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ACF paper bel 20

*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 04:19:00 -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/t1229858390zmbxxryy0uce0cy.htm/, Retrieved Sun, 21 Dec 2008 12:19:52 +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/t1229858390zmbxxryy0uce0cy.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 «

1995 1947 1766 1635 1833 1910 1960 1970 2061 2093 2121 2175 2197 2350 2440 2409 2473 2408 2455 2448 2498 2646 2757 2849 2921 2982 3081 3106 3119 3061 3097 3162 3257 3277 3295 3364 3494 3667 3813 3918 3896 3801 3570 3702 3862 3970 4139 4200 4291 4444 4503 4357 4591 4697 4621 4563 4203 4296 4435 4105 4117

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	0.968401	7.5635	0
2	0.932105	7.28	0
3	0.885118	6.913	0
4	0.834768	6.5197	0
5	0.791089	6.1786	0
6	0.739049	5.7722	0
7	0.686202	5.3594	1e-06
8	0.633246	4.9458	3e-06
9	0.581235	4.5396	1.4e-05
10	0.530841	4.146	5.3e-05
11	0.478762	3.7393	0.000205
12	0.429176	3.352	0.000691
13	0.380984	2.9756	0.002094
14	0.336059	2.6247	0.005472
15	0.289507	2.2611	0.013665
16	0.243278	1.9001	0.031077
17	0.199983	1.5619	0.061741
18	0.155371	1.2135	0.114812
19	0.113478	0.8863	0.18947
20	0.067746	0.5291	0.299325
21	0.022179	0.1732	0.431525
22	-0.020303	-0.1586	0.437264
23	-0.059543	-0.465	0.321778
24	-0.094863	-0.7409	0.230797
25	-0.125803	-0.9826	0.164854
26	-0.154559	-1.2071	0.116018
27	-0.181804	-1.4199	0.080359
28	-0.210157	-1.6414	0.052933
29	-0.238165	-1.8601	0.033845
30	-0.265107	-2.0705	0.02132
31	-0.290728	-2.2707	0.013355
32	-0.315474	-2.4639	0.008288
33	-0.340274	-2.6576	0.005016
34	-0.363996	-2.8429	0.003037
35	-0.386147	-3.0159	0.001866
36	-0.403542	-3.1518	0.001258
37	-0.41625	-3.251	0.000937
38	-0.422762	-3.3019	0.000804
39	-0.423088	-3.3044	0.000798
40	-0.422103	-3.2967	0.000817
41	-0.420521	-3.2844	0.000848
42	-0.420413	-3.2835	0.00085
43	-0.425801	-3.3256	0.000749
44	-0.4251	-3.3201	0.000761
45	-0.42253	-3.3001	0.000809
46	-0.415756	-3.2472	0.000948
47	-0.403799	-3.1538	0.001251
48	-0.387545	-3.0268	0.001808
49	-0.366426	-2.8619	0.002881
50	-0.341367	-2.6662	0.004904
51	-0.312225	-2.4386	0.008836
52	-0.284377	-2.2211	0.015035
53	-0.24949	-1.9486	0.027975
54	-0.211862	-1.6547	0.051562
55	-0.17703	-1.3826	0.085907
56	-0.141005	-1.1013	0.137549
57	-0.112452	-0.8783	0.19162
58	-0.079023	-0.6172	0.269704
59	-0.044993	-0.3514	0.363248
60	-0.022192	-0.1733	0.431484

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.968401	7.5635	0
2	-0.091567	-0.7152	0.238618
3	-0.186656	-1.4578	0.075009
4	-0.059553	-0.4651	0.321748
5	0.117677	0.9191	0.180834
6	-0.166354	-1.2993	0.099371
7	-0.070761	-0.5527	0.291258
8	0.009851	0.0769	0.469461
9	0.018929	0.1478	0.441479
10	-0.053222	-0.4157	0.339551
11	-0.065583	-0.5122	0.305174
12	0.022177	0.1732	0.431531
13	-8.9e-05	-7e-04	0.499725
14	-0.006535	-0.051	0.47973
15	-0.094456	-0.7377	0.231754
16	-0.019883	-0.1553	0.438552
17	0.028766	0.2247	0.411493
18	-0.06749	-0.5271	0.300014
19	-0.039095	-0.3053	0.380572
20	-0.088808	-0.6936	0.245279
21	-0.015521	-0.1212	0.451957
22	0.006394	0.0499	0.480167
23	0.011761	0.0919	0.463556
24	-0.023541	-0.1839	0.427365
25	0.037067	0.2895	0.386589
26	-0.009945	-0.0777	0.469172
27	-0.050285	-0.3927	0.347941
28	-0.085936	-0.6712	0.252319
29	-0.024781	-0.1935	0.423589
30	-0.008947	-0.0699	0.472259
31	-0.041087	-0.3209	0.374693
32	-0.054192	-0.4233	0.3368
33	-0.042114	-0.3289	0.37167
34	-0.006274	-0.049	0.480538
35	-0.01779	-0.1389	0.444977
36	0.013978	0.1092	0.456713
37	0.0267	0.2085	0.417754
38	0.056838	0.4439	0.329335
39	0.040585	0.317	0.376171
40	-0.052998	-0.4139	0.340189
41	-0.063533	-0.4962	0.310766
42	-0.056433	-0.4408	0.330475
43	-0.126938	-0.9914	0.1627
44	0.054442	0.4252	0.336091
45	0.022955	0.1793	0.429155
46	0.01876	0.1465	0.441996
47	0.046983	0.3669	0.357463
48	0.096551	0.7541	0.22685
49	0.030463	0.2379	0.406368
50	0.016268	0.1271	0.449656
51	0.04218	0.3294	0.371476
52	-0.049362	-0.3855	0.350594
53	0.093505	0.7303	0.234002
54	0.030265	0.2364	0.406966
55	-0.102035	-0.7969	0.214295
56	-0.023917	-0.1868	0.426219
57	-0.056574	-0.4419	0.330077
58	0.093858	0.7331	0.233166
59	0.029182	0.2279	0.410236
60	-0.169816	-1.3263	0.094841

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858390zmbxxryy0uce0cy/1tyel1229858338.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858390zmbxxryy0uce0cy/1tyel1229858338.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858390zmbxxryy0uce0cy/2rt6i1229858338.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229858390zmbxxryy0uce0cy/2rt6i1229858338.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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