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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 computationWed, 21 Dec 2011 08:46:46 -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/2011/Dec/21/t1324475242tvdn4cdg1lfg0i7.htm/, Retrieved Tue, 07 May 2024 11:09:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158687, Retrieved Tue, 07 May 2024 11:09:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [(P)ACF [D=0;d=0]] [2011-12-21 13:46:46] [3bdb54d050744f47368418ea7c7e8e96] [Current]
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Dataseries X:
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158687&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158687&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158687&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'Gwilym Jenkins' @ jenkins.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95370311.44440
20.89891610.7870
30.85080210.20960
40.8084259.70110
50.7788999.34680
60.7564429.07730
70.7376028.85120
80.7271318.72560
90.7336498.80380
100.7442558.93110
110.7580279.09630
120.7619439.14330
130.7165048.59810
140.6630437.95650
150.6183637.42040
160.5762096.91450
170.5438016.52560
180.5194566.23350
190.5007036.00840
200.4904035.88480
210.4981825.97820

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953703 & 11.4444 & 0 \tabularnewline
2 & 0.898916 & 10.787 & 0 \tabularnewline
3 & 0.850802 & 10.2096 & 0 \tabularnewline
4 & 0.808425 & 9.7011 & 0 \tabularnewline
5 & 0.778899 & 9.3468 & 0 \tabularnewline
6 & 0.756442 & 9.0773 & 0 \tabularnewline
7 & 0.737602 & 8.8512 & 0 \tabularnewline
8 & 0.727131 & 8.7256 & 0 \tabularnewline
9 & 0.733649 & 8.8038 & 0 \tabularnewline
10 & 0.744255 & 8.9311 & 0 \tabularnewline
11 & 0.758027 & 9.0963 & 0 \tabularnewline
12 & 0.761943 & 9.1433 & 0 \tabularnewline
13 & 0.716504 & 8.5981 & 0 \tabularnewline
14 & 0.663043 & 7.9565 & 0 \tabularnewline
15 & 0.618363 & 7.4204 & 0 \tabularnewline
16 & 0.576209 & 6.9145 & 0 \tabularnewline
17 & 0.543801 & 6.5256 & 0 \tabularnewline
18 & 0.519456 & 6.2335 & 0 \tabularnewline
19 & 0.500703 & 6.0084 & 0 \tabularnewline
20 & 0.490403 & 5.8848 & 0 \tabularnewline
21 & 0.498182 & 5.9782 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158687&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]0.953703[/C][C]11.4444[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.898916[/C][C]10.787[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.850802[/C][C]10.2096[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.808425[/C][C]9.7011[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.778899[/C][C]9.3468[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.756442[/C][C]9.0773[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.737602[/C][C]8.8512[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.727131[/C][C]8.7256[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.733649[/C][C]8.8038[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.744255[/C][C]8.9311[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.758027[/C][C]9.0963[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.761943[/C][C]9.1433[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.716504[/C][C]8.5981[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.663043[/C][C]7.9565[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.618363[/C][C]7.4204[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.576209[/C][C]6.9145[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.543801[/C][C]6.5256[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.519456[/C][C]6.2335[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.500703[/C][C]6.0084[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.490403[/C][C]5.8848[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.498182[/C][C]5.9782[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158687&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158687&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
10.95370311.44440
20.89891610.7870
30.85080210.20960
40.8084259.70110
50.7788999.34680
60.7564429.07730
70.7376028.85120
80.7271318.72560
90.7336498.80380
100.7442558.93110
110.7580279.09630
120.7619439.14330
130.7165048.59810
140.6630437.95650
150.6183637.42040
160.5762096.91450
170.5438016.52560
180.5194566.23350
190.5007036.00840
200.4904035.88480
210.4981825.97820







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95370311.44440
2-0.11757-1.41080.080225
30.0542330.65080.258109
40.0237560.28510.387999
50.1158221.38990.083357
60.0443680.53240.297631
70.0380340.45640.324392
80.0996221.19550.116935
90.2040962.44910.00776
100.0639090.76690.222195
110.1060351.27240.102636
12-0.042466-0.50960.305558
13-0.48543-5.82520
14-0.03435-0.41220.340402
150.0422250.50670.306572
16-0.044197-0.53040.298337
170.0276080.33130.370452
180.0371480.44580.328215
190.0416380.49970.309038
200.01440.17280.431526
210.0733120.87970.19023

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953703 & 11.4444 & 0 \tabularnewline
2 & -0.11757 & -1.4108 & 0.080225 \tabularnewline
3 & 0.054233 & 0.6508 & 0.258109 \tabularnewline
4 & 0.023756 & 0.2851 & 0.387999 \tabularnewline
5 & 0.115822 & 1.3899 & 0.083357 \tabularnewline
6 & 0.044368 & 0.5324 & 0.297631 \tabularnewline
7 & 0.038034 & 0.4564 & 0.324392 \tabularnewline
8 & 0.099622 & 1.1955 & 0.116935 \tabularnewline
9 & 0.204096 & 2.4491 & 0.00776 \tabularnewline
10 & 0.063909 & 0.7669 & 0.222195 \tabularnewline
11 & 0.106035 & 1.2724 & 0.102636 \tabularnewline
12 & -0.042466 & -0.5096 & 0.305558 \tabularnewline
13 & -0.48543 & -5.8252 & 0 \tabularnewline
14 & -0.03435 & -0.4122 & 0.340402 \tabularnewline
15 & 0.042225 & 0.5067 & 0.306572 \tabularnewline
16 & -0.044197 & -0.5304 & 0.298337 \tabularnewline
17 & 0.027608 & 0.3313 & 0.370452 \tabularnewline
18 & 0.037148 & 0.4458 & 0.328215 \tabularnewline
19 & 0.041638 & 0.4997 & 0.309038 \tabularnewline
20 & 0.0144 & 0.1728 & 0.431526 \tabularnewline
21 & 0.073312 & 0.8797 & 0.19023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158687&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]0.953703[/C][C]11.4444[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.11757[/C][C]-1.4108[/C][C]0.080225[/C][/ROW]
[ROW][C]3[/C][C]0.054233[/C][C]0.6508[/C][C]0.258109[/C][/ROW]
[ROW][C]4[/C][C]0.023756[/C][C]0.2851[/C][C]0.387999[/C][/ROW]
[ROW][C]5[/C][C]0.115822[/C][C]1.3899[/C][C]0.083357[/C][/ROW]
[ROW][C]6[/C][C]0.044368[/C][C]0.5324[/C][C]0.297631[/C][/ROW]
[ROW][C]7[/C][C]0.038034[/C][C]0.4564[/C][C]0.324392[/C][/ROW]
[ROW][C]8[/C][C]0.099622[/C][C]1.1955[/C][C]0.116935[/C][/ROW]
[ROW][C]9[/C][C]0.204096[/C][C]2.4491[/C][C]0.00776[/C][/ROW]
[ROW][C]10[/C][C]0.063909[/C][C]0.7669[/C][C]0.222195[/C][/ROW]
[ROW][C]11[/C][C]0.106035[/C][C]1.2724[/C][C]0.102636[/C][/ROW]
[ROW][C]12[/C][C]-0.042466[/C][C]-0.5096[/C][C]0.305558[/C][/ROW]
[ROW][C]13[/C][C]-0.48543[/C][C]-5.8252[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.03435[/C][C]-0.4122[/C][C]0.340402[/C][/ROW]
[ROW][C]15[/C][C]0.042225[/C][C]0.5067[/C][C]0.306572[/C][/ROW]
[ROW][C]16[/C][C]-0.044197[/C][C]-0.5304[/C][C]0.298337[/C][/ROW]
[ROW][C]17[/C][C]0.027608[/C][C]0.3313[/C][C]0.370452[/C][/ROW]
[ROW][C]18[/C][C]0.037148[/C][C]0.4458[/C][C]0.328215[/C][/ROW]
[ROW][C]19[/C][C]0.041638[/C][C]0.4997[/C][C]0.309038[/C][/ROW]
[ROW][C]20[/C][C]0.0144[/C][C]0.1728[/C][C]0.431526[/C][/ROW]
[ROW][C]21[/C][C]0.073312[/C][C]0.8797[/C][C]0.19023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158687&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158687&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
10.95370311.44440
2-0.11757-1.41080.080225
30.0542330.65080.258109
40.0237560.28510.387999
50.1158221.38990.083357
60.0443680.53240.297631
70.0380340.45640.324392
80.0996221.19550.116935
90.2040962.44910.00776
100.0639090.76690.222195
110.1060351.27240.102636
12-0.042466-0.50960.305558
13-0.48543-5.82520
14-0.03435-0.41220.340402
150.0422250.50670.306572
16-0.044197-0.53040.298337
170.0276080.33130.370452
180.0371480.44580.328215
190.0416380.49970.309038
200.01440.17280.431526
210.0733120.87970.19023



Parameters (Session):
par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 0.0 ; 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')