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Paper - ACF (48 lags)

*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: Tue, 14 Dec 2010 15:34:10 +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/14/t1292340981lohl1wb461jzwur.htm/, Retrieved Tue, 14 Dec 2010 16:36:21 +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/14/t1292340981lohl1wb461jzwur.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 «

10.81 9.12 11.03 12.74 9.98 11.62 9.40 9.27 7.76 8.78 10.65 10.95 12.36 10.85 11.84 12.14 11.65 8.86 7.63 7.38 7.25 8.03 7.75 7.16 7.18 7.51 7.07 7.11 8.98 9.53 10.54 11.31 10.36 11.44 10.45 10.69 11.28 11.96 13.52 12.89 14.03 16.27 16.17 17.25 19.38 26.20 33.53 32.20 38.45 44.86 41.67 36.06 39.76 36.81 42.65 46.89 53.61 57.59 67.82 71.89 75.51 68.49 62.72 70.39 59.77 57.27 67.96 67.85 76.98 81.08 91.66 84.84 85.73 84.61 92.91 99.80 121.19 122.04 131.76 138.48 153.47 189.95 182.22 198.08 135.36 125.02 143.50 173.95 188.75 167.44 158.95 169.53 113.66 107.59 92.67 85.35 90.13 89.31 105.12 125.83 135.81 142.43 163.39 168.21 185.35 188.50 199.91 210.73 192.06 204.62 235.00 261.09 256.88 251.53 257.25 243.10 283.75

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.950864	10.2852	0
2	0.911178	9.8559	0
3	0.86483	9.3546	0
4	0.822477	8.8964	0
5	0.780154	8.4387	0
6	0.732545	7.9237	0
7	0.692303	7.4884	0
8	0.659188	7.1302	0
9	0.627391	6.7863	0
10	0.591696	6.4002	0
11	0.557784	6.0334	0
12	0.526044	5.69	0
13	0.494406	5.3478	0
14	0.467105	5.0525	1e-06
15	0.44466	4.8097	2e-06
16	0.430872	4.6606	4e-06
17	0.421204	4.556	6e-06
18	0.415589	4.4953	8e-06
19	0.417732	4.5185	7e-06
20	0.424928	4.5963	5e-06
21	0.430224	4.6536	4e-06
22	0.435847	4.7144	3e-06
23	0.440299	4.7626	3e-06
24	0.434387	4.6986	4e-06
25	0.425539	4.6029	5e-06
26	0.399174	4.3177	1.7e-05
27	0.379195	4.1016	3.8e-05
28	0.360085	3.8949	8.2e-05
29	0.330875	3.579	0.000252
30	0.302342	3.2703	0.000706
31	0.278947	3.0173	0.001565
32	0.257529	2.7856	0.003117
33	0.236041	2.5532	0.00598
34	0.192117	2.0781	0.019946
35	0.153195	1.6571	0.050094
36	0.109165	1.1808	0.120039
37	0.075812	0.82	0.206934
38	0.047067	0.5091	0.305817
39	0.020834	0.2254	0.411049
40	-0.002264	-0.0245	0.490251
41	-0.025842	-0.2795	0.390169
42	-0.044686	-0.4834	0.314875
43	-0.063346	-0.6852	0.247289
44	-0.079786	-0.863	0.194946
45	-0.097378	-1.0533	0.147186
46	-0.113694	-1.2298	0.110621
47	-0.13154	-1.4228	0.078724
48	-0.146246	-1.5819	0.058186

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.950864	10.2852	0
2	0.07339	0.7938	0.214451
3	-0.081546	-0.8821	0.189777
4	0.005461	0.0591	0.4765
5	-0.012663	-0.137	0.445645
6	-0.082922	-0.8969	0.185798
7	0.041278	0.4465	0.328034
8	0.071869	0.7774	0.219251
9	-0.004925	-0.0533	0.478805
10	-0.065276	-0.7061	0.240775
11	-0.003214	-0.0348	0.486164
12	0.003258	0.0352	0.485972
13	-0.026361	-0.2851	0.388023
14	0.033397	0.3612	0.359284
15	0.057761	0.6248	0.266664
16	0.074069	0.8012	0.212328
17	0.035778	0.387	0.349729
18	0.039953	0.4322	0.333212
19	0.085553	0.9254	0.178332
20	0.064592	0.6987	0.243072
21	-0.011027	-0.1193	0.452633
22	0.020582	0.2226	0.412107
23	0.013298	0.1438	0.442937
24	-0.11354	-1.2281	0.110932
25	-0.049864	-0.5394	0.295333
26	-0.167145	-1.8079	0.036592
27	0.022038	0.2384	0.406002
28	0.023604	0.2553	0.399465
29	-0.119891	-1.2968	0.098622
30	-0.023228	-0.2513	0.40103
31	0.072903	0.7886	0.215979
32	-0.004769	-0.0516	0.479476
33	-0.0095	-0.1028	0.459167
34	-0.217563	-2.3533	0.010138
35	0.007939	0.0859	0.465858
36	-0.073804	-0.7983	0.213155
37	0.05401	0.5842	0.280101
38	0.080361	0.8692	0.193249
39	-0.001343	-0.0145	0.494216
40	-0.059677	-0.6455	0.259931
41	-0.088503	-0.9573	0.170192
42	-0.028666	-0.3101	0.37853
43	-0.026254	-0.284	0.388462
44	-0.03696	-0.3998	0.345023
45	-0.030754	-0.3327	0.369996
46	0.008887	0.0961	0.461791
47	-0.073959	-0.8	0.21267
48	-0.016677	-0.1804	0.42858

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340981lohl1wb461jzwur/138sw1292340847.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340981lohl1wb461jzwur/138sw1292340847.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340981lohl1wb461jzwur/238sw1292340847.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340981lohl1wb461jzwur/238sw1292340847.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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