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*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: Fri, 24 Dec 2010 12:03:15 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192076gdw9urkll6nfgp0.htm/, Retrieved Fri, 24 Dec 2010 13:01:17 +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/2010/Dec/24/t1293192076gdw9urkll6nfgp0.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

1143,94 1227,85 1261,26 1408,95 1162,58 1259,39 1253,85 1475,32 1211,75 1303,83 1299,37 1430,73 1244,95 1318,58 1318,74 1525,05 1275,88 1360,09 1349,81 1574,04 1294,58 1380,60 1369,22 1565,98 1338,96 1457,57 1456,21 1654,44 1428,47 1530,39 1514,13 1698,25 1454,22 1578,06 1526,53 1714,21 1492,86 1593,42 1555,50 1820,55 1534,57 1636,03 1594,58 1805,13 1565,37 1679,57 1638,26 1854,64 1628,72 1744,97 1694,35 1920,88 1680,26 1778,62 1740,89 2010,56

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.576222	4.3121	3.3e-05
2	0.689424	5.1592	2e-06
3	0.496579	3.7161	0.000234
4	0.817536	6.1179	0
5	0.432948	3.2399	0.001007
6	0.53576	4.0093	9.1e-05
7	0.34544	2.585	0.006184
8	0.646013	4.8343	5e-06
9	0.294436	2.2034	0.01585
10	0.389156	2.9122	0.002573
11	0.216002	1.6164	0.055813
12	0.492383	3.6847	0.000259
13	0.162651	1.2172	0.114322
14	0.244303	1.8282	0.036424
15	0.079656	0.5961	0.276758
16	0.341836	2.5581	0.006629
17	0.032961	0.2467	0.403037
18	0.10437	0.781	0.219035
19	-0.045252	-0.3386	0.368076
20	0.190309	1.4241	0.079976
21	-0.078052	-0.5841	0.280754
22	-0.018319	-0.1371	0.445728
23	-0.158567	-1.1866	0.120197
24	0.048865	0.3657	0.357993
25	-0.19746	-1.4777	0.072552
26	-0.147632	-1.1048	0.136991
27	-0.266569	-1.9948	0.025469
28	-0.076529	-0.5727	0.284573
29	-0.287766	-2.1534	0.017802
30	-0.237128	-1.7745	0.040708
31	-0.33473	-2.5049	0.007593
32	-0.152276	-1.1395	0.129667
33	-0.331859	-2.4834	0.008017
34	-0.279316	-2.0902	0.020576
35	-0.355182	-2.6579	0.005114
36	-0.189217	-1.416	0.081162
37	-0.342891	-2.566	0.006496
38	-0.302417	-2.2631	0.013763
39	-0.363296	-2.7187	0.004355
40	-0.216546	-1.6205	0.055373
41	-0.332117	-2.4853	0.007978
42	-0.29523	-2.2093	0.01563
43	-0.33552	-2.5108	0.00748
44	-0.216632	-1.6211	0.055304
45	-0.29491	-2.2069	0.015719
46	-0.260088	-1.9463	0.02832
47	-0.285935	-2.1397	0.018374
48	-0.176356	-1.3197	0.096148
49	-0.23694	-1.7731	0.040825
50	-0.202319	-1.514	0.067823
51	-0.203946	-1.5262	0.066295
52	-0.108443	-0.8115	0.210253
53	-0.12707	-0.9509	0.17287
54	-0.099608	-0.7454	0.229573
55	-0.080735	-0.6042	0.274086
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.576222	4.3121	3.3e-05
2	0.535043	4.0039	9.3e-05
3	0.007479	0.056	0.477782
4	0.660094	4.9397	4e-06
5	-0.498739	-3.7322	0.000223
6	-0.088401	-0.6615	0.255493
7	0.059526	0.4455	0.328854
8	0.140357	1.0503	0.149037
9	-0.14332	-1.0725	0.144047
10	-0.077621	-0.5809	0.281831
11	0.076747	0.5743	0.284024
12	-0.002115	-0.0158	0.493713
13	-0.118406	-0.8861	0.189685
14	-0.062211	-0.4655	0.321674
15	0.009897	0.0741	0.470611
16	0.025093	0.1878	0.425866
17	-0.086653	-0.6485	0.259671
18	-0.057643	-0.4314	0.333931
19	0.025058	0.1875	0.425968
20	-0.081022	-0.6063	0.273378
21	0.043277	0.3239	0.373628
22	-0.057133	-0.4275	0.335311
23	-0.05922	-0.4432	0.329679
24	-0.072802	-0.5448	0.294027
25	-0.051201	-0.3832	0.351529
26	-0.020294	-0.1519	0.439918
27	-0.004998	-0.0374	0.485148
28	-0.032235	-0.2412	0.405131
29	0.001198	0.009	0.496439
30	-0.002025	-0.0152	0.493983
31	-0.017035	-0.1275	0.449511
32	-0.003778	-0.0283	0.488772
33	-0.003651	-0.0273	0.48915
34	0.010066	0.0753	0.470111
35	0.002569	0.0192	0.492364
36	-0.030429	-0.2277	0.410352
37	-0.020958	-0.1568	0.437968
38	-0.053593	-0.4011	0.344954
39	-0.004425	-0.0331	0.486851
40	-0.033911	-0.2538	0.400302
41	0.067632	0.5061	0.307383
42	-0.012527	-0.0937	0.462822
43	-0.020548	-0.1538	0.439174
44	-0.077806	-0.5822	0.281369
45	0.065556	0.4906	0.312823
46	0.030674	0.2295	0.409641
47	-0.0453	-0.339	0.367941
48	0.039779	0.2977	0.383525
49	-0.029459	-0.2204	0.413162
50	0.02296	0.1718	0.4321
51	0.051823	0.3878	0.349814
52	-0.004257	-0.0319	0.487351
53	0.122566	0.9172	0.181486
54	-0.0192	-0.1437	0.443136
55	0.037168	0.2781	0.390964
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192076gdw9urkll6nfgp0/1k9lj1293192191.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192076gdw9urkll6nfgp0/1k9lj1293192191.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192076gdw9urkll6nfgp0/2k9lj1293192191.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192076gdw9urkll6nfgp0/2k9lj1293192191.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 95% ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 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 (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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