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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 22:39:10 +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/t1293403074fqm54hldpuyllbo.htm/, Retrieved Mon, 06 May 2024 22:06:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115828, Retrieved Mon, 06 May 2024 22:06:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Structural Time Series Models] [] [2010-12-10 13:52:35] [4b03f5b90919097e9115dc18d7ad0ba1]
- RMP       [(Partial) Autocorrelation Function] [] [2010-12-26 22:39:10] [fb9ffa4287a61b751ec239f90a6328c7] [Current]
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Dataseries X:
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
259.9
266
320.6
308.5
282.2
262.7
263.5
313.1
284.3
252.6
250.3
246.5
312.7
333.2
446.4
511.6
515.5
506.4
483.2
522.3
509.8
460.7
405.8
375
378.5
406.8
467.8
469.8
429.8
355.8
332.7
378
360.5
334.7
319.5
323.1
363.6
352.1
411.9
388.6
416.4
360.7
338
417.2
388.4
371.1
331.5
353.7
396.7
447
533.5
565.4
542.3
488.7
467.1
531.3
496.1
444
403.4
386.3
394.1
404.1
462.1
448.1
432.3
386.3
395.2
421.9
382.9
384.2
345.5
323.4
372.6
376
462.7
487
444.2
399.3
394.9
455.4
414
375.5
347
339.4
385.8
378.8
451.8
446.1
422.5
383.1
352.8
445.3
367.5
355.1
326.2
319.8
331.8
340.9
394.1
417.2
369.9
349.2
321.4
405.7
342.9
316.5
284.2
270.9
288.8
278.8
324.4
310.9
299
273
279.3
359.2
305
282.1
250.3
246.5
257.9
266.5
315.9
318.4
295.4
266.4
245.8
362.8
324.9
294.2
289.5
295.2
290.3
272
307.4
328.7
292.9
249.1
230.4
361.5
321.7
277.2
260.7
251
257.6
241.8
287.5
292.3
274.7
254.2
230
339
318.2
287
295.8
284
271
262.7
340.6
379.4
373.3
355.2
338.4
466.9
451
422
429.2
425.9
460.7
463.6
541.4
544.2
517.5
469.4
439.4
549
533
506.1
484
457
481.5
469.5
544.7
541.2
521.5
469.7
434.4
542.6
517.3
485.7
465.8
447
426.6
411.6
467.5
484.5
451.2
417.4
379.9
484.7
455
420.8
416.5
376.3
405.6
405.8
500.8
514
475.5
430.1
414.4
538
526
488.5
520.2
504.4
568.5
610.6
818
830.9
835.9
782
762.3
856.9
820.9
769.6
752.2
724.4
723.1
719.5
817.4
803.3
752.5
689
630.4
765.5
757.7
732.2
702.6
683.3
709.5
702.2
784.8
810.9
755.6
656.8
615.1
745.3
694.1
675.7
643.7
622.1
634.6
588
689.7
673.9
647.9
568.8
545.7
632.6
643.8
593.1
579.7
546
562.9
572.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115828&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115828&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' @ 72.249.127.135







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95646918.44770
20.91206517.59130
30.87738416.92240
40.8614416.61490
50.85101116.41370
60.82017315.81890
70.79878615.40640
80.76029814.66410
90.73019114.08340
100.71951313.87750
110.72369113.95810
120.72797714.04070
130.67541413.02690
140.62508912.05630
150.58990311.37760
160.57672911.12350
170.57407211.07230
180.55541410.71240
190.54837410.57670
200.52446510.11550
210.5091849.82080
220.5132769.89970
230.52890110.20110
240.54631810.5370
250.5083149.8040

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956469 & 18.4477 & 0 \tabularnewline
2 & 0.912065 & 17.5913 & 0 \tabularnewline
3 & 0.877384 & 16.9224 & 0 \tabularnewline
4 & 0.86144 & 16.6149 & 0 \tabularnewline
5 & 0.851011 & 16.4137 & 0 \tabularnewline
6 & 0.820173 & 15.8189 & 0 \tabularnewline
7 & 0.798786 & 15.4064 & 0 \tabularnewline
8 & 0.760298 & 14.6641 & 0 \tabularnewline
9 & 0.730191 & 14.0834 & 0 \tabularnewline
10 & 0.719513 & 13.8775 & 0 \tabularnewline
11 & 0.723691 & 13.9581 & 0 \tabularnewline
12 & 0.727977 & 14.0407 & 0 \tabularnewline
13 & 0.675414 & 13.0269 & 0 \tabularnewline
14 & 0.625089 & 12.0563 & 0 \tabularnewline
15 & 0.589903 & 11.3776 & 0 \tabularnewline
16 & 0.576729 & 11.1235 & 0 \tabularnewline
17 & 0.574072 & 11.0723 & 0 \tabularnewline
18 & 0.555414 & 10.7124 & 0 \tabularnewline
19 & 0.548374 & 10.5767 & 0 \tabularnewline
20 & 0.524465 & 10.1155 & 0 \tabularnewline
21 & 0.509184 & 9.8208 & 0 \tabularnewline
22 & 0.513276 & 9.8997 & 0 \tabularnewline
23 & 0.528901 & 10.2011 & 0 \tabularnewline
24 & 0.546318 & 10.537 & 0 \tabularnewline
25 & 0.508314 & 9.804 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115828&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]0.956469[/C][C]18.4477[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.912065[/C][C]17.5913[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.877384[/C][C]16.9224[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.86144[/C][C]16.6149[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.851011[/C][C]16.4137[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.820173[/C][C]15.8189[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.798786[/C][C]15.4064[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.760298[/C][C]14.6641[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.730191[/C][C]14.0834[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.719513[/C][C]13.8775[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.723691[/C][C]13.9581[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.727977[/C][C]14.0407[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.675414[/C][C]13.0269[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.625089[/C][C]12.0563[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.589903[/C][C]11.3776[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.576729[/C][C]11.1235[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.574072[/C][C]11.0723[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.555414[/C][C]10.7124[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.548374[/C][C]10.5767[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.524465[/C][C]10.1155[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.509184[/C][C]9.8208[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.513276[/C][C]9.8997[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.528901[/C][C]10.2011[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.546318[/C][C]10.537[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.508314[/C][C]9.804[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115828&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
10.95646918.44770
20.91206517.59130
30.87738416.92240
40.8614416.61490
50.85101116.41370
60.82017315.81890
70.79878615.40640
80.76029814.66410
90.73019114.08340
100.71951313.87750
110.72369113.95810
120.72797714.04070
130.67541413.02690
140.62508912.05630
150.58990311.37760
160.57672911.12350
170.57407211.07230
180.55541410.71240
190.54837410.57670
200.52446510.11550
210.5091849.82080
220.5132769.89970
230.52890110.20110
240.54631810.5370
250.5083149.8040







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95646918.44770
2-0.032497-0.62680.265592
30.0911711.75840.039747
40.200723.87136.4e-05
50.0695611.34160.090265
6-0.209037-4.03183.4e-05
70.1668573.21820.000702
8-0.254774-4.91391e-06
90.0483560.93270.175803
100.2322084.47875e-06
110.1668253.21760.000703
12-0.034933-0.67380.250442
13-0.556401-10.73150
140.0447460.8630.194337
150.1402232.70450.003577
160.0809851.5620.05957
170.1502622.89820.001988
180.0537431.03660.150306
190.1052052.02910.021579
20-0.072138-1.39140.082475
210.002760.05320.47879
220.0629611.21430.112692
23-0.032876-0.63410.263205
240.0655851.2650.10334
25-0.266582-5.14170

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956469 & 18.4477 & 0 \tabularnewline
2 & -0.032497 & -0.6268 & 0.265592 \tabularnewline
3 & 0.091171 & 1.7584 & 0.039747 \tabularnewline
4 & 0.20072 & 3.8713 & 6.4e-05 \tabularnewline
5 & 0.069561 & 1.3416 & 0.090265 \tabularnewline
6 & -0.209037 & -4.0318 & 3.4e-05 \tabularnewline
7 & 0.166857 & 3.2182 & 0.000702 \tabularnewline
8 & -0.254774 & -4.9139 & 1e-06 \tabularnewline
9 & 0.048356 & 0.9327 & 0.175803 \tabularnewline
10 & 0.232208 & 4.4787 & 5e-06 \tabularnewline
11 & 0.166825 & 3.2176 & 0.000703 \tabularnewline
12 & -0.034933 & -0.6738 & 0.250442 \tabularnewline
13 & -0.556401 & -10.7315 & 0 \tabularnewline
14 & 0.044746 & 0.863 & 0.194337 \tabularnewline
15 & 0.140223 & 2.7045 & 0.003577 \tabularnewline
16 & 0.080985 & 1.562 & 0.05957 \tabularnewline
17 & 0.150262 & 2.8982 & 0.001988 \tabularnewline
18 & 0.053743 & 1.0366 & 0.150306 \tabularnewline
19 & 0.105205 & 2.0291 & 0.021579 \tabularnewline
20 & -0.072138 & -1.3914 & 0.082475 \tabularnewline
21 & 0.00276 & 0.0532 & 0.47879 \tabularnewline
22 & 0.062961 & 1.2143 & 0.112692 \tabularnewline
23 & -0.032876 & -0.6341 & 0.263205 \tabularnewline
24 & 0.065585 & 1.265 & 0.10334 \tabularnewline
25 & -0.266582 & -5.1417 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115828&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]0.956469[/C][C]18.4477[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.032497[/C][C]-0.6268[/C][C]0.265592[/C][/ROW]
[ROW][C]3[/C][C]0.091171[/C][C]1.7584[/C][C]0.039747[/C][/ROW]
[ROW][C]4[/C][C]0.20072[/C][C]3.8713[/C][C]6.4e-05[/C][/ROW]
[ROW][C]5[/C][C]0.069561[/C][C]1.3416[/C][C]0.090265[/C][/ROW]
[ROW][C]6[/C][C]-0.209037[/C][C]-4.0318[/C][C]3.4e-05[/C][/ROW]
[ROW][C]7[/C][C]0.166857[/C][C]3.2182[/C][C]0.000702[/C][/ROW]
[ROW][C]8[/C][C]-0.254774[/C][C]-4.9139[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.048356[/C][C]0.9327[/C][C]0.175803[/C][/ROW]
[ROW][C]10[/C][C]0.232208[/C][C]4.4787[/C][C]5e-06[/C][/ROW]
[ROW][C]11[/C][C]0.166825[/C][C]3.2176[/C][C]0.000703[/C][/ROW]
[ROW][C]12[/C][C]-0.034933[/C][C]-0.6738[/C][C]0.250442[/C][/ROW]
[ROW][C]13[/C][C]-0.556401[/C][C]-10.7315[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.044746[/C][C]0.863[/C][C]0.194337[/C][/ROW]
[ROW][C]15[/C][C]0.140223[/C][C]2.7045[/C][C]0.003577[/C][/ROW]
[ROW][C]16[/C][C]0.080985[/C][C]1.562[/C][C]0.05957[/C][/ROW]
[ROW][C]17[/C][C]0.150262[/C][C]2.8982[/C][C]0.001988[/C][/ROW]
[ROW][C]18[/C][C]0.053743[/C][C]1.0366[/C][C]0.150306[/C][/ROW]
[ROW][C]19[/C][C]0.105205[/C][C]2.0291[/C][C]0.021579[/C][/ROW]
[ROW][C]20[/C][C]-0.072138[/C][C]-1.3914[/C][C]0.082475[/C][/ROW]
[ROW][C]21[/C][C]0.00276[/C][C]0.0532[/C][C]0.47879[/C][/ROW]
[ROW][C]22[/C][C]0.062961[/C][C]1.2143[/C][C]0.112692[/C][/ROW]
[ROW][C]23[/C][C]-0.032876[/C][C]-0.6341[/C][C]0.263205[/C][/ROW]
[ROW][C]24[/C][C]0.065585[/C][C]1.265[/C][C]0.10334[/C][/ROW]
[ROW][C]25[/C][C]-0.266582[/C][C]-5.1417[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115828&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
10.95646918.44770
2-0.032497-0.62680.265592
30.0911711.75840.039747
40.200723.87136.4e-05
50.0695611.34160.090265
6-0.209037-4.03183.4e-05
70.1668573.21820.000702
8-0.254774-4.91391e-06
90.0483560.93270.175803
100.2322084.47875e-06
110.1668253.21760.000703
12-0.034933-0.67380.250442
13-0.556401-10.73150
140.0447460.8630.194337
150.1402232.70450.003577
160.0809851.5620.05957
170.1502622.89820.001988
180.0537431.03660.150306
190.1052052.02910.021579
20-0.072138-1.39140.082475
210.002760.05320.47879
220.0629611.21430.112692
23-0.032876-0.63410.263205
240.0655851.2650.10334
25-0.266582-5.14170



Parameters (Session):
par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 0.5 ; 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')