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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

Wed, 30 Nov 2016 11:52:33 +0100

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/2016/Nov/30/t1480503184ryr0s2xtmeztbka.htm/, Retrieved Sun, 19 May 2024 02:37:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297334, Retrieved Sun, 19 May 2024 02:37:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2016-11-30 10:52:33] [94ac3c9a028ddd47e8862e80eac9f626] [Current]

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Dataseries X:

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Histogram

Boxplots

-35.68
-39.41
-90.98
-99.79
9.899
-55.35
-82.98
-26.85
-130.7
-196
103.4
-17.23
29.32
217.6
119
73.21
-47.1
-46.35
163
143.1
9.336
159
193.4
312.8
307.3
107.6
95.02
138.2
182.9
179.6
153
269.1
-90.66
143
184.4
26.77
357.3
220.6
237
84.21
353.9
286.6
323
32.15
68.34
127
348.4
488.8
374.3
415.6
79.02
456.2
380.9
246.6
370
255.1
374.3
231
69.4
-15.23
-114.7
-44.41
-49.98
-102.8
108.9
231.6
137
230.1
294.3
228
43.4
-114.2
-145.7
-191.4
54.02
-102.8
-103.1
-145.4
-200
-113.9
-53.66
-288
-143.6
33.77
-249.7
107.6
-191
-89.79
-92.1
-257.4
-116
-329.9
-82.66
-101
-90.6
108.8
-74.68
-146.4
-187
-81.79
-228.1
-46.35
-114
-13.85
-194.7
-164
-48.6
49.77
233.3
-85.41
-34.98
-25.79
-176.1
55.65
15.02
-18.85
-66.66
-166
1.399
96.77
90.32
-102.4
164
-23.79
-66.1
-135.4
-215
-102.9
-64.66
-196
-32.6
41.77
-57.68
-186.4
-91.98
-124.8
-169.1
-44.35
-182
-104.9
-161.7
-22.04
-311.6
-224.2
-248.7
-89.41
-55.98
-80.79
-100.1
-181.4
-0.9764
-146.9
-28.66
88.96
-180.6
-439.2
-266.7
-102.4
-142
-119.8
-135.1
-8.351
-154
27.15
-115.7
0.9611
-50.6
-86.23
-228.7
-94.6
15.83
79.02
9.71
-94.54
-72.17
-122
113.1
33.77
-169.8
-256.4
30.14
13.4
79.83
21.02
70.71
14.46
-24.17
22.96
130.1
121.8
84.21
-6.415

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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297334&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297334&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.645906	8.9499	0
2	0.574709	7.9634	0
3	0.497897	6.8991	0
4	0.460145	6.3759	0
5	0.507066	7.0261	0
6	0.456838	6.3301	0
7	0.446568	6.1878	0
8	0.398769	5.5255	0
9	0.432508	5.993	0
10	0.41484	5.7482	0
11	0.456795	6.3295	0
12	0.438565	6.0769	0
13	0.445787	6.177	0
14	0.362766	5.0266	1e-06
15	0.355107	4.9205	1e-06
16	0.360291	4.9923	1e-06
17	0.332267	4.604	4e-06
18	0.38413	5.3227	0
19	0.289923	4.0173	4.2e-05
20	0.244534	3.3884	0.000427
21	0.205856	2.8524	0.002407
22	0.139944	1.9391	0.026977

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.645906 & 8.9499 & 0 \tabularnewline
2 & 0.574709 & 7.9634 & 0 \tabularnewline
3 & 0.497897 & 6.8991 & 0 \tabularnewline
4 & 0.460145 & 6.3759 & 0 \tabularnewline
5 & 0.507066 & 7.0261 & 0 \tabularnewline
6 & 0.456838 & 6.3301 & 0 \tabularnewline
7 & 0.446568 & 6.1878 & 0 \tabularnewline
8 & 0.398769 & 5.5255 & 0 \tabularnewline
9 & 0.432508 & 5.993 & 0 \tabularnewline
10 & 0.41484 & 5.7482 & 0 \tabularnewline
11 & 0.456795 & 6.3295 & 0 \tabularnewline
12 & 0.438565 & 6.0769 & 0 \tabularnewline
13 & 0.445787 & 6.177 & 0 \tabularnewline
14 & 0.362766 & 5.0266 & 1e-06 \tabularnewline
15 & 0.355107 & 4.9205 & 1e-06 \tabularnewline
16 & 0.360291 & 4.9923 & 1e-06 \tabularnewline
17 & 0.332267 & 4.604 & 4e-06 \tabularnewline
18 & 0.38413 & 5.3227 & 0 \tabularnewline
19 & 0.289923 & 4.0173 & 4.2e-05 \tabularnewline
20 & 0.244534 & 3.3884 & 0.000427 \tabularnewline
21 & 0.205856 & 2.8524 & 0.002407 \tabularnewline
22 & 0.139944 & 1.9391 & 0.026977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297334&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]0.645906[/C][C]8.9499[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.574709[/C][C]7.9634[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.497897[/C][C]6.8991[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.460145[/C][C]6.3759[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.507066[/C][C]7.0261[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.456838[/C][C]6.3301[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.446568[/C][C]6.1878[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.398769[/C][C]5.5255[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.432508[/C][C]5.993[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.41484[/C][C]5.7482[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.456795[/C][C]6.3295[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.438565[/C][C]6.0769[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.445787[/C][C]6.177[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.362766[/C][C]5.0266[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.355107[/C][C]4.9205[/C][C]1e-06[/C][/ROW]
[ROW][C]16[/C][C]0.360291[/C][C]4.9923[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]0.332267[/C][C]4.604[/C][C]4e-06[/C][/ROW]
[ROW][C]18[/C][C]0.38413[/C][C]5.3227[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.289923[/C][C]4.0173[/C][C]4.2e-05[/C][/ROW]
[ROW][C]20[/C][C]0.244534[/C][C]3.3884[/C][C]0.000427[/C][/ROW]
[ROW][C]21[/C][C]0.205856[/C][C]2.8524[/C][C]0.002407[/C][/ROW]
[ROW][C]22[/C][C]0.139944[/C][C]1.9391[/C][C]0.026977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297334&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	0.645906	8.9499	0
2	0.574709	7.9634	0
3	0.497897	6.8991	0
4	0.460145	6.3759	0
5	0.507066	7.0261	0
6	0.456838	6.3301	0
7	0.446568	6.1878	0
8	0.398769	5.5255	0
9	0.432508	5.993	0
10	0.41484	5.7482	0
11	0.456795	6.3295	0
12	0.438565	6.0769	0
13	0.445787	6.177	0
14	0.362766	5.0266	1e-06
15	0.355107	4.9205	1e-06
16	0.360291	4.9923	1e-06
17	0.332267	4.604	4e-06
18	0.38413	5.3227	0
19	0.289923	4.0173	4.2e-05
20	0.244534	3.3884	0.000427
21	0.205856	2.8524	0.002407
22	0.139944	1.9391	0.026977

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.645906	8.9499	0
2	0.270268	3.7449	0.000119
3	0.097083	1.3452	0.090071
4	0.087447	1.2117	0.113558
5	0.215135	2.981	0.001623
6	0.028092	0.3893	0.34876
7	0.05021	0.6957	0.243721
8	-0.004721	-0.0654	0.473954
9	0.13191	1.8278	0.034566
10	0.021799	0.3021	0.381466
11	0.131982	1.8288	0.034491
12	0.028785	0.3989	0.345219
13	0.087001	1.2055	0.114743
14	-0.132294	-1.8331	0.034166
15	0.022197	0.3076	0.379372
16	0.015163	0.2101	0.416905
17	-0.013382	-0.1854	0.426547
18	0.074319	1.0298	0.152201
19	-0.097553	-1.3517	0.089026
20	-0.117365	-1.6263	0.052768
21	-0.065591	-0.9089	0.182283
22	-0.167374	-2.3192	0.010718

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.645906 & 8.9499 & 0 \tabularnewline
2 & 0.270268 & 3.7449 & 0.000119 \tabularnewline
3 & 0.097083 & 1.3452 & 0.090071 \tabularnewline
4 & 0.087447 & 1.2117 & 0.113558 \tabularnewline
5 & 0.215135 & 2.981 & 0.001623 \tabularnewline
6 & 0.028092 & 0.3893 & 0.34876 \tabularnewline
7 & 0.05021 & 0.6957 & 0.243721 \tabularnewline
8 & -0.004721 & -0.0654 & 0.473954 \tabularnewline
9 & 0.13191 & 1.8278 & 0.034566 \tabularnewline
10 & 0.021799 & 0.3021 & 0.381466 \tabularnewline
11 & 0.131982 & 1.8288 & 0.034491 \tabularnewline
12 & 0.028785 & 0.3989 & 0.345219 \tabularnewline
13 & 0.087001 & 1.2055 & 0.114743 \tabularnewline
14 & -0.132294 & -1.8331 & 0.034166 \tabularnewline
15 & 0.022197 & 0.3076 & 0.379372 \tabularnewline
16 & 0.015163 & 0.2101 & 0.416905 \tabularnewline
17 & -0.013382 & -0.1854 & 0.426547 \tabularnewline
18 & 0.074319 & 1.0298 & 0.152201 \tabularnewline
19 & -0.097553 & -1.3517 & 0.089026 \tabularnewline
20 & -0.117365 & -1.6263 & 0.052768 \tabularnewline
21 & -0.065591 & -0.9089 & 0.182283 \tabularnewline
22 & -0.167374 & -2.3192 & 0.010718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297334&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]0.645906[/C][C]8.9499[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.270268[/C][C]3.7449[/C][C]0.000119[/C][/ROW]
[ROW][C]3[/C][C]0.097083[/C][C]1.3452[/C][C]0.090071[/C][/ROW]
[ROW][C]4[/C][C]0.087447[/C][C]1.2117[/C][C]0.113558[/C][/ROW]
[ROW][C]5[/C][C]0.215135[/C][C]2.981[/C][C]0.001623[/C][/ROW]
[ROW][C]6[/C][C]0.028092[/C][C]0.3893[/C][C]0.34876[/C][/ROW]
[ROW][C]7[/C][C]0.05021[/C][C]0.6957[/C][C]0.243721[/C][/ROW]
[ROW][C]8[/C][C]-0.004721[/C][C]-0.0654[/C][C]0.473954[/C][/ROW]
[ROW][C]9[/C][C]0.13191[/C][C]1.8278[/C][C]0.034566[/C][/ROW]
[ROW][C]10[/C][C]0.021799[/C][C]0.3021[/C][C]0.381466[/C][/ROW]
[ROW][C]11[/C][C]0.131982[/C][C]1.8288[/C][C]0.034491[/C][/ROW]
[ROW][C]12[/C][C]0.028785[/C][C]0.3989[/C][C]0.345219[/C][/ROW]
[ROW][C]13[/C][C]0.087001[/C][C]1.2055[/C][C]0.114743[/C][/ROW]
[ROW][C]14[/C][C]-0.132294[/C][C]-1.8331[/C][C]0.034166[/C][/ROW]
[ROW][C]15[/C][C]0.022197[/C][C]0.3076[/C][C]0.379372[/C][/ROW]
[ROW][C]16[/C][C]0.015163[/C][C]0.2101[/C][C]0.416905[/C][/ROW]
[ROW][C]17[/C][C]-0.013382[/C][C]-0.1854[/C][C]0.426547[/C][/ROW]
[ROW][C]18[/C][C]0.074319[/C][C]1.0298[/C][C]0.152201[/C][/ROW]
[ROW][C]19[/C][C]-0.097553[/C][C]-1.3517[/C][C]0.089026[/C][/ROW]
[ROW][C]20[/C][C]-0.117365[/C][C]-1.6263[/C][C]0.052768[/C][/ROW]
[ROW][C]21[/C][C]-0.065591[/C][C]-0.9089[/C][C]0.182283[/C][/ROW]
[ROW][C]22[/C][C]-0.167374[/C][C]-2.3192[/C][C]0.010718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297334&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	0.645906	8.9499	0
2	0.270268	3.7449	0.000119
3	0.097083	1.3452	0.090071
4	0.087447	1.2117	0.113558
5	0.215135	2.981	0.001623
6	0.028092	0.3893	0.34876
7	0.05021	0.6957	0.243721
8	-0.004721	-0.0654	0.473954
9	0.13191	1.8278	0.034566
10	0.021799	0.3021	0.381466
11	0.131982	1.8288	0.034491
12	0.028785	0.3989	0.345219
13	0.087001	1.2055	0.114743
14	-0.132294	-1.8331	0.034166
15	0.022197	0.3076	0.379372
16	0.015163	0.2101	0.416905
17	-0.013382	-0.1854	0.426547
18	0.074319	1.0298	0.152201
19	-0.097553	-1.3517	0.089026
20	-0.117365	-1.6263	0.052768
21	-0.065591	-0.9089	0.182283
22	-0.167374	-2.3192	0.010718

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 = 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 (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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