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Paper: ACF & PACF

*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, 11 Dec 2009 07:11:12 -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/11/t1260540884jps71oklhikay29.htm/, Retrieved Fri, 11 Dec 2009 15:14:46 +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/11/t1260540884jps71oklhikay29.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:

bhschhwsstpaper

Dataseries X:

» Textbox « » Textfile « » CSV «

128.6 128.9 129.06 129.23 129.27 129.33 129.35 129.31 129.4 129.49 129.47 129.46 129.45 129.28 129.2 129.25 129.14 129.11 129.02 129.08 128.99 129.11 129.08 129.19 129.23 129.25 129.31 129.33 129.39 129.55 129.43 129.45 129.57 129.76 129.92 130.08 130.41 130.84 131.24 131.49 131.74 132.34 133.5 134.43 136.5 137.41 138.02 138.15 138.24 138.2 138.31 138.65 139.3 139.8 140.52 141.57 141.77 141.66 141.36 141.17

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	0.956646	7.4102	0
2	0.905267	7.0122	0
3	0.845884	6.5522	0
4	0.781973	6.0571	0
5	0.716638	5.5511	0
6	0.656902	5.0883	2e-06
7	0.599922	4.647	9e-06
8	0.543316	4.2085	4.4e-05
9	0.487909	3.7793	0.000182
10	0.431233	3.3403	0.000722
11	0.371019	2.8739	0.0028
12	0.306459	2.3738	0.010412
13	0.23997	1.8588	0.033981
14	0.172127	1.3333	0.093738
15	0.107782	0.8349	0.20355
16	0.049698	0.385	0.350815
17	0.005875	0.0455	0.481926
18	-0.031998	-0.2479	0.402546
19	-0.062531	-0.4844	0.314945
20	-0.089152	-0.6906	0.246249
21	-0.11465	-0.8881	0.189024
22	-0.138269	-1.071	0.144223
23	-0.159152	-1.2328	0.111233
24	-0.176745	-1.3691	0.088041
25	-0.191587	-1.484	0.071519
26	-0.20507	-1.5885	0.058719
27	-0.217061	-1.6813	0.048947
28	-0.227567	-1.7627	0.041519
29	-0.236829	-1.8345	0.035772
30	-0.245364	-1.9006	0.031082
31	-0.25501	-1.9753	0.02642
32	-0.263291	-2.0394	0.022908
33	-0.270796	-2.0976	0.020082
34	-0.277711	-2.1511	0.017751
35	-0.283898	-2.1991	0.01587
36	-0.289682	-2.2439	0.014272
37	-0.29447	-2.281	0.013058
38	-0.297234	-2.3024	0.0124
39	-0.299103	-2.3168	0.011972
40	-0.29956	-2.3204	0.011869
41	-0.300368	-2.3266	0.011689
42	-0.299471	-2.3197	0.011889
43	-0.29613	-2.2938	0.012659
44	-0.290847	-2.2529	0.013968
45	-0.280262	-2.1709	0.016953
46	-0.26674	-2.0662	0.021569
47	-0.252099	-1.9528	0.027759
48	-0.238466	-1.8472	0.034829
49	-0.224713	-1.7406	0.043438
50	-0.211363	-1.6372	0.053411
51	-0.198104	-1.5345	0.065081
52	-0.183481	-1.4212	0.080213
53	-0.166518	-1.2898	0.101028
54	-0.148602	-1.1511	0.127136
55	-0.128524	-0.9955	0.161735
56	-0.104679	-0.8108	0.210332
57	-0.079812	-0.6182	0.269385
58	-0.053936	-0.4178	0.338798
59	-0.027776	-0.2152	0.415189
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.956646	7.4102	0
2	-0.116769	-0.9045	0.184678
3	-0.114184	-0.8845	0.189988
4	-0.071972	-0.5575	0.289632
5	-0.038772	-0.3003	0.382484
6	0.038823	0.3007	0.382334
7	-0.009506	-0.0736	0.470774
8	-0.046356	-0.3591	0.3604
9	-0.033214	-0.2573	0.398924
10	-0.058479	-0.453	0.326099
11	-0.07792	-0.6036	0.274203
12	-0.086007	-0.6662	0.253915
13	-0.059087	-0.4577	0.324416
14	-0.05572	-0.4316	0.333788
15	-0.006661	-0.0516	0.479512
16	0.01268	0.0982	0.461042
17	0.100042	0.7749	0.220714
18	-0.011397	-0.0883	0.464975
19	0.005948	0.0461	0.481701
20	-0.020356	-0.1577	0.437619
21	-0.036938	-0.2861	0.387887
22	-0.003088	-0.0239	0.4905
23	0.004619	0.0358	0.485789
24	0.00739	0.0572	0.47727
25	-0.005097	-0.0395	0.484319
26	-0.039132	-0.3031	0.381427
27	-0.040221	-0.3116	0.378231
28	-0.038861	-0.301	0.382221
29	-0.034265	-0.2654	0.395799
30	-0.03568	-0.2764	0.391606
31	-0.045951	-0.3559	0.361568
32	-0.00634	-0.0491	0.480498
33	-0.002577	-0.02	0.492071
34	-0.018915	-0.1465	0.442004
35	-0.017811	-0.138	0.445366
36	-0.031094	-0.2409	0.405244
37	-0.020202	-0.1565	0.438088
38	0.002626	0.0203	0.49192
39	-0.010191	-0.0789	0.46867
40	-0.000389	-0.003	0.498804
41	-0.02587	-0.2004	0.420926
42	-0.006123	-0.0474	0.481163
43	0.003402	0.0264	0.489532
44	-0.007727	-0.0599	0.476236
45	0.034327	0.2659	0.395615
46	0.003133	0.0243	0.49036
47	-0.019457	-0.1507	0.440353
48	-0.033173	-0.257	0.399046
49	-0.016585	-0.1285	0.449105
50	-0.012806	-0.0992	0.460656
51	-0.008204	-0.0635	0.474771
52	0.002854	0.0221	0.491218
53	0.013719	0.1063	0.457861
54	-0.001515	-0.0117	0.495338
55	0.01057	0.0819	0.46751
56	0.035854	0.2777	0.39109
57	0.001926	0.0149	0.494072
58	0.013596	0.1053	0.458238
59	0.014247	0.1104	0.456248
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540884jps71oklhikay29/1pxm91260540671.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540884jps71oklhikay29/1pxm91260540671.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540884jps71oklhikay29/2iur71260540671.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540884jps71oklhikay29/2iur71260540671.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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