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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 computationSun, 26 Dec 2010 14:57:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293375310znwe191xmytnovm.htm/, Retrieved Mon, 06 May 2024 19:35:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115635, Retrieved Mon, 06 May 2024 19:35:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [tijdreeks bevolki...] [2010-12-26 10:20:42] [efd13e24149aec704f3383e33c1e842a]
-   PD  [Univariate Data Series] [tijdreeks werkloo...] [2010-12-26 13:12:25] [efd13e24149aec704f3383e33c1e842a]
- RMPD      [(Partial) Autocorrelation Function] [tijdreeks werkloo...] [2010-12-26 14:57:34] [531024149246456e4f6d79ace2e85c12] [Current]
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Dataseries X:
332
369
384
373
378
426
423
397
422
409
430
412
470
491
504
484
474
508
492
452
457
457
471
451
493
514
522
490
484
506
501
462
465
454
464
427
460
473
465
422
415
413
420
363
376
380
384
346
389
407
393
346
348
353
364
305
307
312
312
286
324
336
327
302
299
311
315
264
278
278
287
279
324
354
354
360
363
385
412
370
389
395
417
404
456
478
468
437
432
441
449
386
396
394




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115635&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115635&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115635&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'George Udny Yule' @ 72.249.76.132







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9214038.93330
20.8656318.39260
30.8346348.09210
40.8200287.95050
50.735467.13050
60.6748196.54260
70.6522696.3240
80.6420126.22450
90.572955.5550
100.52095.05031e-06
110.495594.80493e-06
120.4809924.66345e-06
130.3682723.57050.000282
140.2788562.70360.004071
150.2239172.1710.016227
160.1897591.83980.034478
170.1000890.97040.167169
180.0369540.35830.360468
190.0097590.09460.462411

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921403 & 8.9333 & 0 \tabularnewline
2 & 0.865631 & 8.3926 & 0 \tabularnewline
3 & 0.834634 & 8.0921 & 0 \tabularnewline
4 & 0.820028 & 7.9505 & 0 \tabularnewline
5 & 0.73546 & 7.1305 & 0 \tabularnewline
6 & 0.674819 & 6.5426 & 0 \tabularnewline
7 & 0.652269 & 6.324 & 0 \tabularnewline
8 & 0.642012 & 6.2245 & 0 \tabularnewline
9 & 0.57295 & 5.555 & 0 \tabularnewline
10 & 0.5209 & 5.0503 & 1e-06 \tabularnewline
11 & 0.49559 & 4.8049 & 3e-06 \tabularnewline
12 & 0.480992 & 4.6634 & 5e-06 \tabularnewline
13 & 0.368272 & 3.5705 & 0.000282 \tabularnewline
14 & 0.278856 & 2.7036 & 0.004071 \tabularnewline
15 & 0.223917 & 2.171 & 0.016227 \tabularnewline
16 & 0.189759 & 1.8398 & 0.034478 \tabularnewline
17 & 0.100089 & 0.9704 & 0.167169 \tabularnewline
18 & 0.036954 & 0.3583 & 0.360468 \tabularnewline
19 & 0.009759 & 0.0946 & 0.462411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115635&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]0.921403[/C][C]8.9333[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.865631[/C][C]8.3926[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.834634[/C][C]8.0921[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.820028[/C][C]7.9505[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.73546[/C][C]7.1305[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.674819[/C][C]6.5426[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.652269[/C][C]6.324[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.642012[/C][C]6.2245[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.57295[/C][C]5.555[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.5209[/C][C]5.0503[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.49559[/C][C]4.8049[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.480992[/C][C]4.6634[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]0.368272[/C][C]3.5705[/C][C]0.000282[/C][/ROW]
[ROW][C]14[/C][C]0.278856[/C][C]2.7036[/C][C]0.004071[/C][/ROW]
[ROW][C]15[/C][C]0.223917[/C][C]2.171[/C][C]0.016227[/C][/ROW]
[ROW][C]16[/C][C]0.189759[/C][C]1.8398[/C][C]0.034478[/C][/ROW]
[ROW][C]17[/C][C]0.100089[/C][C]0.9704[/C][C]0.167169[/C][/ROW]
[ROW][C]18[/C][C]0.036954[/C][C]0.3583[/C][C]0.360468[/C][/ROW]
[ROW][C]19[/C][C]0.009759[/C][C]0.0946[/C][C]0.462411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115635&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115635&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
10.9214038.93330
20.8656318.39260
30.8346348.09210
40.8200287.95050
50.735467.13050
60.6748196.54260
70.6522696.3240
80.6420126.22450
90.572955.5550
100.52095.05031e-06
110.495594.80493e-06
120.4809924.66345e-06
130.3682723.57050.000282
140.2788562.70360.004071
150.2239172.1710.016227
160.1897591.83980.034478
170.1000890.97040.167169
180.0369540.35830.360468
190.0097590.09460.462411







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9214038.93330
20.1102391.06880.143948
30.1567911.52010.065915
40.1482541.43740.076966
5-0.420945-4.08124.7e-05
60.0426340.41330.340147
70.179351.73890.042666
80.0771080.74760.228286
9-0.187901-1.82180.035835
10-0.023107-0.2240.41161
11-0.011896-0.11530.454212
120.0453270.43950.330667
13-0.528048-5.11961e-06
14-0.08913-0.86420.194852
150.0578840.56120.287997
160.0915520.88760.188504
170.0555930.5390.295582
18-0.018379-0.17820.429477
19-0.051159-0.4960.310525

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921403 & 8.9333 & 0 \tabularnewline
2 & 0.110239 & 1.0688 & 0.143948 \tabularnewline
3 & 0.156791 & 1.5201 & 0.065915 \tabularnewline
4 & 0.148254 & 1.4374 & 0.076966 \tabularnewline
5 & -0.420945 & -4.0812 & 4.7e-05 \tabularnewline
6 & 0.042634 & 0.4133 & 0.340147 \tabularnewline
7 & 0.17935 & 1.7389 & 0.042666 \tabularnewline
8 & 0.077108 & 0.7476 & 0.228286 \tabularnewline
9 & -0.187901 & -1.8218 & 0.035835 \tabularnewline
10 & -0.023107 & -0.224 & 0.41161 \tabularnewline
11 & -0.011896 & -0.1153 & 0.454212 \tabularnewline
12 & 0.045327 & 0.4395 & 0.330667 \tabularnewline
13 & -0.528048 & -5.1196 & 1e-06 \tabularnewline
14 & -0.08913 & -0.8642 & 0.194852 \tabularnewline
15 & 0.057884 & 0.5612 & 0.287997 \tabularnewline
16 & 0.091552 & 0.8876 & 0.188504 \tabularnewline
17 & 0.055593 & 0.539 & 0.295582 \tabularnewline
18 & -0.018379 & -0.1782 & 0.429477 \tabularnewline
19 & -0.051159 & -0.496 & 0.310525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115635&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]0.921403[/C][C]8.9333[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.110239[/C][C]1.0688[/C][C]0.143948[/C][/ROW]
[ROW][C]3[/C][C]0.156791[/C][C]1.5201[/C][C]0.065915[/C][/ROW]
[ROW][C]4[/C][C]0.148254[/C][C]1.4374[/C][C]0.076966[/C][/ROW]
[ROW][C]5[/C][C]-0.420945[/C][C]-4.0812[/C][C]4.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.042634[/C][C]0.4133[/C][C]0.340147[/C][/ROW]
[ROW][C]7[/C][C]0.17935[/C][C]1.7389[/C][C]0.042666[/C][/ROW]
[ROW][C]8[/C][C]0.077108[/C][C]0.7476[/C][C]0.228286[/C][/ROW]
[ROW][C]9[/C][C]-0.187901[/C][C]-1.8218[/C][C]0.035835[/C][/ROW]
[ROW][C]10[/C][C]-0.023107[/C][C]-0.224[/C][C]0.41161[/C][/ROW]
[ROW][C]11[/C][C]-0.011896[/C][C]-0.1153[/C][C]0.454212[/C][/ROW]
[ROW][C]12[/C][C]0.045327[/C][C]0.4395[/C][C]0.330667[/C][/ROW]
[ROW][C]13[/C][C]-0.528048[/C][C]-5.1196[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.08913[/C][C]-0.8642[/C][C]0.194852[/C][/ROW]
[ROW][C]15[/C][C]0.057884[/C][C]0.5612[/C][C]0.287997[/C][/ROW]
[ROW][C]16[/C][C]0.091552[/C][C]0.8876[/C][C]0.188504[/C][/ROW]
[ROW][C]17[/C][C]0.055593[/C][C]0.539[/C][C]0.295582[/C][/ROW]
[ROW][C]18[/C][C]-0.018379[/C][C]-0.1782[/C][C]0.429477[/C][/ROW]
[ROW][C]19[/C][C]-0.051159[/C][C]-0.496[/C][C]0.310525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115635&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115635&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
10.9214038.93330
20.1102391.06880.143948
30.1567911.52010.065915
40.1482541.43740.076966
5-0.420945-4.08124.7e-05
60.0426340.41330.340147
70.179351.73890.042666
80.0771080.74760.228286
9-0.187901-1.82180.035835
10-0.023107-0.2240.41161
11-0.011896-0.11530.454212
120.0453270.43950.330667
13-0.528048-5.11961e-06
14-0.08913-0.86420.194852
150.0578840.56120.287997
160.0915520.88760.188504
170.0555930.5390.295582
18-0.018379-0.17820.429477
19-0.051159-0.4960.310525



Parameters (Session):
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')