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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationThu, 01 Feb 2018 10:39:07 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Feb/01/t15174779610muqy9bvx700uzb.htm/, Retrieved Sun, 28 Apr 2024 21:17:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=314258, Retrieved Sun, 28 Apr 2024 21:17:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact40

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2018-02-01 09:39:07] [f6e7862e4a89eb2e52e485da90fc243d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62.4
67.4
76.1
67.4
74.5
72.6
60.5
66.1
76.5
76.8
77
71
74.8
73.7
80.5
71.8
76.9
79.9
65.9
69.5
75.1
79.6
75.2
68
72.8
71.5
78.5
76.8
75.3
76.7
69.7
67.8
77.5
82.5
75.3
70.9
76
73.7
79.7
77.8
73.3
78.3
71.9
67
82
83.7
74.8
80
74.3
76.8
89
81.9
76.8
88.9
75.8
75.5
89.1
88
85.9
89.3
82.9
81.2
90.5
86.4
81.8
91.3
73.4
76.6
91
87
89.7
90.7
86.5
86.6
98.8
84.4
91.4
95.7
78.5
81.7
94.3
98.5
95.4
91.7
92.8
90.5
102.2
91.8
95
102
88.9
89.6
97.9
108.6
100.8
95.1
101
100.9
102.5
105.4
98.4
105.3
96.5
88.1
107.9
107
92.5
95.7
85.2
85.5
94.7
86.2
88.8
93.4
83.4
82.9
96.7
96.2
92.8
92.8
90
95.4
108.3
96.3
95
109
92
92.3
107
105.5
105.4
103.9
99.2
102.2
121.5
102.3
110
105.9
91.9
100
111.7
104.9
103.3
101.8
100.8
104.2
116.5
97.9
100.7
107
96.3
96
104.5
107.4
102.4
94.9
98.8
96.8
108.2
103.8
102.3
107.2
102
92.6
105.2
113
105.6
101.6
101.7
102.7
109
105.5
103.3
108.6
98.2
90
112.4
111.9
102.1
102.4
101.7
98.7
114
105.1
98.3
110
96.5
92.2
112
111.4
107.5
103.4
103.5
107.4
117.6
110.2
104.3
115.9
98.9
101.9
113.5
109.5
110
114.2
106.9
109.2
124.2
104.7
111.9
119
102.9
106.3

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314258&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=314258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314258&T=0

As an alternative you can also use a QR Code:  
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 Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5244377.41670
20.5300317.49580
30.6191058.75550
40.3743175.29360
50.4236645.99150
60.3492234.93881e-06
70.1282941.81440.035561
80.1312381.8560.032463
90.0598180.8460.199296
10-0.059098-0.83580.202139
11-0.081615-1.15420.124895
12-0.261471-3.69780.00014
13-0.252927-3.57690.000218
14-0.23726-3.35540.000474
15-0.298356-4.21941.9e-05
16-0.339111-4.79582e-06
17-0.300921-4.25571.6e-05
18-0.314691-4.45047e-06
19-0.377929-5.34470
20-0.272098-3.84818e-05
21-0.283815-4.01374.2e-05
22-0.339184-4.79682e-06
23-0.142645-2.01730.0225

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.524437 & 7.4167 & 0 \tabularnewline
2 & 0.530031 & 7.4958 & 0 \tabularnewline
3 & 0.619105 & 8.7555 & 0 \tabularnewline
4 & 0.374317 & 5.2936 & 0 \tabularnewline
5 & 0.423664 & 5.9915 & 0 \tabularnewline
6 & 0.349223 & 4.9388 & 1e-06 \tabularnewline
7 & 0.128294 & 1.8144 & 0.035561 \tabularnewline
8 & 0.131238 & 1.856 & 0.032463 \tabularnewline
9 & 0.059818 & 0.846 & 0.199296 \tabularnewline
10 & -0.059098 & -0.8358 & 0.202139 \tabularnewline
11 & -0.081615 & -1.1542 & 0.124895 \tabularnewline
12 & -0.261471 & -3.6978 & 0.00014 \tabularnewline
13 & -0.252927 & -3.5769 & 0.000218 \tabularnewline
14 & -0.23726 & -3.3554 & 0.000474 \tabularnewline
15 & -0.298356 & -4.2194 & 1.9e-05 \tabularnewline
16 & -0.339111 & -4.7958 & 2e-06 \tabularnewline
17 & -0.300921 & -4.2557 & 1.6e-05 \tabularnewline
18 & -0.314691 & -4.4504 & 7e-06 \tabularnewline
19 & -0.377929 & -5.3447 & 0 \tabularnewline
20 & -0.272098 & -3.8481 & 8e-05 \tabularnewline
21 & -0.283815 & -4.0137 & 4.2e-05 \tabularnewline
22 & -0.339184 & -4.7968 & 2e-06 \tabularnewline
23 & -0.142645 & -2.0173 & 0.0225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314258&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]0.524437[/C][C]7.4167[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.530031[/C][C]7.4958[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.619105[/C][C]8.7555[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.374317[/C][C]5.2936[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.423664[/C][C]5.9915[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.349223[/C][C]4.9388[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.128294[/C][C]1.8144[/C][C]0.035561[/C][/ROW]
[ROW][C]8[/C][C]0.131238[/C][C]1.856[/C][C]0.032463[/C][/ROW]
[ROW][C]9[/C][C]0.059818[/C][C]0.846[/C][C]0.199296[/C][/ROW]
[ROW][C]10[/C][C]-0.059098[/C][C]-0.8358[/C][C]0.202139[/C][/ROW]
[ROW][C]11[/C][C]-0.081615[/C][C]-1.1542[/C][C]0.124895[/C][/ROW]
[ROW][C]12[/C][C]-0.261471[/C][C]-3.6978[/C][C]0.00014[/C][/ROW]
[ROW][C]13[/C][C]-0.252927[/C][C]-3.5769[/C][C]0.000218[/C][/ROW]
[ROW][C]14[/C][C]-0.23726[/C][C]-3.3554[/C][C]0.000474[/C][/ROW]
[ROW][C]15[/C][C]-0.298356[/C][C]-4.2194[/C][C]1.9e-05[/C][/ROW]
[ROW][C]16[/C][C]-0.339111[/C][C]-4.7958[/C][C]2e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.300921[/C][C]-4.2557[/C][C]1.6e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.314691[/C][C]-4.4504[/C][C]7e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.377929[/C][C]-5.3447[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.272098[/C][C]-3.8481[/C][C]8e-05[/C][/ROW]
[ROW][C]21[/C][C]-0.283815[/C][C]-4.0137[/C][C]4.2e-05[/C][/ROW]
[ROW][C]22[/C][C]-0.339184[/C][C]-4.7968[/C][C]2e-06[/C][/ROW]
[ROW][C]23[/C][C]-0.142645[/C][C]-2.0173[/C][C]0.0225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314258&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5244377.41670
20.5300317.49580
30.6191058.75550
40.3743175.29360
50.4236645.99150
60.3492234.93881e-06
70.1282941.81440.035561
80.1312381.8560.032463
90.0598180.8460.199296
10-0.059098-0.83580.202139
11-0.081615-1.15420.124895
12-0.261471-3.69780.00014
13-0.252927-3.57690.000218
14-0.23726-3.35540.000474
15-0.298356-4.21941.9e-05
16-0.339111-4.79582e-06
17-0.300921-4.25571.6e-05
18-0.314691-4.45047e-06
19-0.377929-5.34470
20-0.272098-3.84818e-05
21-0.283815-4.01374.2e-05
22-0.339184-4.79682e-06
23-0.142645-2.01730.0225






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5244377.41670
20.3517364.97431e-06
30.4005295.66430
4-0.137339-1.94230.026754
50.0420460.59460.276386
6-0.091936-1.30020.097519
7-0.256753-3.6310.000179
8-0.171392-2.42380.008123
9-0.048329-0.68350.247551
10-0.026522-0.37510.354
11-0.041831-0.59160.277401
12-0.24247-3.4290.000368
13-0.001826-0.02580.489713
140.0652740.92310.178529
150.1167841.65160.050095
16-0.105061-1.48580.069455
170.0513150.72570.234435
180.021510.30420.380646
19-0.230556-3.26060.000654
20-0.058079-0.82140.206208
210.0355410.50260.307891
22-0.081042-1.14610.12656
230.1496312.11610.017786

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.524437 & 7.4167 & 0 \tabularnewline
2 & 0.351736 & 4.9743 & 1e-06 \tabularnewline
3 & 0.400529 & 5.6643 & 0 \tabularnewline
4 & -0.137339 & -1.9423 & 0.026754 \tabularnewline
5 & 0.042046 & 0.5946 & 0.276386 \tabularnewline
6 & -0.091936 & -1.3002 & 0.097519 \tabularnewline
7 & -0.256753 & -3.631 & 0.000179 \tabularnewline
8 & -0.171392 & -2.4238 & 0.008123 \tabularnewline
9 & -0.048329 & -0.6835 & 0.247551 \tabularnewline
10 & -0.026522 & -0.3751 & 0.354 \tabularnewline
11 & -0.041831 & -0.5916 & 0.277401 \tabularnewline
12 & -0.24247 & -3.429 & 0.000368 \tabularnewline
13 & -0.001826 & -0.0258 & 0.489713 \tabularnewline
14 & 0.065274 & 0.9231 & 0.178529 \tabularnewline
15 & 0.116784 & 1.6516 & 0.050095 \tabularnewline
16 & -0.105061 & -1.4858 & 0.069455 \tabularnewline
17 & 0.051315 & 0.7257 & 0.234435 \tabularnewline
18 & 0.02151 & 0.3042 & 0.380646 \tabularnewline
19 & -0.230556 & -3.2606 & 0.000654 \tabularnewline
20 & -0.058079 & -0.8214 & 0.206208 \tabularnewline
21 & 0.035541 & 0.5026 & 0.307891 \tabularnewline
22 & -0.081042 & -1.1461 & 0.12656 \tabularnewline
23 & 0.149631 & 2.1161 & 0.017786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314258&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]0.524437[/C][C]7.4167[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.351736[/C][C]4.9743[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.400529[/C][C]5.6643[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.137339[/C][C]-1.9423[/C][C]0.026754[/C][/ROW]
[ROW][C]5[/C][C]0.042046[/C][C]0.5946[/C][C]0.276386[/C][/ROW]
[ROW][C]6[/C][C]-0.091936[/C][C]-1.3002[/C][C]0.097519[/C][/ROW]
[ROW][C]7[/C][C]-0.256753[/C][C]-3.631[/C][C]0.000179[/C][/ROW]
[ROW][C]8[/C][C]-0.171392[/C][C]-2.4238[/C][C]0.008123[/C][/ROW]
[ROW][C]9[/C][C]-0.048329[/C][C]-0.6835[/C][C]0.247551[/C][/ROW]
[ROW][C]10[/C][C]-0.026522[/C][C]-0.3751[/C][C]0.354[/C][/ROW]
[ROW][C]11[/C][C]-0.041831[/C][C]-0.5916[/C][C]0.277401[/C][/ROW]
[ROW][C]12[/C][C]-0.24247[/C][C]-3.429[/C][C]0.000368[/C][/ROW]
[ROW][C]13[/C][C]-0.001826[/C][C]-0.0258[/C][C]0.489713[/C][/ROW]
[ROW][C]14[/C][C]0.065274[/C][C]0.9231[/C][C]0.178529[/C][/ROW]
[ROW][C]15[/C][C]0.116784[/C][C]1.6516[/C][C]0.050095[/C][/ROW]
[ROW][C]16[/C][C]-0.105061[/C][C]-1.4858[/C][C]0.069455[/C][/ROW]
[ROW][C]17[/C][C]0.051315[/C][C]0.7257[/C][C]0.234435[/C][/ROW]
[ROW][C]18[/C][C]0.02151[/C][C]0.3042[/C][C]0.380646[/C][/ROW]
[ROW][C]19[/C][C]-0.230556[/C][C]-3.2606[/C][C]0.000654[/C][/ROW]
[ROW][C]20[/C][C]-0.058079[/C][C]-0.8214[/C][C]0.206208[/C][/ROW]
[ROW][C]21[/C][C]0.035541[/C][C]0.5026[/C][C]0.307891[/C][/ROW]
[ROW][C]22[/C][C]-0.081042[/C][C]-1.1461[/C][C]0.12656[/C][/ROW]
[ROW][C]23[/C][C]0.149631[/C][C]2.1161[/C][C]0.017786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314258&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5244377.41670
20.3517364.97431e-06
30.4005295.66430
4-0.137339-1.94230.026754
50.0420460.59460.276386
6-0.091936-1.30020.097519
7-0.256753-3.6310.000179
8-0.171392-2.42380.008123
9-0.048329-0.68350.247551
10-0.026522-0.37510.354
11-0.041831-0.59160.277401
12-0.24247-3.4290.000368
13-0.001826-0.02580.489713
140.0652740.92310.178529
150.1167841.65160.050095
16-0.105061-1.48580.069455
170.0513150.72570.234435
180.021510.30420.380646
19-0.230556-3.26060.000654
20-0.058079-0.82140.206208
210.0355410.50260.307891
22-0.081042-1.14610.12656
230.1496312.11610.017786


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; par8 = ;
R code (references can be found in the software module):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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')