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Paper - ACF

*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 12:55:13 -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/t12298893529647gbgxdd8236y.htm/, Retrieved Sun, 21 Dec 2008 20:55:54 +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/t12298893529647gbgxdd8236y.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 «

90.8 96.4 90 92.1 97.2 95.1 88.5 91 90.5 75 66.3 66 68.4 70.6 83.9 90.1 90.6 87.1 90.8 94.1 99.8 96.8 87 96.3 107.1 115.2 106.1 89.5 91.3 97.6 100.7 104.6 94.7 101.8 102.5 105.3 110.3 109.8 117.3 118.8 131.3 125.9 133.1 147 145.8 164.4 149.8 137.7 151.7 156.8 180 180.4 170.4 191.6 199.5 218.2 217.5 205 194 199.3

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	0.115857	0.8899	0.188563
2	-0.168235	-1.2922	0.100657
3	-0.164038	-1.26	0.106315
4	-0.127117	-0.9764	0.166425
5	0.273653	2.102	0.019917
6	-0.019664	-0.151	0.44023
7	-0.085968	-0.6603	0.255806
8	-0.179091	-1.3756	0.087069
9	-0.095539	-0.7338	0.232973
10	0.221968	1.705	0.04673
11	0.064524	0.4956	0.311002
12	-0.032336	-0.2484	0.402352
13	-0.143043	-1.0987	0.138174
14	-0.083325	-0.64	0.262314
15	0.064351	0.4943	0.311469
16	-0.039221	-0.3013	0.382137
17	0.127101	0.9763	0.166455
18	-0.126114	-0.9687	0.168325
19	0.079735	0.6125	0.271294
20	0.18205	1.3984	0.083621
21	-0.052801	-0.4056	0.343262
22	-0.010695	-0.0822	0.467402
23	-0.184658	-1.4184	0.08067
24	0.043819	0.3366	0.368814
25	0.216774	1.6651	0.0506
26	0.012489	0.0959	0.461951
27	-0.115254	-0.8853	0.1898
28	-0.127615	-0.9802	0.165488
29	-0.007749	-0.0595	0.476369
30	0.169826	1.3045	0.098572
31	0.034155	0.2624	0.396982
32	-0.069074	-0.5306	0.298855
33	-0.181421	-1.3935	0.084345
34	-0.083286	-0.6397	0.262412
35	0.064231	0.4934	0.311793
36	0.073401	0.5638	0.287512
37	0.054143	0.4159	0.339502
38	-0.0256	-0.1966	0.422395
39	-0.010409	-0.08	0.468271
40	-0.040337	-0.3098	0.378889
41	0.025096	0.1928	0.423903
42	0.005249	0.0403	0.483987
43	-0.098257	-0.7547	0.226708
44	-0.097411	-0.7482	0.228646
45	-0.055193	-0.4239	0.336574
46	-0.036191	-0.278	0.390996
47	0.031719	0.2436	0.404178
48	0.021085	0.162	0.435945
49	0.048449	0.3721	0.355559
50	0.010979	0.0843	0.46654
51	-0.008963	-0.0688	0.472672
52	0.034505	0.265	0.395952
53	-0.020978	-0.1611	0.436269
54	0.002881	0.0221	0.49121
55	0.015502	0.1191	0.452811
56	0.007273	0.0559	0.477821
57	-0.013174	-0.1012	0.459872
58	0.001941	0.0149	0.494078
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.115857	0.8899	0.188563
2	-0.184129	-1.4143	0.081261
3	-0.125508	-0.964	0.169479
4	-0.129987	-0.9985	0.161069
5	0.272788	2.0953	0.020222
6	-0.168612	-1.2951	0.100159
7	-0.001852	-0.0142	0.49435
8	-0.182485	-1.4017	0.083123
9	0.007613	0.0585	0.476784
10	0.081407	0.6253	0.267094
11	0.008763	0.0673	0.473281
12	-0.047227	-0.3628	0.359041
13	-0.05355	-0.4113	0.341162
14	-0.015566	-0.1196	0.452616
15	-0.062272	-0.4783	0.317094
16	-0.10578	-0.8125	0.209882
17	0.15821	1.2152	0.114559
18	-0.166697	-1.2804	0.102703
19	0.252637	1.9405	0.028548
20	0.013093	0.1006	0.460117
21	-0.001597	-0.0123	0.495128
22	-0.11498	-0.8832	0.190362
23	-0.011997	-0.0922	0.463445
24	0.011018	0.0846	0.46642
25	0.196965	1.5129	0.06782
26	-0.032331	-0.2483	0.402367
27	-0.119526	-0.9181	0.181153
28	0.065942	0.5065	0.307193
29	-0.069863	-0.5366	0.296772
30	0.045179	0.347	0.364903
31	-0.040561	-0.3116	0.37824
32	0.047111	0.3619	0.359373
33	-0.08246	-0.6334	0.264464
34	-0.048945	-0.376	0.354151
35	-0.055939	-0.4297	0.334498
36	-0.065773	-0.5052	0.307646
37	0.086166	0.6619	0.255321
38	0.082355	0.6326	0.264725
39	-0.027175	-0.2087	0.417686
40	-0.055154	-0.4236	0.336682
41	-0.030031	-0.2307	0.409183
42	-0.085223	-0.6546	0.25763
43	-0.078312	-0.6015	0.274898
44	-0.067126	-0.5156	0.304028
45	-0.139273	-1.0698	0.144538
46	0.008344	0.0641	0.474557
47	-0.061562	-0.4729	0.319027
48	0.019558	0.1502	0.440547
49	-0.04	-0.3072	0.379869
50	-0.038414	-0.2951	0.38449
51	0.02661	0.2044	0.419374
52	0.070132	0.5387	0.296064
53	0.029577	0.2272	0.410531
54	-0.071979	-0.5529	0.291217
55	0.016635	0.1278	0.449382
56	-0.049509	-0.3803	0.35255
57	-0.005628	-0.0432	0.482831
58	-0.0134	-0.1029	0.459184
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298893529647gbgxdd8236y/1qy311229889312.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298893529647gbgxdd8236y/1qy311229889312.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298893529647gbgxdd8236y/2ox871229889312.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298893529647gbgxdd8236y/2ox871229889312.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 0.0 ; 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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