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rwasp_autocorrelation.wasp

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(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 06:28:22 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t12287429563cr9qwhamssd1al.htm/, Retrieved Thu, 16 May 2024 23:03:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30475, Retrieved Thu, 16 May 2024 23:03:05 +0000

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User-defined keywords

(P)ACF

Estimated Impact

184

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]
F RMP   [(Partial) Autocorrelation Function] [ARMA processing Q2] [2008-12-08 12:50:33] [c96f3dce3a823a83b6ede18389e1cfd4]
F   P     [(Partial) Autocorrelation Function] [ARMa processing Q2] [2008-12-08 12:56:23] [c96f3dce3a823a83b6ede18389e1cfd4]
F   P       [(Partial) Autocorrelation Function] [ARMA processing Q2] [2008-12-08 13:01:17] [c96f3dce3a823a83b6ede18389e1cfd4]
F   P           [(Partial) Autocorrelation Function] [ARMAprocessing Q4] [2008-12-08 13:28:22] [3bdbbe597ac6c61989658933956ee6ac] [Current]
F RMP             [Spectral Analysis] [ARMA processing Q4] [2008-12-08 13:32:19] [c96f3dce3a823a83b6ede18389e1cfd4] 
F RMP               [ARIMA Backward Selection] [ARMA processing Q5] [2008-12-08 13:36:59] [c96f3dce3a823a83b6ede18389e1cfd4] 
F   PD            [(Partial) Autocorrelation Function] [ARMA processing Q...] [2008-12-09 09:20:47] [c96f3dce3a823a83b6ede18389e1cfd4] 

Feedback Forum

2008-12-14 11:14:00 [Gert-Jan Geudens] [reply] 
Het antwoord is correct, we moeten  bepalen of er een AM en/of AR proces aanwezig is. Er is hier –zoals door de student reeds beschreven- inderdaad een AR-proces aanwezig. Een AR-proces kunnen we afleiden uit de autocorrelatie. We herkennen hier duidelijk het typische patroon voor een AR-proces. Om parameter p te bepalen moeten we naar het aantal significante coëfficiënten in de partiële autocorrelatie kijken. We concluderen dat de eerste 3 significant zijn. Over de derde zijn we echter niet helemaal zeker maar we nemen er voor alle zekerheid 1 bij. We kunnen deze steeds –indien nodig- verwijderen. Voorlopig hebben we dus volgende parameters gevonden : lambda =0.5, d=1, D=1, p=3. 
In de autocorrelatie is er geen sprake van seizonaliteit en dus is de parameter P gelijk aan 0. 
Om te bepalen of er een MA-proces aanwezig is moeten we het theorethisch model vergelijken met de door ons gevonden partiële autocorrelatie. We kunnen hier duidelijk geen MA-proces afleiden. q is dus gelijk 0.  Er is wel sprake van seizonaliteit in de partiële autocorrelatie. Om Q te bepalen moeten we naar de significante autocorrelatiecoëfficiënten. In dit geval er slechts één en dus is Q gelijk aan 1. 
De gevonden parameters zijn dus d=1, D=1, p=3, P=0, q=0, Q=1. 
 
Theorie : 
 
(1-phi1B- phi2B^2- phi3B^3-…-phipB^p) (1- hoodletter phi1B12- hoodletter phi2B12^2-hoodletter phi3B12^3-…-PPB12^P) nabla nabla12 yt^lambda = (1-thèta1B-thèta2B^2-thèta3B^3-…-thètaqB^q)(1-hoofdletter thèta1B12-hoofdletter thèta2B12^2-hoodletter thèta3B12^3-…- hoofdletter thètaQB12^Q)et 
 
p = kleine letter p , q = kleine letter q 
P = hoofdletter P ,  Q = hoofdletter Q 
 
Het vermoedelijke model is dus : (1-phi1B- phi2B^2- phi3B^3) nabla nabla12 yt^0.5 = (1-hoofdletter thèta1B12)et 
2008-12-14 11:15:57 [Gert-Jan Geudens] [reply] 
We willen aan onze vorige feedback nog even toevoegen dat we hier blijkbaar een verkeerde weergave krijgen van sommige letters. Onze excuses hiervoor.

Post a new message

Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=30475&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=30475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30475&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.317794	6.0213	0
3	0.179563	3.4022	0.000372
4	0.155303	2.9426	0.001733
5	0.127596	2.4176	0.008061
6	0.06371	1.2071	0.114087
7	-0.054701	-1.0364	0.150347
8	-0.011735	-0.2224	0.412083
9	-0.080833	-1.5316	0.063255
10	-0.174708	-3.3102	0.000513
11	-0.055263	-1.0471	0.147883
12	-0.480698	-9.1079	0
13	-0.168514	-3.1929	0.000767
14	-0.172913	-3.2762	0.000577
15	-0.128287	-2.4307	0.007779
16	-0.163167	-3.0916	0.001073
17	-0.121097	-2.2945	0.01117
18	-0.103099	-1.9534	0.025772
19	0.020128	0.3814	0.351578
20	-0.002775	-0.0526	0.479049
21	-0.006426	-0.1217	0.451583
22	-0.006358	-0.1205	0.45209
23	-0.004364	-0.0827	0.467075
24	-0.006343	-0.1202	0.452205
25	0.094911	1.7983	0.036484
26	-0.008505	-0.1611	0.436036
27	0.017661	0.3346	0.369052
28	0.077035	1.4596	0.072638
29	0.068023	1.2888	0.09914
30	0.041632	0.7888	0.215369
31	0.032895	0.6233	0.266752
32	-0.068171	-1.2917	0.098653
33	0.011323	0.2145	0.415122
34	0.002674	0.0507	0.479811
35	-0.0721	-1.3661	0.08638
36	-0.031172	-0.5906	0.277571
37	-0.113841	-2.157	0.015835
38	-0.00152	-0.0288	0.488517
39	-0.046567	-0.8823	0.189098
40	-0.067976	-1.288	0.099295
41	-0.105451	-1.998	0.023234
42	-0.033256	-0.6301	0.264511
43	-0.158298	-2.9993	0.001447
44	0.01837	0.3481	0.364001
45	-0.043872	-0.8313	0.203191
46	0.021162	0.401	0.34434
47	0.042179	0.7992	0.21236
48	0.097675	1.8507	0.032519
49	0.125528	2.3784	0.008955
50	0.090564	1.7159	0.043518
51	0.082527	1.5637	0.059388
52	0.128164	2.4284	0.007829
53	0.160308	3.0374	0.00128
54	0.042213	0.7998	0.212173
55	0.160649	3.0439	0.001254
56	0.042494	0.8052	0.210633
57	0.055698	1.0553	0.145992
58	0.043943	0.8326	0.202814
59	0.043887	0.8315	0.203111
60	-0.02979	-0.5644	0.286401

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.187552 & 3.5536 & 0.000215 \tabularnewline
2 & 0.317794 & 6.0213 & 0 \tabularnewline
3 & 0.179563 & 3.4022 & 0.000372 \tabularnewline
4 & 0.155303 & 2.9426 & 0.001733 \tabularnewline
5 & 0.127596 & 2.4176 & 0.008061 \tabularnewline
6 & 0.06371 & 1.2071 & 0.114087 \tabularnewline
7 & -0.054701 & -1.0364 & 0.150347 \tabularnewline
8 & -0.011735 & -0.2224 & 0.412083 \tabularnewline
9 & -0.080833 & -1.5316 & 0.063255 \tabularnewline
10 & -0.174708 & -3.3102 & 0.000513 \tabularnewline
11 & -0.055263 & -1.0471 & 0.147883 \tabularnewline
12 & -0.480698 & -9.1079 & 0 \tabularnewline
13 & -0.168514 & -3.1929 & 0.000767 \tabularnewline
14 & -0.172913 & -3.2762 & 0.000577 \tabularnewline
15 & -0.128287 & -2.4307 & 0.007779 \tabularnewline
16 & -0.163167 & -3.0916 & 0.001073 \tabularnewline
17 & -0.121097 & -2.2945 & 0.01117 \tabularnewline
18 & -0.103099 & -1.9534 & 0.025772 \tabularnewline
19 & 0.020128 & 0.3814 & 0.351578 \tabularnewline
20 & -0.002775 & -0.0526 & 0.479049 \tabularnewline
21 & -0.006426 & -0.1217 & 0.451583 \tabularnewline
22 & -0.006358 & -0.1205 & 0.45209 \tabularnewline
23 & -0.004364 & -0.0827 & 0.467075 \tabularnewline
24 & -0.006343 & -0.1202 & 0.452205 \tabularnewline
25 & 0.094911 & 1.7983 & 0.036484 \tabularnewline
26 & -0.008505 & -0.1611 & 0.436036 \tabularnewline
27 & 0.017661 & 0.3346 & 0.369052 \tabularnewline
28 & 0.077035 & 1.4596 & 0.072638 \tabularnewline
29 & 0.068023 & 1.2888 & 0.09914 \tabularnewline
30 & 0.041632 & 0.7888 & 0.215369 \tabularnewline
31 & 0.032895 & 0.6233 & 0.266752 \tabularnewline
32 & -0.068171 & -1.2917 & 0.098653 \tabularnewline
33 & 0.011323 & 0.2145 & 0.415122 \tabularnewline
34 & 0.002674 & 0.0507 & 0.479811 \tabularnewline
35 & -0.0721 & -1.3661 & 0.08638 \tabularnewline
36 & -0.031172 & -0.5906 & 0.277571 \tabularnewline
37 & -0.113841 & -2.157 & 0.015835 \tabularnewline
38 & -0.00152 & -0.0288 & 0.488517 \tabularnewline
39 & -0.046567 & -0.8823 & 0.189098 \tabularnewline
40 & -0.067976 & -1.288 & 0.099295 \tabularnewline
41 & -0.105451 & -1.998 & 0.023234 \tabularnewline
42 & -0.033256 & -0.6301 & 0.264511 \tabularnewline
43 & -0.158298 & -2.9993 & 0.001447 \tabularnewline
44 & 0.01837 & 0.3481 & 0.364001 \tabularnewline
45 & -0.043872 & -0.8313 & 0.203191 \tabularnewline
46 & 0.021162 & 0.401 & 0.34434 \tabularnewline
47 & 0.042179 & 0.7992 & 0.21236 \tabularnewline
48 & 0.097675 & 1.8507 & 0.032519 \tabularnewline
49 & 0.125528 & 2.3784 & 0.008955 \tabularnewline
50 & 0.090564 & 1.7159 & 0.043518 \tabularnewline
51 & 0.082527 & 1.5637 & 0.059388 \tabularnewline
52 & 0.128164 & 2.4284 & 0.007829 \tabularnewline
53 & 0.160308 & 3.0374 & 0.00128 \tabularnewline
54 & 0.042213 & 0.7998 & 0.212173 \tabularnewline
55 & 0.160649 & 3.0439 & 0.001254 \tabularnewline
56 & 0.042494 & 0.8052 & 0.210633 \tabularnewline
57 & 0.055698 & 1.0553 & 0.145992 \tabularnewline
58 & 0.043943 & 0.8326 & 0.202814 \tabularnewline
59 & 0.043887 & 0.8315 & 0.203111 \tabularnewline
60 & -0.02979 & -0.5644 & 0.286401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30475&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]0.187552[/C][C]3.5536[/C][C]0.000215[/C][/ROW]
[ROW][C]2[/C][C]0.317794[/C][C]6.0213[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.179563[/C][C]3.4022[/C][C]0.000372[/C][/ROW]
[ROW][C]4[/C][C]0.155303[/C][C]2.9426[/C][C]0.001733[/C][/ROW]
[ROW][C]5[/C][C]0.127596[/C][C]2.4176[/C][C]0.008061[/C][/ROW]
[ROW][C]6[/C][C]0.06371[/C][C]1.2071[/C][C]0.114087[/C][/ROW]
[ROW][C]7[/C][C]-0.054701[/C][C]-1.0364[/C][C]0.150347[/C][/ROW]
[ROW][C]8[/C][C]-0.011735[/C][C]-0.2224[/C][C]0.412083[/C][/ROW]
[ROW][C]9[/C][C]-0.080833[/C][C]-1.5316[/C][C]0.063255[/C][/ROW]
[ROW][C]10[/C][C]-0.174708[/C][C]-3.3102[/C][C]0.000513[/C][/ROW]
[ROW][C]11[/C][C]-0.055263[/C][C]-1.0471[/C][C]0.147883[/C][/ROW]
[ROW][C]12[/C][C]-0.480698[/C][C]-9.1079[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.168514[/C][C]-3.1929[/C][C]0.000767[/C][/ROW]
[ROW][C]14[/C][C]-0.172913[/C][C]-3.2762[/C][C]0.000577[/C][/ROW]
[ROW][C]15[/C][C]-0.128287[/C][C]-2.4307[/C][C]0.007779[/C][/ROW]
[ROW][C]16[/C][C]-0.163167[/C][C]-3.0916[/C][C]0.001073[/C][/ROW]
[ROW][C]17[/C][C]-0.121097[/C][C]-2.2945[/C][C]0.01117[/C][/ROW]
[ROW][C]18[/C][C]-0.103099[/C][C]-1.9534[/C][C]0.025772[/C][/ROW]
[ROW][C]19[/C][C]0.020128[/C][C]0.3814[/C][C]0.351578[/C][/ROW]
[ROW][C]20[/C][C]-0.002775[/C][C]-0.0526[/C][C]0.479049[/C][/ROW]
[ROW][C]21[/C][C]-0.006426[/C][C]-0.1217[/C][C]0.451583[/C][/ROW]
[ROW][C]22[/C][C]-0.006358[/C][C]-0.1205[/C][C]0.45209[/C][/ROW]
[ROW][C]23[/C][C]-0.004364[/C][C]-0.0827[/C][C]0.467075[/C][/ROW]
[ROW][C]24[/C][C]-0.006343[/C][C]-0.1202[/C][C]0.452205[/C][/ROW]
[ROW][C]25[/C][C]0.094911[/C][C]1.7983[/C][C]0.036484[/C][/ROW]
[ROW][C]26[/C][C]-0.008505[/C][C]-0.1611[/C][C]0.436036[/C][/ROW]
[ROW][C]27[/C][C]0.017661[/C][C]0.3346[/C][C]0.369052[/C][/ROW]
[ROW][C]28[/C][C]0.077035[/C][C]1.4596[/C][C]0.072638[/C][/ROW]
[ROW][C]29[/C][C]0.068023[/C][C]1.2888[/C][C]0.09914[/C][/ROW]
[ROW][C]30[/C][C]0.041632[/C][C]0.7888[/C][C]0.215369[/C][/ROW]
[ROW][C]31[/C][C]0.032895[/C][C]0.6233[/C][C]0.266752[/C][/ROW]
[ROW][C]32[/C][C]-0.068171[/C][C]-1.2917[/C][C]0.098653[/C][/ROW]
[ROW][C]33[/C][C]0.011323[/C][C]0.2145[/C][C]0.415122[/C][/ROW]
[ROW][C]34[/C][C]0.002674[/C][C]0.0507[/C][C]0.479811[/C][/ROW]
[ROW][C]35[/C][C]-0.0721[/C][C]-1.3661[/C][C]0.08638[/C][/ROW]
[ROW][C]36[/C][C]-0.031172[/C][C]-0.5906[/C][C]0.277571[/C][/ROW]
[ROW][C]37[/C][C]-0.113841[/C][C]-2.157[/C][C]0.015835[/C][/ROW]
[ROW][C]38[/C][C]-0.00152[/C][C]-0.0288[/C][C]0.488517[/C][/ROW]
[ROW][C]39[/C][C]-0.046567[/C][C]-0.8823[/C][C]0.189098[/C][/ROW]
[ROW][C]40[/C][C]-0.067976[/C][C]-1.288[/C][C]0.099295[/C][/ROW]
[ROW][C]41[/C][C]-0.105451[/C][C]-1.998[/C][C]0.023234[/C][/ROW]
[ROW][C]42[/C][C]-0.033256[/C][C]-0.6301[/C][C]0.264511[/C][/ROW]
[ROW][C]43[/C][C]-0.158298[/C][C]-2.9993[/C][C]0.001447[/C][/ROW]
[ROW][C]44[/C][C]0.01837[/C][C]0.3481[/C][C]0.364001[/C][/ROW]
[ROW][C]45[/C][C]-0.043872[/C][C]-0.8313[/C][C]0.203191[/C][/ROW]
[ROW][C]46[/C][C]0.021162[/C][C]0.401[/C][C]0.34434[/C][/ROW]
[ROW][C]47[/C][C]0.042179[/C][C]0.7992[/C][C]0.21236[/C][/ROW]
[ROW][C]48[/C][C]0.097675[/C][C]1.8507[/C][C]0.032519[/C][/ROW]
[ROW][C]49[/C][C]0.125528[/C][C]2.3784[/C][C]0.008955[/C][/ROW]
[ROW][C]50[/C][C]0.090564[/C][C]1.7159[/C][C]0.043518[/C][/ROW]
[ROW][C]51[/C][C]0.082527[/C][C]1.5637[/C][C]0.059388[/C][/ROW]
[ROW][C]52[/C][C]0.128164[/C][C]2.4284[/C][C]0.007829[/C][/ROW]
[ROW][C]53[/C][C]0.160308[/C][C]3.0374[/C][C]0.00128[/C][/ROW]
[ROW][C]54[/C][C]0.042213[/C][C]0.7998[/C][C]0.212173[/C][/ROW]
[ROW][C]55[/C][C]0.160649[/C][C]3.0439[/C][C]0.001254[/C][/ROW]
[ROW][C]56[/C][C]0.042494[/C][C]0.8052[/C][C]0.210633[/C][/ROW]
[ROW][C]57[/C][C]0.055698[/C][C]1.0553[/C][C]0.145992[/C][/ROW]
[ROW][C]58[/C][C]0.043943[/C][C]0.8326[/C][C]0.202814[/C][/ROW]
[ROW][C]59[/C][C]0.043887[/C][C]0.8315[/C][C]0.203111[/C][/ROW]
[ROW][C]60[/C][C]-0.02979[/C][C]-0.5644[/C][C]0.286401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30475&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 k	ACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.317794	6.0213	0
3	0.179563	3.4022	0.000372
4	0.155303	2.9426	0.001733
5	0.127596	2.4176	0.008061
6	0.06371	1.2071	0.114087
7	-0.054701	-1.0364	0.150347
8	-0.011735	-0.2224	0.412083
9	-0.080833	-1.5316	0.063255
10	-0.174708	-3.3102	0.000513
11	-0.055263	-1.0471	0.147883
12	-0.480698	-9.1079	0
13	-0.168514	-3.1929	0.000767
14	-0.172913	-3.2762	0.000577
15	-0.128287	-2.4307	0.007779
16	-0.163167	-3.0916	0.001073
17	-0.121097	-2.2945	0.01117
18	-0.103099	-1.9534	0.025772
19	0.020128	0.3814	0.351578
20	-0.002775	-0.0526	0.479049
21	-0.006426	-0.1217	0.451583
22	-0.006358	-0.1205	0.45209
23	-0.004364	-0.0827	0.467075
24	-0.006343	-0.1202	0.452205
25	0.094911	1.7983	0.036484
26	-0.008505	-0.1611	0.436036
27	0.017661	0.3346	0.369052
28	0.077035	1.4596	0.072638
29	0.068023	1.2888	0.09914
30	0.041632	0.7888	0.215369
31	0.032895	0.6233	0.266752
32	-0.068171	-1.2917	0.098653
33	0.011323	0.2145	0.415122
34	0.002674	0.0507	0.479811
35	-0.0721	-1.3661	0.08638
36	-0.031172	-0.5906	0.277571
37	-0.113841	-2.157	0.015835
38	-0.00152	-0.0288	0.488517
39	-0.046567	-0.8823	0.189098
40	-0.067976	-1.288	0.099295
41	-0.105451	-1.998	0.023234
42	-0.033256	-0.6301	0.264511
43	-0.158298	-2.9993	0.001447
44	0.01837	0.3481	0.364001
45	-0.043872	-0.8313	0.203191
46	0.021162	0.401	0.34434
47	0.042179	0.7992	0.21236
48	0.097675	1.8507	0.032519
49	0.125528	2.3784	0.008955
50	0.090564	1.7159	0.043518
51	0.082527	1.5637	0.059388
52	0.128164	2.4284	0.007829
53	0.160308	3.0374	0.00128
54	0.042213	0.7998	0.212173
55	0.160649	3.0439	0.001254
56	0.042494	0.8052	0.210633
57	0.055698	1.0553	0.145992
58	0.043943	0.8326	0.202814
59	0.043887	0.8315	0.203111
60	-0.02979	-0.5644	0.286401

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.292922	5.5501	0
3	0.093512	1.7718	0.038638
4	0.033995	0.6441	0.259959
5	0.032214	0.6104	0.271005
6	-0.024285	-0.4601	0.322846
7	-0.139405	-2.6414	0.004309
8	-0.030697	-0.5816	0.280592
9	-0.045877	-0.8693	0.192645
10	-0.156693	-2.9689	0.001595
11	0.037591	0.7122	0.238389
12	-0.427945	-8.1084	0
13	-0.036401	-0.6897	0.245414
14	0.123319	2.3366	0.010006
15	0.047112	0.8926	0.186322
16	-0.060609	-1.1484	0.125789
17	-0.017722	-0.3358	0.368615
18	0.007818	0.1481	0.44116
19	0.023368	0.4428	0.329106
20	0.047983	0.9091	0.181941
21	-0.03962	-0.7507	0.226664
22	-0.157258	-2.9796	0.001541
23	0.010195	0.1932	0.42347
24	-0.263321	-4.9892	0
25	0.056986	1.0797	0.140495
26	0.017452	0.3307	0.370544
27	-0.01152	-0.2183	0.413674
28	0.033761	0.6397	0.261394
29	0.035746	0.6773	0.249331
30	-0.027638	-0.5237	0.300414
31	0.037568	0.7118	0.238523
32	-0.076586	-1.4511	0.073812
33	-0.04242	-0.8037	0.211038
34	-0.086262	-1.6344	0.051522
35	-0.078156	-1.4808	0.069763
36	-0.219062	-4.1506	2.1e-05
37	-0.029885	-0.5662	0.285794
38	0.062408	1.1825	0.118901
39	-0.055153	-1.045	0.148363
40	-0.019687	-0.373	0.354676
41	-0.030763	-0.5829	0.280174
42	-0.01269	-0.2404	0.405061
43	-0.11499	-2.1787	0.015
44	-0.017441	-0.3305	0.37062
45	-0.006089	-0.1154	0.454112
46	0.002743	0.052	0.479293
47	-0.026375	-0.4997	0.308785
48	-0.056646	-1.0733	0.141932
49	0.037272	0.7062	0.240259
50	0.038077	0.7214	0.235552
51	-0.031982	-0.606	0.272461
52	0.055379	1.0493	0.147378
53	0.0148	0.2804	0.389656
54	-0.095807	-1.8153	0.035157
55	-0.024197	-0.4585	0.323449
56	-0.032014	-0.6066	0.272256
57	-0.058488	-1.1082	0.134259
58	0.043184	0.8182	0.206889
59	0.009712	0.184	0.427053
60	-0.049846	-0.9444	0.172791

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.187552 & 3.5536 & 0.000215 \tabularnewline
2 & 0.292922 & 5.5501 & 0 \tabularnewline
3 & 0.093512 & 1.7718 & 0.038638 \tabularnewline
4 & 0.033995 & 0.6441 & 0.259959 \tabularnewline
5 & 0.032214 & 0.6104 & 0.271005 \tabularnewline
6 & -0.024285 & -0.4601 & 0.322846 \tabularnewline
7 & -0.139405 & -2.6414 & 0.004309 \tabularnewline
8 & -0.030697 & -0.5816 & 0.280592 \tabularnewline
9 & -0.045877 & -0.8693 & 0.192645 \tabularnewline
10 & -0.156693 & -2.9689 & 0.001595 \tabularnewline
11 & 0.037591 & 0.7122 & 0.238389 \tabularnewline
12 & -0.427945 & -8.1084 & 0 \tabularnewline
13 & -0.036401 & -0.6897 & 0.245414 \tabularnewline
14 & 0.123319 & 2.3366 & 0.010006 \tabularnewline
15 & 0.047112 & 0.8926 & 0.186322 \tabularnewline
16 & -0.060609 & -1.1484 & 0.125789 \tabularnewline
17 & -0.017722 & -0.3358 & 0.368615 \tabularnewline
18 & 0.007818 & 0.1481 & 0.44116 \tabularnewline
19 & 0.023368 & 0.4428 & 0.329106 \tabularnewline
20 & 0.047983 & 0.9091 & 0.181941 \tabularnewline
21 & -0.03962 & -0.7507 & 0.226664 \tabularnewline
22 & -0.157258 & -2.9796 & 0.001541 \tabularnewline
23 & 0.010195 & 0.1932 & 0.42347 \tabularnewline
24 & -0.263321 & -4.9892 & 0 \tabularnewline
25 & 0.056986 & 1.0797 & 0.140495 \tabularnewline
26 & 0.017452 & 0.3307 & 0.370544 \tabularnewline
27 & -0.01152 & -0.2183 & 0.413674 \tabularnewline
28 & 0.033761 & 0.6397 & 0.261394 \tabularnewline
29 & 0.035746 & 0.6773 & 0.249331 \tabularnewline
30 & -0.027638 & -0.5237 & 0.300414 \tabularnewline
31 & 0.037568 & 0.7118 & 0.238523 \tabularnewline
32 & -0.076586 & -1.4511 & 0.073812 \tabularnewline
33 & -0.04242 & -0.8037 & 0.211038 \tabularnewline
34 & -0.086262 & -1.6344 & 0.051522 \tabularnewline
35 & -0.078156 & -1.4808 & 0.069763 \tabularnewline
36 & -0.219062 & -4.1506 & 2.1e-05 \tabularnewline
37 & -0.029885 & -0.5662 & 0.285794 \tabularnewline
38 & 0.062408 & 1.1825 & 0.118901 \tabularnewline
39 & -0.055153 & -1.045 & 0.148363 \tabularnewline
40 & -0.019687 & -0.373 & 0.354676 \tabularnewline
41 & -0.030763 & -0.5829 & 0.280174 \tabularnewline
42 & -0.01269 & -0.2404 & 0.405061 \tabularnewline
43 & -0.11499 & -2.1787 & 0.015 \tabularnewline
44 & -0.017441 & -0.3305 & 0.37062 \tabularnewline
45 & -0.006089 & -0.1154 & 0.454112 \tabularnewline
46 & 0.002743 & 0.052 & 0.479293 \tabularnewline
47 & -0.026375 & -0.4997 & 0.308785 \tabularnewline
48 & -0.056646 & -1.0733 & 0.141932 \tabularnewline
49 & 0.037272 & 0.7062 & 0.240259 \tabularnewline
50 & 0.038077 & 0.7214 & 0.235552 \tabularnewline
51 & -0.031982 & -0.606 & 0.272461 \tabularnewline
52 & 0.055379 & 1.0493 & 0.147378 \tabularnewline
53 & 0.0148 & 0.2804 & 0.389656 \tabularnewline
54 & -0.095807 & -1.8153 & 0.035157 \tabularnewline
55 & -0.024197 & -0.4585 & 0.323449 \tabularnewline
56 & -0.032014 & -0.6066 & 0.272256 \tabularnewline
57 & -0.058488 & -1.1082 & 0.134259 \tabularnewline
58 & 0.043184 & 0.8182 & 0.206889 \tabularnewline
59 & 0.009712 & 0.184 & 0.427053 \tabularnewline
60 & -0.049846 & -0.9444 & 0.172791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30475&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]0.187552[/C][C]3.5536[/C][C]0.000215[/C][/ROW]
[ROW][C]2[/C][C]0.292922[/C][C]5.5501[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.093512[/C][C]1.7718[/C][C]0.038638[/C][/ROW]
[ROW][C]4[/C][C]0.033995[/C][C]0.6441[/C][C]0.259959[/C][/ROW]
[ROW][C]5[/C][C]0.032214[/C][C]0.6104[/C][C]0.271005[/C][/ROW]
[ROW][C]6[/C][C]-0.024285[/C][C]-0.4601[/C][C]0.322846[/C][/ROW]
[ROW][C]7[/C][C]-0.139405[/C][C]-2.6414[/C][C]0.004309[/C][/ROW]
[ROW][C]8[/C][C]-0.030697[/C][C]-0.5816[/C][C]0.280592[/C][/ROW]
[ROW][C]9[/C][C]-0.045877[/C][C]-0.8693[/C][C]0.192645[/C][/ROW]
[ROW][C]10[/C][C]-0.156693[/C][C]-2.9689[/C][C]0.001595[/C][/ROW]
[ROW][C]11[/C][C]0.037591[/C][C]0.7122[/C][C]0.238389[/C][/ROW]
[ROW][C]12[/C][C]-0.427945[/C][C]-8.1084[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.036401[/C][C]-0.6897[/C][C]0.245414[/C][/ROW]
[ROW][C]14[/C][C]0.123319[/C][C]2.3366[/C][C]0.010006[/C][/ROW]
[ROW][C]15[/C][C]0.047112[/C][C]0.8926[/C][C]0.186322[/C][/ROW]
[ROW][C]16[/C][C]-0.060609[/C][C]-1.1484[/C][C]0.125789[/C][/ROW]
[ROW][C]17[/C][C]-0.017722[/C][C]-0.3358[/C][C]0.368615[/C][/ROW]
[ROW][C]18[/C][C]0.007818[/C][C]0.1481[/C][C]0.44116[/C][/ROW]
[ROW][C]19[/C][C]0.023368[/C][C]0.4428[/C][C]0.329106[/C][/ROW]
[ROW][C]20[/C][C]0.047983[/C][C]0.9091[/C][C]0.181941[/C][/ROW]
[ROW][C]21[/C][C]-0.03962[/C][C]-0.7507[/C][C]0.226664[/C][/ROW]
[ROW][C]22[/C][C]-0.157258[/C][C]-2.9796[/C][C]0.001541[/C][/ROW]
[ROW][C]23[/C][C]0.010195[/C][C]0.1932[/C][C]0.42347[/C][/ROW]
[ROW][C]24[/C][C]-0.263321[/C][C]-4.9892[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.056986[/C][C]1.0797[/C][C]0.140495[/C][/ROW]
[ROW][C]26[/C][C]0.017452[/C][C]0.3307[/C][C]0.370544[/C][/ROW]
[ROW][C]27[/C][C]-0.01152[/C][C]-0.2183[/C][C]0.413674[/C][/ROW]
[ROW][C]28[/C][C]0.033761[/C][C]0.6397[/C][C]0.261394[/C][/ROW]
[ROW][C]29[/C][C]0.035746[/C][C]0.6773[/C][C]0.249331[/C][/ROW]
[ROW][C]30[/C][C]-0.027638[/C][C]-0.5237[/C][C]0.300414[/C][/ROW]
[ROW][C]31[/C][C]0.037568[/C][C]0.7118[/C][C]0.238523[/C][/ROW]
[ROW][C]32[/C][C]-0.076586[/C][C]-1.4511[/C][C]0.073812[/C][/ROW]
[ROW][C]33[/C][C]-0.04242[/C][C]-0.8037[/C][C]0.211038[/C][/ROW]
[ROW][C]34[/C][C]-0.086262[/C][C]-1.6344[/C][C]0.051522[/C][/ROW]
[ROW][C]35[/C][C]-0.078156[/C][C]-1.4808[/C][C]0.069763[/C][/ROW]
[ROW][C]36[/C][C]-0.219062[/C][C]-4.1506[/C][C]2.1e-05[/C][/ROW]
[ROW][C]37[/C][C]-0.029885[/C][C]-0.5662[/C][C]0.285794[/C][/ROW]
[ROW][C]38[/C][C]0.062408[/C][C]1.1825[/C][C]0.118901[/C][/ROW]
[ROW][C]39[/C][C]-0.055153[/C][C]-1.045[/C][C]0.148363[/C][/ROW]
[ROW][C]40[/C][C]-0.019687[/C][C]-0.373[/C][C]0.354676[/C][/ROW]
[ROW][C]41[/C][C]-0.030763[/C][C]-0.5829[/C][C]0.280174[/C][/ROW]
[ROW][C]42[/C][C]-0.01269[/C][C]-0.2404[/C][C]0.405061[/C][/ROW]
[ROW][C]43[/C][C]-0.11499[/C][C]-2.1787[/C][C]0.015[/C][/ROW]
[ROW][C]44[/C][C]-0.017441[/C][C]-0.3305[/C][C]0.37062[/C][/ROW]
[ROW][C]45[/C][C]-0.006089[/C][C]-0.1154[/C][C]0.454112[/C][/ROW]
[ROW][C]46[/C][C]0.002743[/C][C]0.052[/C][C]0.479293[/C][/ROW]
[ROW][C]47[/C][C]-0.026375[/C][C]-0.4997[/C][C]0.308785[/C][/ROW]
[ROW][C]48[/C][C]-0.056646[/C][C]-1.0733[/C][C]0.141932[/C][/ROW]
[ROW][C]49[/C][C]0.037272[/C][C]0.7062[/C][C]0.240259[/C][/ROW]
[ROW][C]50[/C][C]0.038077[/C][C]0.7214[/C][C]0.235552[/C][/ROW]
[ROW][C]51[/C][C]-0.031982[/C][C]-0.606[/C][C]0.272461[/C][/ROW]
[ROW][C]52[/C][C]0.055379[/C][C]1.0493[/C][C]0.147378[/C][/ROW]
[ROW][C]53[/C][C]0.0148[/C][C]0.2804[/C][C]0.389656[/C][/ROW]
[ROW][C]54[/C][C]-0.095807[/C][C]-1.8153[/C][C]0.035157[/C][/ROW]
[ROW][C]55[/C][C]-0.024197[/C][C]-0.4585[/C][C]0.323449[/C][/ROW]
[ROW][C]56[/C][C]-0.032014[/C][C]-0.6066[/C][C]0.272256[/C][/ROW]
[ROW][C]57[/C][C]-0.058488[/C][C]-1.1082[/C][C]0.134259[/C][/ROW]
[ROW][C]58[/C][C]0.043184[/C][C]0.8182[/C][C]0.206889[/C][/ROW]
[ROW][C]59[/C][C]0.009712[/C][C]0.184[/C][C]0.427053[/C][/ROW]
[ROW][C]60[/C][C]-0.049846[/C][C]-0.9444[/C][C]0.172791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30475&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30475&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 k	PACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.292922	5.5501	0
3	0.093512	1.7718	0.038638
4	0.033995	0.6441	0.259959
5	0.032214	0.6104	0.271005
6	-0.024285	-0.4601	0.322846
7	-0.139405	-2.6414	0.004309
8	-0.030697	-0.5816	0.280592
9	-0.045877	-0.8693	0.192645
10	-0.156693	-2.9689	0.001595
11	0.037591	0.7122	0.238389
12	-0.427945	-8.1084	0
13	-0.036401	-0.6897	0.245414
14	0.123319	2.3366	0.010006
15	0.047112	0.8926	0.186322
16	-0.060609	-1.1484	0.125789
17	-0.017722	-0.3358	0.368615
18	0.007818	0.1481	0.44116
19	0.023368	0.4428	0.329106
20	0.047983	0.9091	0.181941
21	-0.03962	-0.7507	0.226664
22	-0.157258	-2.9796	0.001541
23	0.010195	0.1932	0.42347
24	-0.263321	-4.9892	0
25	0.056986	1.0797	0.140495
26	0.017452	0.3307	0.370544
27	-0.01152	-0.2183	0.413674
28	0.033761	0.6397	0.261394
29	0.035746	0.6773	0.249331
30	-0.027638	-0.5237	0.300414
31	0.037568	0.7118	0.238523
32	-0.076586	-1.4511	0.073812
33	-0.04242	-0.8037	0.211038
34	-0.086262	-1.6344	0.051522
35	-0.078156	-1.4808	0.069763
36	-0.219062	-4.1506	2.1e-05
37	-0.029885	-0.5662	0.285794
38	0.062408	1.1825	0.118901
39	-0.055153	-1.045	0.148363
40	-0.019687	-0.373	0.354676
41	-0.030763	-0.5829	0.280174
42	-0.01269	-0.2404	0.405061
43	-0.11499	-2.1787	0.015
44	-0.017441	-0.3305	0.37062
45	-0.006089	-0.1154	0.454112
46	0.002743	0.052	0.479293
47	-0.026375	-0.4997	0.308785
48	-0.056646	-1.0733	0.141932
49	0.037272	0.7062	0.240259
50	0.038077	0.7214	0.235552
51	-0.031982	-0.606	0.272461
52	0.055379	1.0493	0.147378
53	0.0148	0.2804	0.389656
54	-0.095807	-1.8153	0.035157
55	-0.024197	-0.4585	0.323449
56	-0.032014	-0.6066	0.272256
57	-0.058488	-1.1082	0.134259
58	0.043184	0.8182	0.206889
59	0.009712	0.184	0.427053
60	-0.049846	-0.9444	0.172791

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code