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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 18 Dec 2009 04:39:58 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136422qqerhxfczjvdsuf.htm/, Retrieved Fri, 18 Dec 2009 12:40:25 +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/2009/Dec/18/t1261136422qqerhxfczjvdsuf.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

100.00 100.00 93.55 88.17 89.25 91.40 92.47 91.40 88.17 87.10 84.95 92.47 93.55 93.55 91.40 90.32 91.40 93.55 93.55 92.47 91.40 89.25 86.02 88.17 87.10 87.10 86.02 84.95 84.95 86.02 86.02 84.95 86.02 82.80 77.42 80.65 78.49 75.27 75.27 75.27 77.42 78.49 76.34 73.12 68.82 65.59 69.89 82.80 84.95 80.65 74.19 70.97 74.19 82.80 86.02 86.02 82.80 78.49 79.57 87.10 89.25

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.338087	2.6188	0.005578
2	-0.295585	-2.2896	0.012789
3	-0.525179	-4.068	7e-05
4	-0.352056	-2.727	0.004184
5	0.144597	1.12	0.133579
6	0.53455	4.1406	5.5e-05
7	0.35274	2.7323	0.004125
8	-0.057328	-0.4441	0.329299
9	-0.337762	-2.6163	0.005615
10	-0.319812	-2.4773	0.008037
11	-0.014082	-0.1091	0.456753
12	0.363424	2.8151	0.003294
13	0.082846	0.6417	0.261748
14	-0.06568	-0.5088	0.306396
15	-0.078723	-0.6098	0.272154
16	-0.088736	-0.6873	0.247258
17	-0.004284	-0.0332	0.486818
18	0.093299	0.7227	0.236338
19	0.025063	0.1941	0.423361
20	-0.053174	-0.4119	0.340947
21	-0.061141	-0.4736	0.318754
22	-0.057299	-0.4438	0.329379
23	0.043672	0.3383	0.368167
24	0.162875	1.2616	0.105984
25	-0.107472	-0.8325	0.20422
26	-0.142776	-1.1059	0.136584
27	-0.072378	-0.5606	0.288567
28	-0.014652	-0.1135	0.455008
29	0.082919	0.6423	0.261567
30	0.129292	1.0015	0.160306
31	0.039005	0.3021	0.381799
32	-0.119974	-0.9293	0.178226
33	-0.168425	-1.3046	0.098503
34	0.005163	0.04	0.484115
35	0.170687	1.3221	0.09557
36	0.234147	1.8137	0.037363
37	-0.023159	-0.1794	0.429119
38	-0.177244	-1.3729	0.087442
39	-0.192009	-1.4873	0.071087
40	-0.036799	-0.285	0.388296
41	0.162749	1.2607	0.106157
42	0.266809	2.0667	0.021543
43	0.072279	0.5599	0.288825
44	-0.190231	-1.4735	0.072918
45	-0.260447	-2.0174	0.024066
46	-0.062972	-0.4878	0.313742
47	0.134385	1.0409	0.151039
48	0.207473	1.6071	0.056644
49	0.048393	0.3749	0.354547
50	-0.104083	-0.8062	0.211649
51	-0.147456	-1.1422	0.128956
52	-0.061849	-0.4791	0.316811
53	0.027369	0.212	0.416414
54	0.0838	0.6491	0.259371
55	0.045124	0.3495	0.363959
56	-0.060884	-0.4716	0.31946
57	-0.080072	-0.6202	0.268726
58	-0.017581	-0.1362	0.446067
59	0.000555	0.0043	0.498293
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.338087	2.6188	0.005578
2	-0.462786	-3.5847	0.000339
3	-0.319732	-2.4766	0.00805
4	-0.24325	-1.8842	0.032192
5	0.090088	0.6978	0.243994
6	0.259632	2.0111	0.024407
7	0.04387	0.3398	0.367591
8	0.075113	0.5818	0.281434
9	0.039098	0.3029	0.381525
10	0.001689	0.0131	0.494803
11	0.006271	0.0486	0.48071
12	0.152725	1.183	0.120737
13	-0.46302	-3.5865	0.000337
14	0.119928	0.929	0.178316
15	0.076418	0.5919	0.27806
16	0.009037	0.07	0.472215
17	-0.054986	-0.4259	0.335845
18	-0.008136	-0.063	0.474981
19	0.095564	0.7402	0.231023
20	-0.019882	-0.154	0.439061
21	-0.0425	-0.3292	0.371574
22	-0.149778	-1.1602	0.125287
23	0.068071	0.5273	0.299973
24	0.0493	0.3819	0.351952
25	-0.1623	-1.2572	0.106782
26	-0.080311	-0.6221	0.26812
27	-0.094278	-0.7303	0.234031
28	0.064778	0.5018	0.308834
29	-0.011388	-0.0882	0.465002
30	-0.026166	-0.2027	0.420035
31	0.063382	0.491	0.312626
32	-0.031396	-0.2432	0.404344
33	3e-05	2e-04	0.499907
34	0.243449	1.8857	0.032086
35	-0.00103	-0.008	0.496831
36	0.027821	0.2155	0.415054
37	0.038657	0.2994	0.382822
38	-0.100684	-0.7799	0.219259
39	-0.083027	-0.6431	0.261297
40	-0.020185	-0.1564	0.438139
41	-0.044329	-0.3434	0.36626
42	0.101496	0.7862	0.217426
43	-0.093199	-0.7219	0.236576
44	0.048297	0.3741	0.354821
45	0.066707	0.5167	0.303629
46	-0.017598	-0.1363	0.446016
47	-0.028618	-0.2217	0.412662
48	-0.107585	-0.8333	0.203977
49	0.005242	0.0406	0.483872
50	-0.072284	-0.5599	0.288813
51	0.035751	0.2769	0.391393
52	-0.096745	-0.7494	0.228278
53	-0.033247	-0.2575	0.398827
54	-0.059313	-0.4594	0.323791
55	0.044456	0.3444	0.365892
56	0.004569	0.0354	0.485944
57	-0.057506	-0.4454	0.328802
58	-0.084703	-0.6561	0.257132
59	0.069266	0.5365	0.296788
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136422qqerhxfczjvdsuf/1yfsu1261136397.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136422qqerhxfczjvdsuf/1yfsu1261136397.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136422qqerhxfczjvdsuf/22api1261136397.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261136422qqerhxfczjvdsuf/22api1261136397.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

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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