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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 computationFri, 21 Dec 2012 09:12:03 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t13560991410f0b0ams6u197e4.htm/, Retrieved Fri, 29 Mar 2024 02:34:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203693, Retrieved Fri, 29 Mar 2024 02:34:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [Arima Backward Se...] [2012-12-21 13:27:11] [1655ef4f70a4add09e51daeee7c8dd65]
- RMP     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2012-12-21 14:12:03] [e5cf4d544f75f57c12196ef0ffd71d75] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203693&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203693&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.92765610.07690
20.8810939.57110
30.8534239.27050
40.8078368.77530
50.7965028.65220
60.7744168.41230
70.7492568.1390
80.744458.08680
90.7116737.73080
100.681217.39980
110.6839857.430
120.6684977.26170
130.6284346.82650
140.5994256.51140
150.5503815.97870
160.5194515.64270
170.5053515.48950
180.4832075.2490
190.4775995.18810
200.4645275.04611e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927656 & 10.0769 & 0 \tabularnewline
2 & 0.881093 & 9.5711 & 0 \tabularnewline
3 & 0.853423 & 9.2705 & 0 \tabularnewline
4 & 0.807836 & 8.7753 & 0 \tabularnewline
5 & 0.796502 & 8.6522 & 0 \tabularnewline
6 & 0.774416 & 8.4123 & 0 \tabularnewline
7 & 0.749256 & 8.139 & 0 \tabularnewline
8 & 0.74445 & 8.0868 & 0 \tabularnewline
9 & 0.711673 & 7.7308 & 0 \tabularnewline
10 & 0.68121 & 7.3998 & 0 \tabularnewline
11 & 0.683985 & 7.43 & 0 \tabularnewline
12 & 0.668497 & 7.2617 & 0 \tabularnewline
13 & 0.628434 & 6.8265 & 0 \tabularnewline
14 & 0.599425 & 6.5114 & 0 \tabularnewline
15 & 0.550381 & 5.9787 & 0 \tabularnewline
16 & 0.519451 & 5.6427 & 0 \tabularnewline
17 & 0.505351 & 5.4895 & 0 \tabularnewline
18 & 0.483207 & 5.249 & 0 \tabularnewline
19 & 0.477599 & 5.1881 & 0 \tabularnewline
20 & 0.464527 & 5.0461 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203693&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]0.927656[/C][C]10.0769[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.881093[/C][C]9.5711[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.853423[/C][C]9.2705[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.807836[/C][C]8.7753[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.796502[/C][C]8.6522[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.774416[/C][C]8.4123[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.749256[/C][C]8.139[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.74445[/C][C]8.0868[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.711673[/C][C]7.7308[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.68121[/C][C]7.3998[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.683985[/C][C]7.43[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.668497[/C][C]7.2617[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.628434[/C][C]6.8265[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.599425[/C][C]6.5114[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.550381[/C][C]5.9787[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.519451[/C][C]5.6427[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.505351[/C][C]5.4895[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.483207[/C][C]5.249[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.477599[/C][C]5.1881[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.464527[/C][C]5.0461[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203693&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 kACF(k)T-STATP-value
10.92765610.07690
20.8810939.57110
30.8534239.27050
40.8078368.77530
50.7965028.65220
60.7744168.41230
70.7492568.1390
80.744458.08680
90.7116737.73080
100.681217.39980
110.6839857.430
120.6684977.26170
130.6284346.82650
140.5994256.51140
150.5503815.97870
160.5194515.64270
170.5053515.48950
180.4832075.2490
190.4775995.18810
200.4645275.04611e-06







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.92765610.07690
20.1473461.60060.056071
30.1452661.5780.058622
4-0.091894-0.99820.160107
50.217082.35810.010007
6-0.033553-0.36450.358077
70.0317060.34440.365573
80.0918130.99730.160319
9-0.11603-1.26040.105005
10-0.032385-0.35180.36281
110.1880272.04250.021665
12-0.006822-0.07410.470525
13-0.245318-2.66480.004391
14-0.024909-0.27060.393592
15-0.123749-1.34430.090722
160.0314620.34180.366569
170.0652760.70910.239837
180.0654210.71070.239349
19-0.004895-0.05320.478841
20-0.017456-0.18960.424968

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927656 & 10.0769 & 0 \tabularnewline
2 & 0.147346 & 1.6006 & 0.056071 \tabularnewline
3 & 0.145266 & 1.578 & 0.058622 \tabularnewline
4 & -0.091894 & -0.9982 & 0.160107 \tabularnewline
5 & 0.21708 & 2.3581 & 0.010007 \tabularnewline
6 & -0.033553 & -0.3645 & 0.358077 \tabularnewline
7 & 0.031706 & 0.3444 & 0.365573 \tabularnewline
8 & 0.091813 & 0.9973 & 0.160319 \tabularnewline
9 & -0.11603 & -1.2604 & 0.105005 \tabularnewline
10 & -0.032385 & -0.3518 & 0.36281 \tabularnewline
11 & 0.188027 & 2.0425 & 0.021665 \tabularnewline
12 & -0.006822 & -0.0741 & 0.470525 \tabularnewline
13 & -0.245318 & -2.6648 & 0.004391 \tabularnewline
14 & -0.024909 & -0.2706 & 0.393592 \tabularnewline
15 & -0.123749 & -1.3443 & 0.090722 \tabularnewline
16 & 0.031462 & 0.3418 & 0.366569 \tabularnewline
17 & 0.065276 & 0.7091 & 0.239837 \tabularnewline
18 & 0.065421 & 0.7107 & 0.239349 \tabularnewline
19 & -0.004895 & -0.0532 & 0.478841 \tabularnewline
20 & -0.017456 & -0.1896 & 0.424968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203693&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]0.927656[/C][C]10.0769[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.147346[/C][C]1.6006[/C][C]0.056071[/C][/ROW]
[ROW][C]3[/C][C]0.145266[/C][C]1.578[/C][C]0.058622[/C][/ROW]
[ROW][C]4[/C][C]-0.091894[/C][C]-0.9982[/C][C]0.160107[/C][/ROW]
[ROW][C]5[/C][C]0.21708[/C][C]2.3581[/C][C]0.010007[/C][/ROW]
[ROW][C]6[/C][C]-0.033553[/C][C]-0.3645[/C][C]0.358077[/C][/ROW]
[ROW][C]7[/C][C]0.031706[/C][C]0.3444[/C][C]0.365573[/C][/ROW]
[ROW][C]8[/C][C]0.091813[/C][C]0.9973[/C][C]0.160319[/C][/ROW]
[ROW][C]9[/C][C]-0.11603[/C][C]-1.2604[/C][C]0.105005[/C][/ROW]
[ROW][C]10[/C][C]-0.032385[/C][C]-0.3518[/C][C]0.36281[/C][/ROW]
[ROW][C]11[/C][C]0.188027[/C][C]2.0425[/C][C]0.021665[/C][/ROW]
[ROW][C]12[/C][C]-0.006822[/C][C]-0.0741[/C][C]0.470525[/C][/ROW]
[ROW][C]13[/C][C]-0.245318[/C][C]-2.6648[/C][C]0.004391[/C][/ROW]
[ROW][C]14[/C][C]-0.024909[/C][C]-0.2706[/C][C]0.393592[/C][/ROW]
[ROW][C]15[/C][C]-0.123749[/C][C]-1.3443[/C][C]0.090722[/C][/ROW]
[ROW][C]16[/C][C]0.031462[/C][C]0.3418[/C][C]0.366569[/C][/ROW]
[ROW][C]17[/C][C]0.065276[/C][C]0.7091[/C][C]0.239837[/C][/ROW]
[ROW][C]18[/C][C]0.065421[/C][C]0.7107[/C][C]0.239349[/C][/ROW]
[ROW][C]19[/C][C]-0.004895[/C][C]-0.0532[/C][C]0.478841[/C][/ROW]
[ROW][C]20[/C][C]-0.017456[/C][C]-0.1896[/C][C]0.424968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203693&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 kPACF(k)T-STATP-value
10.92765610.07690
20.1473461.60060.056071
30.1452661.5780.058622
4-0.091894-0.99820.160107
50.217082.35810.010007
6-0.033553-0.36450.358077
70.0317060.34440.365573
80.0918130.99730.160319
9-0.11603-1.26040.105005
10-0.032385-0.35180.36281
110.1880272.04250.021665
12-0.006822-0.07410.470525
13-0.245318-2.66480.004391
14-0.024909-0.27060.393592
15-0.123749-1.34430.090722
160.0314620.34180.366569
170.0652760.70910.239837
180.0654210.71070.239349
19-0.004895-0.05320.478841
20-0.017456-0.18960.424968



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)
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')