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(Partial) Autocorrelation Function

*The author of this computation has been verified*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sat, 13 Dec 2008 09:08:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/13/t1229184649217k13gcaupy4zu.htm/, Retrieved Sat, 13 Dec 2008 17:10:51 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/13/t1229184649217k13gcaupy4zu.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

205597 205471 211064 212856 217036 219302 219759 221388 220834 221788 222358 222972 224164 224915 226294 224690 227021 229284 229189 230032 229389 231053 232560 232681 231555 231428 232141 234939 235424 235471 236355 238693 236958 237060 239282 238252 241552 236230 238909 240723 242120 242100 243276 244677 243494 244902 245247 245578 243052 238121 241863 241203 243634 242351 245180 246126 244424 245166 247258 245094 246020 243082 245555 243685 247277 245029 246169 246778 244577 246048 245775 245328 245477 241903 243219 248088 248521 247389 249057 248916 249193 250768 253106 249829 249447 246755 250785 250140 255755 254671 253919 253741 252729 253810 256653 255231 258405 251061 254811 254895 258325 257608 258759 258621 257852 260560 262358 260812 261165 257164 260720 259581 264743 261845 262262 261631 258953 259966 262850 262204 263418 262752 266433 267722 266003 262971 265521 264676 270223 269508 268457 265814 266680 263018 269285 269829 270911 266844 271244 269907 271296 270157 271322 267179 264101 265518 269419 268714 272482 268351 268175 270674 272764 272599 270333 270846 270491 269160 274027 273784 276663 274525 271344 271115 270798 273911 273985 271917 273338 270601 273547 275363 281229 277793 279913 282500 280041 282166 290304 283519 287816 285226 287595 289741 289148 288301 290155 289648 288225 289351 294735 305333

Output produced by software:

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.955371	13.238	0
2	0.922769	12.7863	0
3	0.894962	12.401	0
4	0.872728	12.0929	0
5	0.851498	11.7987	0
6	0.831583	11.5228	0
7	0.809921	11.2226	0
8	0.788749	10.9292	0
9	0.76425	10.5898	0
10	0.746108	10.3384	0
11	0.727461	10.08	0
12	0.710001	9.8381	0
13	0.689459	9.5534	0
14	0.665634	9.2233	0
15	0.645252	8.9409	0
16	0.629564	8.7235	0
17	0.612398	8.4856	0
18	0.597847	8.284	0
19	0.582916	8.0771	0
20	0.565354	7.8338	0
21	0.54838	7.5986	0
22	0.538033	7.4552	0
23	0.528928	7.329	0
24	0.519909	7.2041	0
25	0.505058	6.9983	0
26	0.490726	6.7997	0
27	0.474102	6.5694	0
28	0.464464	6.4358	0
29	0.454077	6.2919	0
30	0.445188	6.1687	0
31	0.431684	5.9816	0
32	0.419999	5.8197	0
33	0.406535	5.6331	0
34	0.395048	5.4739	0
35	0.386257	5.3521	0
36	0.378574	5.2457	0
37	0.367357	5.0903	0
38	0.355946	4.9321	1e-06
39	0.342346	4.7437	2e-06
40	0.332933	4.6133	4e-06
41	0.322336	4.4664	7e-06
42	0.31505	4.3655	1e-05
43	0.307277	4.2578	1.6e-05
44	0.298179	4.1317	2.7e-05
45	0.289342	4.0092	4.4e-05
46	0.283961	3.9347	5.8e-05
47	0.277745	3.8486	8.1e-05
48	0.276256	3.8279	8.7e-05
49	0.265659	3.6811	0.000151
50	0.252024	3.4921	0.000297
51	0.239447	3.3179	0.000542
52	0.228877	3.1714	0.000883
53	0.217893	3.0192	0.001439
54	0.204593	2.8349	0.002537
55	0.19579	2.713	0.003637
56	0.185241	2.5668	0.005513
57	0.174043	2.4116	0.008412
58	0.164465	2.2789	0.011887
59	0.159336	2.2078	0.01422
60	0.151626	2.101	0.018473

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.955371	13.238	0
2	0.114999	1.5935	0.056349
3	0.056786	0.7868	0.216172
4	0.067733	0.9385	0.174573
5	0.024534	0.3399	0.367134
6	0.020613	0.2856	0.38774
7	-0.015998	-0.2217	0.4124
8	-0.003125	-0.0433	0.482751
9	-0.046872	-0.6495	0.258404
10	0.050174	0.6952	0.243873
11	-0.001629	-0.0226	0.491009
12	0.007957	0.1103	0.456163
13	-0.033174	-0.4597	0.323134
14	-0.054642	-0.7571	0.224948
15	0.016558	0.2294	0.409389
16	0.041618	0.5767	0.282419
17	-0.011726	-0.1625	0.435549
18	0.022399	0.3104	0.378308
19	0.006603	0.0915	0.4636
20	-0.031793	-0.4405	0.330021
21	-0.002062	-0.0286	0.488621
22	0.065656	0.9098	0.182046
23	0.021378	0.2962	0.383692
24	0.011181	0.1549	0.438522
25	-0.052708	-0.7303	0.233033
26	-0.011036	-0.1529	0.439313
27	-0.035222	-0.488	0.313038
28	0.053606	0.7428	0.22926
29	-0.006199	-0.0859	0.465819
30	0.012941	0.1793	0.428941
31	-0.041105	-0.5696	0.284817
32	0.00872	0.1208	0.451975
33	-0.013282	-0.184	0.427089
34	-0.005328	-0.0738	0.470615
35	0.021746	0.3013	0.381746
36	0.01064	0.1474	0.441471
37	-0.019033	-0.2637	0.396137
38	-0.008774	-0.1216	0.451684
39	-0.025424	-0.3523	0.362503
40	0.020589	0.2853	0.387865
41	-0.020341	-0.2819	0.389179
42	0.026099	0.3616	0.359009
43	0.012365	0.1713	0.432072
44	-0.006997	-0.0969	0.461434
45	0.00475	0.0658	0.473793
46	0.026847	0.372	0.355151
47	-0.008103	-0.1123	0.455361
48	0.042397	0.5875	0.278789
49	-0.074394	-1.0308	0.151959
50	-0.054977	-0.7618	0.223561
51	-0.006317	-0.0875	0.465169
52	-0.009668	-0.134	0.446788
53	-0.018412	-0.2551	0.399451
54	-0.051752	-0.7171	0.237091
55	0.047987	0.6649	0.253448
56	-0.01966	-0.2724	0.392799
57	0.008402	0.1164	0.453718
58	-0.004321	-0.0599	0.476158
59	0.041492	0.5749	0.283005
60	-0.024743	-0.3429	0.366042

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229184649217k13gcaupy4zu/1mu281229184527.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229184649217k13gcaupy4zu/1mu281229184527.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229184649217k13gcaupy4zu/2w8v61229184527.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229184649217k13gcaupy4zu/2w8v61229184527.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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('http://www.xycoon.com/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('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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