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ACF paper

*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: Sun, 21 Dec 2008 04:22:09 -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/21/t1229858591fdbhkohcx97fqws.htm/, Retrieved Sun, 21 Dec 2008 12:23:13 +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/21/t1229858591fdbhkohcx97fqws.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 «

1995 1947 1766 1635 1833 1910 1960 1970 2061 2093 2121 2175 2197 2350 2440 2409 2473 2408 2455 2448 2498 2646 2757 2849 2921 2982 3081 3106 3119 3061 3097 3162 3257 3277 3295 3364 3494 3667 3813 3918 3896 3801 3570 3702 3862 3970 4139 4200 4291 4444 4503 4357 4591 4697 4621 4563 4203 4296 4435 4105 4117

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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.139385	1.0797	0.142304
2	-0.107352	-0.8315	0.204482
3	0.054535	0.4224	0.337113
4	-0.125083	-0.9689	0.168245
5	0.093333	0.723	0.236259
6	-0.069929	-0.5417	0.295027
7	-0.199038	-1.5417	0.064197
8	0.075862	0.5876	0.279495
9	0.105052	0.8137	0.20951
10	-0.144423	-1.1187	0.133865
11	-0.124592	-0.9651	0.169188
12	0.012386	0.0959	0.461944
13	0.027697	0.2145	0.415427
14	0.210425	1.6299	0.054176
15	0.037927	0.2938	0.384968
16	-0.048881	-0.3786	0.35315
17	0.08811	0.6825	0.248776
18	-0.023826	-0.1846	0.427099
19	-0.129358	-1.002	0.160183
20	-0.140034	-1.0847	0.141197
21	-0.087199	-0.6754	0.250995
22	0.003856	0.0299	0.488136
23	-0.010033	-0.0777	0.469155
24	-0.028066	-0.2174	0.414318
25	0.049873	0.3863	0.350314
26	0.083592	0.6475	0.25989
27	0.077877	0.6032	0.274313
28	-0.028841	-0.2234	0.41199
29	-0.092713	-0.7181	0.237726
30	-0.000134	-0.001	0.499587
31	0.040232	0.3116	0.378198
32	0.03351	0.2596	0.398043
33	-0.06668	-0.5165	0.303702
34	-0.086232	-0.668	0.253363
35	-0.117423	-0.9096	0.183348
36	-0.059294	-0.4593	0.323844
37	-0.067531	-0.5231	0.301419
38	-0.074849	-0.5798	0.282116
39	0.19961	1.5462	0.063661
40	0.101876	0.7891	0.216572
41	0.004377	0.0339	0.486534
42	-0.025416	-0.1969	0.422297
43	-0.139551	-1.081	0.142021
44	0.038727	0.3	0.382614
45	-0.028722	-0.2225	0.412349
46	-0.105265	-0.8154	0.209039
47	-0.064775	-0.5017	0.308841
48	0.027346	0.2118	0.416483
49	0.031192	0.2416	0.404953
50	-0.077422	-0.5997	0.27548
51	-0.08408	-0.6513	0.258677
52	-0.023438	-0.1816	0.428273
53	0.130771	1.013	0.157576
54	0.106731	0.8267	0.205832
55	-0.071719	-0.5555	0.290297
56	0.037347	0.2893	0.386679
57	0.093252	0.7223	0.23645
58	0.044574	0.3453	0.365551
59	0.002445	0.0189	0.492477
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.139385	1.0797	0.142304
2	-0.129292	-1.0015	0.160306
3	0.092777	0.7186	0.237573
4	-0.17021	-1.3184	0.096183
5	0.17503	1.3558	0.090126
6	-0.186837	-1.4472	0.076518
7	-0.087437	-0.6773	0.250414
8	0.056295	0.4361	0.332181
9	0.105227	0.8151	0.209125
10	-0.218159	-1.6899	0.048123
11	-0.065072	-0.504	0.308037
12	0.05124	0.3969	0.346425
13	0.002331	0.0181	0.492826
14	0.164165	1.2716	0.104209
15	0.00384	0.0297	0.488186
16	0.032784	0.2539	0.400204
17	-0.038328	-0.2969	0.38379
18	0.008536	0.0661	0.473753
19	-0.127165	-0.985	0.164285
20	-0.095609	-0.7406	0.230918
21	-0.040656	-0.3149	0.376958
22	-0.025432	-0.197	0.422249
23	-0.067927	-0.5262	0.300357
24	0.049249	0.3815	0.352098
25	0.09859	0.7637	0.224028
26	0.003545	0.0275	0.489091
27	0.070441	0.5456	0.293669
28	-0.074787	-0.5793	0.282279
29	-0.093304	-0.7227	0.236326
30	-0.067094	-0.5197	0.302589
31	0.027733	0.2148	0.41532
32	0.030816	0.2387	0.406074
33	-0.058428	-0.4526	0.326242
34	-1.4e-05	-1e-04	0.499957
35	-0.146149	-1.1321	0.131056
36	0.005266	0.0408	0.4838
37	-0.0802	-0.6212	0.268402
38	-0.010569	-0.0819	0.467512
39	0.122371	0.9479	0.173497
40	-0.033719	-0.2612	0.397423
41	-0.033524	-0.2597	0.398001
42	-0.099695	-0.7722	0.221503
43	-0.042789	-0.3314	0.370732
44	0.005235	0.0406	0.483893
45	-0.073895	-0.5724	0.284598
46	-0.044225	-0.3426	0.36656
47	-0.113962	-0.8827	0.190449
48	0.031827	0.2465	0.403055
49	6e-04	0.0046	0.498155
50	-0.022908	-0.1774	0.429879
51	-0.078391	-0.6072	0.272999
52	-0.005118	-0.0396	0.484255
53	-0.026522	-0.2054	0.418962
54	0.007456	0.0578	0.477069
55	-0.095823	-0.7422	0.230419
56	0.037816	0.2929	0.385295
57	0.014688	0.1138	0.454898
58	0.009292	0.072	0.47143
59	0.05194	0.4023	0.344436
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858591fdbhkohcx97fqws/1tmtl1229858527.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858591fdbhkohcx97fqws/1tmtl1229858527.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858591fdbhkohcx97fqws/2wzul1229858527.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858591fdbhkohcx97fqws/2wzul1229858527.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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