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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

Sat, 04 Dec 2010 10:56:02 +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/04/t12914600545zxyqprr66hwhlw.htm/, Retrieved Sun, 05 May 2024 03:16:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105087, Retrieved Sun, 05 May 2024 03:16:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

178

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]
-  MPD  [Univariate Data Series] [CPI] [2010-12-04 10:34:06] [6bc4f9343b7ea3ef5a59412d1f72bb2b]
- RMPD      [(Partial) Autocorrelation Function] [ACF CPI] [2010-12-04 10:56:02] [b6992a7b26e556359948e164e4227eba] [Current]
- RMP         [Spectral Analysis] [Spectraal CPI] [2010-12-04 10:58:57] [6bc4f9343b7ea3ef5a59412d1f72bb2b] 
- RMP         [Variance Reduction Matrix] [VRM CPI] [2010-12-04 11:01:10] [6bc4f9343b7ea3ef5a59412d1f72bb2b] 

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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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105087&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105087&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.985182	14.0367	0
2	0.970331	13.8251	0
3	0.955292	13.6108	0
4	0.940413	13.3988	0
5	0.925598	13.1877	0
6	0.910745	12.9761	0
7	0.896014	12.7662	0
8	0.881476	12.5591	0
9	0.866983	12.3526	0
10	0.852357	12.1442	0
11	0.838114	11.9413	0
12	0.824062	11.7411	0
13	0.810169	11.5431	0
14	0.79652	11.3487	0
15	0.782865	11.1541	0
16	0.768921	10.9554	0
17	0.754996	10.757	0
18	0.740875	10.5558	0
19	0.72644	10.3502	0
20	0.711799	10.1416	0
21	0.696818	9.9281	0
22	0.680722	9.6988	0
23	0.664759	9.4714	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.985182 & 14.0367 & 0 \tabularnewline
2 & 0.970331 & 13.8251 & 0 \tabularnewline
3 & 0.955292 & 13.6108 & 0 \tabularnewline
4 & 0.940413 & 13.3988 & 0 \tabularnewline
5 & 0.925598 & 13.1877 & 0 \tabularnewline
6 & 0.910745 & 12.9761 & 0 \tabularnewline
7 & 0.896014 & 12.7662 & 0 \tabularnewline
8 & 0.881476 & 12.5591 & 0 \tabularnewline
9 & 0.866983 & 12.3526 & 0 \tabularnewline
10 & 0.852357 & 12.1442 & 0 \tabularnewline
11 & 0.838114 & 11.9413 & 0 \tabularnewline
12 & 0.824062 & 11.7411 & 0 \tabularnewline
13 & 0.810169 & 11.5431 & 0 \tabularnewline
14 & 0.79652 & 11.3487 & 0 \tabularnewline
15 & 0.782865 & 11.1541 & 0 \tabularnewline
16 & 0.768921 & 10.9554 & 0 \tabularnewline
17 & 0.754996 & 10.757 & 0 \tabularnewline
18 & 0.740875 & 10.5558 & 0 \tabularnewline
19 & 0.72644 & 10.3502 & 0 \tabularnewline
20 & 0.711799 & 10.1416 & 0 \tabularnewline
21 & 0.696818 & 9.9281 & 0 \tabularnewline
22 & 0.680722 & 9.6988 & 0 \tabularnewline
23 & 0.664759 & 9.4714 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105087&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]0.985182[/C][C]14.0367[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.970331[/C][C]13.8251[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.955292[/C][C]13.6108[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.940413[/C][C]13.3988[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.925598[/C][C]13.1877[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.910745[/C][C]12.9761[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.896014[/C][C]12.7662[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.881476[/C][C]12.5591[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.866983[/C][C]12.3526[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.852357[/C][C]12.1442[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.838114[/C][C]11.9413[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.824062[/C][C]11.7411[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.810169[/C][C]11.5431[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.79652[/C][C]11.3487[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.782865[/C][C]11.1541[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.768921[/C][C]10.9554[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.754996[/C][C]10.757[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.740875[/C][C]10.5558[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.72644[/C][C]10.3502[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.711799[/C][C]10.1416[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.696818[/C][C]9.9281[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.680722[/C][C]9.6988[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.664759[/C][C]9.4714[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105087&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	0.985182	14.0367	0
2	0.970331	13.8251	0
3	0.955292	13.6108	0
4	0.940413	13.3988	0
5	0.925598	13.1877	0
6	0.910745	12.9761	0
7	0.896014	12.7662	0
8	0.881476	12.5591	0
9	0.866983	12.3526	0
10	0.852357	12.1442	0
11	0.838114	11.9413	0
12	0.824062	11.7411	0
13	0.810169	11.5431	0
14	0.79652	11.3487	0
15	0.782865	11.1541	0
16	0.768921	10.9554	0
17	0.754996	10.757	0
18	0.740875	10.5558	0
19	0.72644	10.3502	0
20	0.711799	10.1416	0
21	0.696818	9.9281	0
22	0.680722	9.6988	0
23	0.664759	9.4714	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.985182	14.0367	0
2	-0.008629	-0.1229	0.451139
3	-0.013871	-0.1976	0.421764
4	-0.002262	-0.0322	0.487158
5	-0.005471	-0.078	0.468972
6	-0.009064	-0.1291	0.448689
7	-0.003607	-0.0514	0.479532
8	-0.001166	-0.0166	0.493378
9	-0.006285	-0.0895	0.46437
10	-0.01235	-0.176	0.430249
11	0.005205	0.0742	0.470477
12	-0.00116	-0.0165	0.493413
13	-0.002567	-0.0366	0.485432
14	0.000716	0.0102	0.495933
15	-0.007734	-0.1102	0.456181
16	-0.017594	-0.2507	0.401162
17	-0.007066	-0.1007	0.459952
18	-0.014251	-0.203	0.419652
19	-0.018765	-0.2674	0.39473
20	-0.015268	-0.2175	0.414007
21	-0.019754	-0.2815	0.389325
22	-0.046815	-0.667	0.252762
23	-0.004988	-0.0711	0.471708

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.985182 & 14.0367 & 0 \tabularnewline
2 & -0.008629 & -0.1229 & 0.451139 \tabularnewline
3 & -0.013871 & -0.1976 & 0.421764 \tabularnewline
4 & -0.002262 & -0.0322 & 0.487158 \tabularnewline
5 & -0.005471 & -0.078 & 0.468972 \tabularnewline
6 & -0.009064 & -0.1291 & 0.448689 \tabularnewline
7 & -0.003607 & -0.0514 & 0.479532 \tabularnewline
8 & -0.001166 & -0.0166 & 0.493378 \tabularnewline
9 & -0.006285 & -0.0895 & 0.46437 \tabularnewline
10 & -0.01235 & -0.176 & 0.430249 \tabularnewline
11 & 0.005205 & 0.0742 & 0.470477 \tabularnewline
12 & -0.00116 & -0.0165 & 0.493413 \tabularnewline
13 & -0.002567 & -0.0366 & 0.485432 \tabularnewline
14 & 0.000716 & 0.0102 & 0.495933 \tabularnewline
15 & -0.007734 & -0.1102 & 0.456181 \tabularnewline
16 & -0.017594 & -0.2507 & 0.401162 \tabularnewline
17 & -0.007066 & -0.1007 & 0.459952 \tabularnewline
18 & -0.014251 & -0.203 & 0.419652 \tabularnewline
19 & -0.018765 & -0.2674 & 0.39473 \tabularnewline
20 & -0.015268 & -0.2175 & 0.414007 \tabularnewline
21 & -0.019754 & -0.2815 & 0.389325 \tabularnewline
22 & -0.046815 & -0.667 & 0.252762 \tabularnewline
23 & -0.004988 & -0.0711 & 0.471708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105087&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]0.985182[/C][C]14.0367[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.008629[/C][C]-0.1229[/C][C]0.451139[/C][/ROW]
[ROW][C]3[/C][C]-0.013871[/C][C]-0.1976[/C][C]0.421764[/C][/ROW]
[ROW][C]4[/C][C]-0.002262[/C][C]-0.0322[/C][C]0.487158[/C][/ROW]
[ROW][C]5[/C][C]-0.005471[/C][C]-0.078[/C][C]0.468972[/C][/ROW]
[ROW][C]6[/C][C]-0.009064[/C][C]-0.1291[/C][C]0.448689[/C][/ROW]
[ROW][C]7[/C][C]-0.003607[/C][C]-0.0514[/C][C]0.479532[/C][/ROW]
[ROW][C]8[/C][C]-0.001166[/C][C]-0.0166[/C][C]0.493378[/C][/ROW]
[ROW][C]9[/C][C]-0.006285[/C][C]-0.0895[/C][C]0.46437[/C][/ROW]
[ROW][C]10[/C][C]-0.01235[/C][C]-0.176[/C][C]0.430249[/C][/ROW]
[ROW][C]11[/C][C]0.005205[/C][C]0.0742[/C][C]0.470477[/C][/ROW]
[ROW][C]12[/C][C]-0.00116[/C][C]-0.0165[/C][C]0.493413[/C][/ROW]
[ROW][C]13[/C][C]-0.002567[/C][C]-0.0366[/C][C]0.485432[/C][/ROW]
[ROW][C]14[/C][C]0.000716[/C][C]0.0102[/C][C]0.495933[/C][/ROW]
[ROW][C]15[/C][C]-0.007734[/C][C]-0.1102[/C][C]0.456181[/C][/ROW]
[ROW][C]16[/C][C]-0.017594[/C][C]-0.2507[/C][C]0.401162[/C][/ROW]
[ROW][C]17[/C][C]-0.007066[/C][C]-0.1007[/C][C]0.459952[/C][/ROW]
[ROW][C]18[/C][C]-0.014251[/C][C]-0.203[/C][C]0.419652[/C][/ROW]
[ROW][C]19[/C][C]-0.018765[/C][C]-0.2674[/C][C]0.39473[/C][/ROW]
[ROW][C]20[/C][C]-0.015268[/C][C]-0.2175[/C][C]0.414007[/C][/ROW]
[ROW][C]21[/C][C]-0.019754[/C][C]-0.2815[/C][C]0.389325[/C][/ROW]
[ROW][C]22[/C][C]-0.046815[/C][C]-0.667[/C][C]0.252762[/C][/ROW]
[ROW][C]23[/C][C]-0.004988[/C][C]-0.0711[/C][C]0.471708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105087&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105087&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	0.985182	14.0367	0
2	-0.008629	-0.1229	0.451139
3	-0.013871	-0.1976	0.421764
4	-0.002262	-0.0322	0.487158
5	-0.005471	-0.078	0.468972
6	-0.009064	-0.1291	0.448689
7	-0.003607	-0.0514	0.479532
8	-0.001166	-0.0166	0.493378
9	-0.006285	-0.0895	0.46437
10	-0.01235	-0.176	0.430249
11	0.005205	0.0742	0.470477
12	-0.00116	-0.0165	0.493413
13	-0.002567	-0.0366	0.485432
14	0.000716	0.0102	0.495933
15	-0.007734	-0.1102	0.456181
16	-0.017594	-0.2507	0.401162
17	-0.007066	-0.1007	0.459952
18	-0.014251	-0.203	0.419652
19	-0.018765	-0.2674	0.39473
20	-0.015268	-0.2175	0.414007
21	-0.019754	-0.2815	0.389325
22	-0.046815	-0.667	0.252762
23	-0.004988	-0.0711	0.471708

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code