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bel 20 - 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, 19 Dec 2009 09:16:40 -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/19/t1261239466nkwbj9izs5ztnhh.htm/, Retrieved Mon, 20 May 2013 18:21:14 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t122893495671lpdin9hfn9g3x (pk = 32071)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

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	0.96631	7.485	0
2	0.921266	7.1361	0
3	0.872315	6.7569	0
4	0.810665	6.2794	0
5	0.734047	5.6859	0
6	0.644415	4.9916	3e-06
7	0.556628	4.3116	3.1e-05
8	0.46744	3.6208	0.000303
9	0.368549	2.8548	0.002953
10	0.271256	2.1011	0.019919
11	0.182973	1.4173	0.080783
12	0.088733	0.6873	0.247264
13	-0.000823	-0.0064	0.497467
14	-0.08328	-0.6451	0.260666
15	-0.151082	-1.1703	0.123258
16	-0.213683	-1.6552	0.051555
17	-0.278821	-2.1597	0.0174
18	-0.329669	-2.5536	0.00661
19	-0.368964	-2.858	0.002926
20	-0.406549	-3.1491	0.001276
21	-0.442063	-3.4242	0.000559
22	-0.467907	-3.6244	0.000299
23	-0.48155	-3.7301	0.000213
24	-0.481777	-3.7318	0.000212
25	-0.476089	-3.6878	0.000244
26	-0.458987	-3.5553	0.000372
27	-0.438772	-3.3987	0.000604
28	-0.420719	-3.2589	0.000922
29	-0.395258	-3.0617	0.001646
30	-0.36593	-2.8345	0.003123
31	-0.334039	-2.5875	0.006055
32	-0.301343	-2.3342	0.011476
33	-0.276211	-2.1395	0.018236
34	-0.245317	-1.9002	0.031106
35	-0.210274	-1.6288	0.0543
36	-0.176651	-1.3683	0.088155
37	-0.142861	-1.1066	0.136443
38	-0.112768	-0.8735	0.192938
39	-0.085969	-0.6659	0.25401
40	-0.059507	-0.4609	0.323254
41	-0.032503	-0.2518	0.401041
42	-0.00938	-0.0727	0.47116
43	0.014838	0.1149	0.45444
44	0.035286	0.2733	0.392771
45	0.056739	0.4395	0.330939
46	0.075097	0.5817	0.281475
47	0.08238	0.6381	0.262914
48	0.084379	0.6536	0.257934
49	0.082045	0.6355	0.263754
50	0.078273	0.6063	0.273301
51	0.072338	0.5603	0.288672
52	0.064046	0.4961	0.310818
53	0.055665	0.4312	0.333943
54	0.047747	0.3698	0.356401
55	0.038127	0.2953	0.384382
56	0.029439	0.228	0.410197
57	0.022391	0.1734	0.431446
58	0.016337	0.1265	0.449863
59	0.009023	0.0699	0.472256
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.96631	7.485	0
2	-0.188526	-1.4603	0.07471
3	-0.055871	-0.4328	0.333365
4	-0.210868	-1.6334	0.053813
5	-0.219727	-1.702	0.046966
6	-0.208053	-1.6116	0.056152
7	0.039266	0.3042	0.381033
8	-0.036109	-0.2797	0.390335
9	-0.143159	-1.1089	0.135948
10	0.011674	0.0904	0.464124
11	0.06626	0.5133	0.30483
12	-0.211678	-1.6396	0.053156
13	0.042702	0.3308	0.370987
14	-0.002757	-0.0214	0.491517
15	0.105129	0.8143	0.209339
16	-0.066885	-0.5181	0.30315
17	-0.112922	-0.8747	0.192615
18	0.041649	0.3226	0.374055
19	-0.03918	-0.3035	0.381285
20	-0.0925	-0.7165	0.238231
21	-0.066549	-0.5155	0.304053
22	-0.002787	-0.0216	0.491425
23	0.033351	0.2583	0.398516
24	0.138808	1.0752	0.143295
25	0.064604	0.5004	0.309304
26	0.014217	0.1101	0.45634
27	-0.149255	-1.1561	0.126107
28	-0.116719	-0.9041	0.184779
29	-0.005219	-0.0404	0.483943
30	-0.038455	-0.2979	0.383415
31	0.000412	0.0032	0.498731
32	0.06256	0.4846	0.314866
33	-0.173909	-1.3471	0.091508
34	0.018846	0.146	0.442213
35	0.024098	0.1867	0.426278
36	0.078034	0.6045	0.273911
37	0.014822	0.1148	0.454488
38	-0.011348	-0.0879	0.465125
39	-0.076246	-0.5906	0.278505
40	-0.042708	-0.3308	0.370969
41	0.065204	0.5051	0.307682
42	-0.085656	-0.6635	0.254779
43	0.059471	0.4607	0.323353
44	-0.033638	-0.2606	0.397661
45	-0.016787	-0.13	0.448488
46	-0.005435	-0.0421	0.483279
47	-0.139191	-1.0782	0.142638
48	-0.047964	-0.3715	0.355776
49	-0.00924	-0.0716	0.47159
50	-0.013264	-0.1027	0.459254
51	0.007843	0.0608	0.475879
52	0.020607	0.1596	0.436858
53	0.061079	0.4731	0.318924
54	-0.0215	-0.1665	0.434147
55	-0.010415	-0.0807	0.467984
56	-0.095883	-0.7427	0.230278
57	0.01896	0.1469	0.441866
58	0.064887	0.5026	0.308538
59	0.00121	0.0094	0.496276
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239466nkwbj9izs5ztnhh/1f20v1261239399.png (opens in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239466nkwbj9izs5ztnhh/1f20v1261239399.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239466nkwbj9izs5ztnhh/2ekhd1261239399.png (opens in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239466nkwbj9izs5ztnhh/2ekhd1261239399.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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')