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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 Nov 2013 10:51:25 -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/2013/Nov/21/t1385049125h2u2jnd34qojz63.htm/, Retrieved Fri, 03 May 2024 14:37:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=227263, Retrieved Fri, 03 May 2024 14:37:16 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2013-11-21 15:51:25] [ffc6217b42a6800413892efb2ef7f057] [Current]
-   P     [(Partial) Autocorrelation Function] [] [2013-11-21 21:22:44] [7693d6bd9b394a2eae1da409a7dd3216] 
- R PD    [(Partial) Autocorrelation Function] [] [2014-01-12 14:35:40] [7693d6bd9b394a2eae1da409a7dd3216] 
-   PD      [(Partial) Autocorrelation Function] [] [2014-01-12 14:48:55] [7693d6bd9b394a2eae1da409a7dd3216] 

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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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227263&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227263&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227263&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.786994	3.935	0.000293
2	0.50315	2.5157	0.009335
3	0.25514	1.2757	0.106894
4	0.100561	0.5028	0.309751
5	0.020586	0.1029	0.459419
6	-0.055869	-0.2793	0.39114
7	-0.167031	-0.8352	0.205771
8	-0.358582	-1.7929	0.042548
9	-0.458922	-2.2946	0.015213
10	-0.371507	-1.8575	0.037526
11	-0.219356	-1.0968	0.141595
12	-0.113946	-0.5697	0.286973
13	-0.068653	-0.3433	0.367135
14	-0.064319	-0.3216	0.375216
15	-0.039249	-0.1962	0.423003
16	-0.03247	-0.1623	0.436168
17	0.054555	0.2728	0.393633
18	0.086785	0.4339	0.334033
19	0.019996	0.1	0.460578
20	-0.055804	-0.279	0.391262
21	-0.104217	-0.5211	0.303446
22	-0.100744	-0.5037	0.309435
23	-0.083763	-0.4188	0.339465
24	-0.033336	-0.1667	0.434481

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.786994 & 3.935 & 0.000293 \tabularnewline
2 & 0.50315 & 2.5157 & 0.009335 \tabularnewline
3 & 0.25514 & 1.2757 & 0.106894 \tabularnewline
4 & 0.100561 & 0.5028 & 0.309751 \tabularnewline
5 & 0.020586 & 0.1029 & 0.459419 \tabularnewline
6 & -0.055869 & -0.2793 & 0.39114 \tabularnewline
7 & -0.167031 & -0.8352 & 0.205771 \tabularnewline
8 & -0.358582 & -1.7929 & 0.042548 \tabularnewline
9 & -0.458922 & -2.2946 & 0.015213 \tabularnewline
10 & -0.371507 & -1.8575 & 0.037526 \tabularnewline
11 & -0.219356 & -1.0968 & 0.141595 \tabularnewline
12 & -0.113946 & -0.5697 & 0.286973 \tabularnewline
13 & -0.068653 & -0.3433 & 0.367135 \tabularnewline
14 & -0.064319 & -0.3216 & 0.375216 \tabularnewline
15 & -0.039249 & -0.1962 & 0.423003 \tabularnewline
16 & -0.03247 & -0.1623 & 0.436168 \tabularnewline
17 & 0.054555 & 0.2728 & 0.393633 \tabularnewline
18 & 0.086785 & 0.4339 & 0.334033 \tabularnewline
19 & 0.019996 & 0.1 & 0.460578 \tabularnewline
20 & -0.055804 & -0.279 & 0.391262 \tabularnewline
21 & -0.104217 & -0.5211 & 0.303446 \tabularnewline
22 & -0.100744 & -0.5037 & 0.309435 \tabularnewline
23 & -0.083763 & -0.4188 & 0.339465 \tabularnewline
24 & -0.033336 & -0.1667 & 0.434481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227263&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]0.786994[/C][C]3.935[/C][C]0.000293[/C][/ROW]
[ROW][C]2[/C][C]0.50315[/C][C]2.5157[/C][C]0.009335[/C][/ROW]
[ROW][C]3[/C][C]0.25514[/C][C]1.2757[/C][C]0.106894[/C][/ROW]
[ROW][C]4[/C][C]0.100561[/C][C]0.5028[/C][C]0.309751[/C][/ROW]
[ROW][C]5[/C][C]0.020586[/C][C]0.1029[/C][C]0.459419[/C][/ROW]
[ROW][C]6[/C][C]-0.055869[/C][C]-0.2793[/C][C]0.39114[/C][/ROW]
[ROW][C]7[/C][C]-0.167031[/C][C]-0.8352[/C][C]0.205771[/C][/ROW]
[ROW][C]8[/C][C]-0.358582[/C][C]-1.7929[/C][C]0.042548[/C][/ROW]
[ROW][C]9[/C][C]-0.458922[/C][C]-2.2946[/C][C]0.015213[/C][/ROW]
[ROW][C]10[/C][C]-0.371507[/C][C]-1.8575[/C][C]0.037526[/C][/ROW]
[ROW][C]11[/C][C]-0.219356[/C][C]-1.0968[/C][C]0.141595[/C][/ROW]
[ROW][C]12[/C][C]-0.113946[/C][C]-0.5697[/C][C]0.286973[/C][/ROW]
[ROW][C]13[/C][C]-0.068653[/C][C]-0.3433[/C][C]0.367135[/C][/ROW]
[ROW][C]14[/C][C]-0.064319[/C][C]-0.3216[/C][C]0.375216[/C][/ROW]
[ROW][C]15[/C][C]-0.039249[/C][C]-0.1962[/C][C]0.423003[/C][/ROW]
[ROW][C]16[/C][C]-0.03247[/C][C]-0.1623[/C][C]0.436168[/C][/ROW]
[ROW][C]17[/C][C]0.054555[/C][C]0.2728[/C][C]0.393633[/C][/ROW]
[ROW][C]18[/C][C]0.086785[/C][C]0.4339[/C][C]0.334033[/C][/ROW]
[ROW][C]19[/C][C]0.019996[/C][C]0.1[/C][C]0.460578[/C][/ROW]
[ROW][C]20[/C][C]-0.055804[/C][C]-0.279[/C][C]0.391262[/C][/ROW]
[ROW][C]21[/C][C]-0.104217[/C][C]-0.5211[/C][C]0.303446[/C][/ROW]
[ROW][C]22[/C][C]-0.100744[/C][C]-0.5037[/C][C]0.309435[/C][/ROW]
[ROW][C]23[/C][C]-0.083763[/C][C]-0.4188[/C][C]0.339465[/C][/ROW]
[ROW][C]24[/C][C]-0.033336[/C][C]-0.1667[/C][C]0.434481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227263&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227263&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	0.786994	3.935	0.000293
2	0.50315	2.5157	0.009335
3	0.25514	1.2757	0.106894
4	0.100561	0.5028	0.309751
5	0.020586	0.1029	0.459419
6	-0.055869	-0.2793	0.39114
7	-0.167031	-0.8352	0.205771
8	-0.358582	-1.7929	0.042548
9	-0.458922	-2.2946	0.015213
10	-0.371507	-1.8575	0.037526
11	-0.219356	-1.0968	0.141595
12	-0.113946	-0.5697	0.286973
13	-0.068653	-0.3433	0.367135
14	-0.064319	-0.3216	0.375216
15	-0.039249	-0.1962	0.423003
16	-0.03247	-0.1623	0.436168
17	0.054555	0.2728	0.393633
18	0.086785	0.4339	0.334033
19	0.019996	0.1	0.460578
20	-0.055804	-0.279	0.391262
21	-0.104217	-0.5211	0.303446
22	-0.100744	-0.5037	0.309435
23	-0.083763	-0.4188	0.339465
24	-0.033336	-0.1667	0.434481

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.786994	3.935	0.000293
2	-0.3053	-1.5265	0.06972
3	-0.062169	-0.3108	0.379248
4	0.039884	0.1994	0.421773
5	-0.00521	-0.0261	0.489712
6	-0.132557	-0.6628	0.256766
7	-0.172804	-0.864	0.197896
8	-0.336627	-1.6831	0.052399
9	0.083729	0.4186	0.339525
10	0.27518	1.3759	0.090527
11	-0.05027	-0.2514	0.401799
12	-0.177602	-0.888	0.1915
13	-0.002873	-0.0144	0.494327
14	0.027316	0.1366	0.446227
15	0.096721	0.4836	0.316438
16	-0.301264	-1.5063	0.072259
17	0.065455	0.3273	0.373093
18	-0.027922	-0.1396	0.445043
19	-0.053114	-0.2656	0.396374
20	-0.014803	-0.074	0.470794
21	-0.087988	-0.4399	0.33188
22	-0.036364	-0.1818	0.428594
23	0.078114	0.3906	0.349712
24	0.025411	0.1271	0.449957

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.786994 & 3.935 & 0.000293 \tabularnewline
2 & -0.3053 & -1.5265 & 0.06972 \tabularnewline
3 & -0.062169 & -0.3108 & 0.379248 \tabularnewline
4 & 0.039884 & 0.1994 & 0.421773 \tabularnewline
5 & -0.00521 & -0.0261 & 0.489712 \tabularnewline
6 & -0.132557 & -0.6628 & 0.256766 \tabularnewline
7 & -0.172804 & -0.864 & 0.197896 \tabularnewline
8 & -0.336627 & -1.6831 & 0.052399 \tabularnewline
9 & 0.083729 & 0.4186 & 0.339525 \tabularnewline
10 & 0.27518 & 1.3759 & 0.090527 \tabularnewline
11 & -0.05027 & -0.2514 & 0.401799 \tabularnewline
12 & -0.177602 & -0.888 & 0.1915 \tabularnewline
13 & -0.002873 & -0.0144 & 0.494327 \tabularnewline
14 & 0.027316 & 0.1366 & 0.446227 \tabularnewline
15 & 0.096721 & 0.4836 & 0.316438 \tabularnewline
16 & -0.301264 & -1.5063 & 0.072259 \tabularnewline
17 & 0.065455 & 0.3273 & 0.373093 \tabularnewline
18 & -0.027922 & -0.1396 & 0.445043 \tabularnewline
19 & -0.053114 & -0.2656 & 0.396374 \tabularnewline
20 & -0.014803 & -0.074 & 0.470794 \tabularnewline
21 & -0.087988 & -0.4399 & 0.33188 \tabularnewline
22 & -0.036364 & -0.1818 & 0.428594 \tabularnewline
23 & 0.078114 & 0.3906 & 0.349712 \tabularnewline
24 & 0.025411 & 0.1271 & 0.449957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227263&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]0.786994[/C][C]3.935[/C][C]0.000293[/C][/ROW]
[ROW][C]2[/C][C]-0.3053[/C][C]-1.5265[/C][C]0.06972[/C][/ROW]
[ROW][C]3[/C][C]-0.062169[/C][C]-0.3108[/C][C]0.379248[/C][/ROW]
[ROW][C]4[/C][C]0.039884[/C][C]0.1994[/C][C]0.421773[/C][/ROW]
[ROW][C]5[/C][C]-0.00521[/C][C]-0.0261[/C][C]0.489712[/C][/ROW]
[ROW][C]6[/C][C]-0.132557[/C][C]-0.6628[/C][C]0.256766[/C][/ROW]
[ROW][C]7[/C][C]-0.172804[/C][C]-0.864[/C][C]0.197896[/C][/ROW]
[ROW][C]8[/C][C]-0.336627[/C][C]-1.6831[/C][C]0.052399[/C][/ROW]
[ROW][C]9[/C][C]0.083729[/C][C]0.4186[/C][C]0.339525[/C][/ROW]
[ROW][C]10[/C][C]0.27518[/C][C]1.3759[/C][C]0.090527[/C][/ROW]
[ROW][C]11[/C][C]-0.05027[/C][C]-0.2514[/C][C]0.401799[/C][/ROW]
[ROW][C]12[/C][C]-0.177602[/C][C]-0.888[/C][C]0.1915[/C][/ROW]
[ROW][C]13[/C][C]-0.002873[/C][C]-0.0144[/C][C]0.494327[/C][/ROW]
[ROW][C]14[/C][C]0.027316[/C][C]0.1366[/C][C]0.446227[/C][/ROW]
[ROW][C]15[/C][C]0.096721[/C][C]0.4836[/C][C]0.316438[/C][/ROW]
[ROW][C]16[/C][C]-0.301264[/C][C]-1.5063[/C][C]0.072259[/C][/ROW]
[ROW][C]17[/C][C]0.065455[/C][C]0.3273[/C][C]0.373093[/C][/ROW]
[ROW][C]18[/C][C]-0.027922[/C][C]-0.1396[/C][C]0.445043[/C][/ROW]
[ROW][C]19[/C][C]-0.053114[/C][C]-0.2656[/C][C]0.396374[/C][/ROW]
[ROW][C]20[/C][C]-0.014803[/C][C]-0.074[/C][C]0.470794[/C][/ROW]
[ROW][C]21[/C][C]-0.087988[/C][C]-0.4399[/C][C]0.33188[/C][/ROW]
[ROW][C]22[/C][C]-0.036364[/C][C]-0.1818[/C][C]0.428594[/C][/ROW]
[ROW][C]23[/C][C]0.078114[/C][C]0.3906[/C][C]0.349712[/C][/ROW]
[ROW][C]24[/C][C]0.025411[/C][C]0.1271[/C][C]0.449957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227263&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227263&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	0.786994	3.935	0.000293
2	-0.3053	-1.5265	0.06972
3	-0.062169	-0.3108	0.379248
4	0.039884	0.1994	0.421773
5	-0.00521	-0.0261	0.489712
6	-0.132557	-0.6628	0.256766
7	-0.172804	-0.864	0.197896
8	-0.336627	-1.6831	0.052399
9	0.083729	0.4186	0.339525
10	0.27518	1.3759	0.090527
11	-0.05027	-0.2514	0.401799
12	-0.177602	-0.888	0.1915
13	-0.002873	-0.0144	0.494327
14	0.027316	0.1366	0.446227
15	0.096721	0.4836	0.316438
16	-0.301264	-1.5063	0.072259
17	0.065455	0.3273	0.373093
18	-0.027922	-0.1396	0.445043
19	-0.053114	-0.2656	0.396374
20	-0.014803	-0.074	0.470794
21	-0.087988	-0.4399	0.33188
22	-0.036364	-0.1818	0.428594
23	0.078114	0.3906	0.349712
24	0.025411	0.1271	0.449957

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 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; 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 (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