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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: Sat, 12 Dec 2009 09:02:30 -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/12/t1260633820i0mvy19nnv03b4m.htm/, Retrieved Sat, 12 Dec 2009 17:03:42 +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/12/t1260633820i0mvy19nnv03b4m.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 «

17192.4 15386.1 14287.1 17526.6 14497 14398.3 16629.6 16670.7 16614.8 16869.2 15663.9 16359.9 18447.7 16889 16505 18320.9 15052.1 15699.8 18135.3 16768.7 18883 19021 18101.9 17776.1 21489.9 17065.3 18690 18953.1 16398.9 16895.6 18553 19270 19422.1 17579.4 18637.3 18076.7 20438.6 18075.2 19563 19899.2 19227.5 17789.6 19220.8 21968.9 21131.5 19484.6 22168.7 20866.8 22176.2 23533.8 21479.6 24347.7 22751.6 20328.3 23650.4 23335.7 19614.9 18042.3 17282.5 16847.2 18159.5

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	0.694937	5.4276	1e-06
2	0.612527	4.784	6e-06
3	0.657186	5.1328	2e-06
4	0.509555	3.9798	9.3e-05
5	0.454088	3.5465	0.000378
6	0.460958	3.6002	0.00032
7	0.315243	2.4621	0.008326
8	0.296733	2.3176	0.011922
9	0.28147	2.1983	0.015864
10	0.162079	1.2659	0.105185
11	0.184458	1.4407	0.077396
12	0.281253	2.1967	0.015927
13	0.106223	0.8296	0.204991
14	0.068182	0.5325	0.29815
15	0.100641	0.786	0.217447
16	0.061395	0.4795	0.316646
17	0.030127	0.2353	0.407381
18	0.025775	0.2013	0.420563
19	-0.000792	-0.0062	0.497543
20	-0.046809	-0.3656	0.357967
21	-0.047816	-0.3735	0.355051
22	-0.059695	-0.4662	0.321354
23	-0.041518	-0.3243	0.373424
24	0.008657	0.0676	0.473157
25	-0.013477	-0.1053	0.458259
26	-0.104544	-0.8165	0.208693
27	-0.06811	-0.532	0.298345
28	-0.032551	-0.2542	0.400085
29	-0.10908	-0.8519	0.198789
30	-0.109131	-0.8523	0.19868
31	-0.079198	-0.6186	0.269257
32	-0.190131	-1.485	0.071351
33	-0.195583	-1.5275	0.065897
34	-0.214808	-1.6777	0.049261
35	-0.273104	-2.133	0.018478
36	-0.236756	-1.8491	0.034643
37	-0.246323	-1.9238	0.029522
38	-0.331667	-2.5904	0.005987
39	-0.278854	-2.1779	0.016644
40	-0.233616	-1.8246	0.03648
41	-0.291169	-2.2741	0.013245
42	-0.280046	-2.1872	0.016285
43	-0.255861	-1.9983	0.025071
44	-0.310548	-2.4255	0.009132
45	-0.289623	-2.262	0.013635
46	-0.27841	-2.1745	0.01678
47	-0.285496	-2.2298	0.014726
48	-0.219825	-1.7169	0.045537
49	-0.218385	-1.7056	0.046581
50	-0.222384	-1.7369	0.043728
51	-0.145025	-1.1327	0.130891
52	-0.09631	-0.7522	0.227411
53	-0.081385	-0.6356	0.263695
54	-0.036349	-0.2839	0.388726
55	0.008097	0.0632	0.474892
56	0.027738	0.2166	0.414605
57	0.037396	0.2921	0.385613
58	0.026843	0.2097	0.417318
59	0.011065	0.0864	0.465709
60	0.001749	0.0137	0.494572

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.694937	5.4276	1e-06
2	0.250627	1.9575	0.027436
3	0.338501	2.6438	0.005204
4	-0.134498	-1.0505	0.148825
5	0.008404	0.0656	0.473942
6	0.045198	0.353	0.362649
7	-0.164779	-1.287	0.101485
8	0.049209	0.3843	0.351034
9	-0.023451	-0.1832	0.427642
10	-0.082183	-0.6419	0.261682
11	0.09071	0.7085	0.240677
12	0.266998	2.0853	0.020616
13	-0.255223	-1.9934	0.02535
14	-0.126947	-0.9915	0.162682
15	-0.034946	-0.2729	0.392912
16	0.16211	1.2661	0.105142
17	-0.072238	-0.5642	0.287346
18	-0.073811	-0.5765	0.283206
19	0.093497	0.7302	0.234022
20	-0.147126	-1.1491	0.127502
21	0.02607	0.2036	0.419667
22	0.072391	0.5654	0.286942
23	0.07284	0.5689	0.285756
24	-0.050007	-0.3906	0.348738
25	0.09143	0.7141	0.238948
26	-0.201795	-1.5761	0.060091
27	-0.035223	-0.2751	0.392086
28	0.040667	0.3176	0.37593
29	-0.036391	-0.2842	0.388603
30	-0.054686	-0.4271	0.3354
31	0.001228	0.0096	0.496189
32	-0.068897	-0.5381	0.296233
33	-0.097757	-0.7635	0.224053
34	-0.094746	-0.74	0.231072
35	-0.04665	-0.3643	0.35843
36	0.023965	0.1872	0.426074
37	-0.024139	-0.1885	0.425543
38	0.07778	0.6075	0.272892
39	-0.037206	-0.2906	0.386175
40	-0.001518	-0.0119	0.49529
41	-0.031716	-0.2477	0.402596
42	-0.081839	-0.6392	0.262549
43	-0.078302	-0.6116	0.271551
44	-0.001439	-0.0112	0.495535
45	0.041893	0.3272	0.372321
46	-0.029502	-0.2304	0.409269
47	0.0074	0.0578	0.477051
48	0.063038	0.4923	0.312121
49	-0.026175	-0.2044	0.419346
50	0.037677	0.2943	0.384777
51	0.124854	0.9751	0.16667
52	-0.033142	-0.2589	0.398311
53	0.000158	0.0012	0.49951
54	0.053818	0.4203	0.337861
55	0.034831	0.272	0.393257
56	-0.039321	-0.3071	0.379904
57	0.024641	0.1925	0.424013
58	-0.064528	-0.504	0.308045
59	-0.144441	-1.1281	0.131843
60	-0.065032	-0.5079	0.306672

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260633820i0mvy19nnv03b4m/160kr1260633749.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260633820i0mvy19nnv03b4m/160kr1260633749.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260633820i0mvy19nnv03b4m/2u9c01260633749.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260633820i0mvy19nnv03b4m/2u9c01260633749.ps (open in new window)

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')

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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