-0.138388	-2.6184	0.004604
4	-0.20755	-3.927	5.2e-05
5	-0.08539	-1.6156	0.053526
6	-0.00514	-0.0973	0.461288
7	-0.079485	-1.5039	0.06674
8	-0.016891	-0.3196	0.374733
9	0.031202	0.5904	0.277657
10	-0.163185	-3.0876	0.001088
11	0.265386	5.0213	0
12	-0.107108	-2.0266	0.021723
13	-0.22046	-4.1713	1.9e-05
14	-0.152404	-2.8836	0.002085
15	-0.046781	-0.8851	0.188339
16	-0.14899	-2.819	0.002542
17	-0.095205	-1.8014	0.036243
18	-0.135702	-2.5676	0.005323
19	-0.160256	-3.0322	0.001302
20	0.000354	0.0067	0.497332
21	0.06628	1.2541	0.105315
22	-0.070773	-1.3391	0.090694
23	0.12587	2.3816	0.00888
24	-0.15412	-2.9161	0.001884
25	-0.131835	-2.4944	0.006533

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.557901 & -10.556 & 0 \tabularnewline
2 & -0.317078 & -5.9994 & 0 \tabularnewline
3 & -0.138388 & -2.6184 & 0.004604 \tabularnewline
4 & -0.20755 & -3.927 & 5.2e-05 \tabularnewline
5 & -0.08539 & -1.6156 & 0.053526 \tabularnewline
6 & -0.00514 & -0.0973 & 0.461288 \tabularnewline
7 & -0.079485 & -1.5039 & 0.06674 \tabularnewline
8 & -0.016891 & -0.3196 & 0.374733 \tabularnewline
9 & 0.031202 & 0.5904 & 0.277657 \tabularnewline
10 & -0.163185 & -3.0876 & 0.001088 \tabularnewline
11 & 0.265386 & 5.0213 & 0 \tabularnewline
12 & -0.107108 & -2.0266 & 0.021723 \tabularnewline
13 & -0.22046 & -4.1713 & 1.9e-05 \tabularnewline
14 & -0.152404 & -2.8836 & 0.002085 \tabularnewline
15 & -0.046781 & -0.8851 & 0.188339 \tabularnewline
16 & -0.14899 & -2.819 & 0.002542 \tabularnewline
17 & -0.095205 & -1.8014 & 0.036243 \tabularnewline
18 & -0.135702 & -2.5676 & 0.005323 \tabularnewline
19 & -0.160256 & -3.0322 & 0.001302 \tabularnewline
20 & 0.000354 & 0.0067 & 0.497332 \tabularnewline
21 & 0.06628 & 1.2541 & 0.105315 \tabularnewline
22 & -0.070773 & -1.3391 & 0.090694 \tabularnewline
23 & 0.12587 & 2.3816 & 0.00888 \tabularnewline
24 & -0.15412 & -2.9161 & 0.001884 \tabularnewline
25 & -0.131835 & -2.4944 & 0.006533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31434&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]-0.557901[/C][C]-10.556[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.317078[/C][C]-5.9994[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.138388[/C][C]-2.6184[/C][C]0.004604[/C][/ROW]
[ROW][C]4[/C][C]-0.20755[/C][C]-3.927[/C][C]5.2e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.08539[/C][C]-1.6156[/C][C]0.053526[/C][/ROW]
[ROW][C]6[/C][C]-0.00514[/C][C]-0.0973[/C][C]0.461288[/C][/ROW]
[ROW][C]7[/C][C]-0.079485[/C][C]-1.5039[/C][C]0.06674[/C][/ROW]
[ROW][C]8[/C][C]-0.016891[/C][C]-0.3196[/C][C]0.374733[/C][/ROW]
[ROW][C]9[/C][C]0.031202[/C][C]0.5904[/C][C]0.277657[/C][/ROW]
[ROW][C]10[/C][C]-0.163185[/C][C]-3.0876[/C][C]0.001088[/C][/ROW]
[ROW][C]11[/C][C]0.265386[/C][C]5.0213[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]-0.107108[/C][C]-2.0266[/C][C]0.021723[/C][/ROW]
[ROW][C]13[/C][C]-0.22046[/C][C]-4.1713[/C][C]1.9e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.152404[/C][C]-2.8836[/C][C]0.002085[/C][/ROW]
[ROW][C]15[/C][C]-0.046781[/C][C]-0.8851[/C][C]0.188339[/C][/ROW]
[ROW][C]16[/C][C]-0.14899[/C][C]-2.819[/C][C]0.002542[/C][/ROW]
[ROW][C]17[/C][C]-0.095205[/C][C]-1.8014[/C][C]0.036243[/C][/ROW]
[ROW][C]18[/C][C]-0.135702[/C][C]-2.5676[/C][C]0.005323[/C][/ROW]
[ROW][C]19[/C][C]-0.160256[/C][C]-3.0322[/C][C]0.001302[/C][/ROW]
[ROW][C]20[/C][C]0.000354[/C][C]0.0067[/C][C]0.497332[/C][/ROW]
[ROW][C]21[/C][C]0.06628[/C][C]1.2541[/C][C]0.105315[/C][/ROW]
[ROW][C]22[/C][C]-0.070773[/C][C]-1.3391[/C][C]0.090694[/C][/ROW]
[ROW][C]23[/C][C]0.12587[/C][C]2.3816[/C][C]0.00888[/C][/ROW]
[ROW][C]24[/C][C]-0.15412[/C][C]-2.9161[/C][C]0.001884[/C][/ROW]
[ROW][C]25[/C][C]-0.131835[/C][C]-2.4944[/C][C]0.006533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31434&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31434&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	-0.557901	-10.556	0
2	-0.317078	-5.9994	0
3	-0.138388	-2.6184	0.004604
4	-0.20755	-3.927	5.2e-05
5	-0.08539	-1.6156	0.053526
6	-0.00514	-0.0973	0.461288
7	-0.079485	-1.5039	0.06674
8	-0.016891	-0.3196	0.374733
9	0.031202	0.5904	0.277657
10	-0.163185	-3.0876	0.001088
11	0.265386	5.0213	0
12	-0.107108	-2.0266	0.021723
13	-0.22046	-4.1713	1.9e-05
14	-0.152404	-2.8836	0.002085
15	-0.046781	-0.8851	0.188339
16	-0.14899	-2.819	0.002542
17	-0.095205	-1.8014	0.036243
18	-0.135702	-2.5676	0.005323
19	-0.160256	-3.0322	0.001302
20	0.000354	0.0067	0.497332
21	0.06628	1.2541	0.105315
22	-0.070773	-1.3391	0.090694
23	0.12587	2.3816	0.00888
24	-0.15412	-2.9161	0.001884
25	-0.131835	-2.4944	0.006533

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 ;

Parameters (R input):

par1 = Default ; par2 = -0.5 ; par3 = 2 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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