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Paper 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, 19 Dec 2009 09:35:13 -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/t1261240553vy6fijcu9xxrr4o.htm/, Retrieved Sat, 19 Dec 2009 17:35:55 +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/19/t1261240553vy6fijcu9xxrr4o.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 «

13.4 13.5 14.8 14.3 14.3 14 13.2 12.2 14.3 15.7 14.2 14.6 14.5 14.3 15.3 14.4 13.7 14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5

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	-0.375641	-3.1652	0.001142
2	-0.301875	-2.5436	0.006574
3	0.34392	2.8979	0.002496
4	-0.191342	-1.6123	0.05567
5	-0.150497	-1.2681	0.104451
6	0.394336	3.3227	0.000706
7	-0.26263	-2.213	0.015058
8	-0.074493	-0.6277	0.26611
9	0.364276	3.0694	0.001518
10	-0.426428	-3.5931	0.000299
11	-0.113187	-0.9537	0.171728
12	0.649521	5.473	0
13	-0.321674	-2.7105	0.004209
14	-0.10374	-0.8741	0.192497
15	0.196635	1.6569	0.050979
16	-0.245604	-2.0695	0.02107
17	0.029761	0.2508	0.401356
18	0.253321	2.1345	0.018127
19	-0.236542	-1.9931	0.025045
20	0.023734	0.2	0.42103
21	0.241378	2.0339	0.02285
22	-0.419568	-3.5353	0.000361
23	0.126665	1.0673	0.144726
24	0.307923	2.5946	0.005748
25	-0.198513	-1.6727	0.049394
26	-0.011705	-0.0986	0.460857
27	0.087343	0.736	0.232088
28	-0.200791	-1.6919	0.047526
29	0.102228	0.8614	0.195961
30	0.079822	0.6726	0.251694
31	-0.1407	-1.1856	0.119875
32	0.121649	1.025	0.154413
33	0.029576	0.2492	0.401959
34	-0.257224	-2.1674	0.01678
35	0.115054	0.9695	0.167804
36	0.173107	1.4586	0.074539
37	-0.063857	-0.5381	0.296107
38	-0.039746	-0.3349	0.369341
39	0.018793	0.1584	0.437315
40	-0.067562	-0.5693	0.285478
41	0.04086	0.3443	0.365822
42	0.020983	0.1768	0.430082
43	-0.074923	-0.6313	0.264932
44	0.122071	1.0286	0.153583
45	-0.038113	-0.3211	0.374521
46	-0.089449	-0.7537	0.226756
47	-0.013576	-0.1144	0.454625
48	0.147941	1.2466	0.108325
49	-0.000791	-0.0067	0.497351
50	-0.075495	-0.6361	0.263369
51	-0.016706	-0.1408	0.444227
52	-0.002283	-0.0192	0.492351
53	0.011705	0.0986	0.460855
54	0.008905	0.075	0.470201
55	-0.006995	-0.0589	0.476581
56	0.034604	0.2916	0.385729
57	-0.015542	-0.131	0.448089
58	-0.020899	-0.1761	0.430359
59	-0.040721	-0.3431	0.366259
60	0.07725	0.6509	0.258599

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.375641	-3.1652	0.001142
2	-0.515757	-4.3458	2.3e-05
3	-0.034423	-0.29	0.386312
4	-0.260381	-2.194	0.015754
5	-0.318312	-2.6821	0.004546
6	0.06534	0.5506	0.291831
7	-0.192167	-1.6192	0.054916
8	-0.106928	-0.901	0.18532
9	0.146248	1.2323	0.110949
10	-0.31691	-2.6703	0.004694
11	-0.49292	-4.1534	4.5e-05
12	0.140869	1.187	0.119596
13	0.081849	0.6897	0.246325
14	0.187414	1.5792	0.05937
15	-0.064171	-0.5407	0.295199
16	-0.080672	-0.6798	0.249436
17	-0.004866	-0.041	0.483704
18	-0.131469	-1.1078	0.135849
19	0.050532	0.4258	0.335775
20	-0.045695	-0.385	0.350681
21	-0.05976	-0.5035	0.308068
22	-0.17856	-1.5046	0.068435
23	0.054691	0.4608	0.323164
24	-0.044563	-0.3755	0.354206
25	0.072774	0.6132	0.27085
26	-0.059922	-0.5049	0.307594
27	0.006585	0.0555	0.477952
28	0.0758	0.6387	0.262535
29	0.047814	0.4029	0.344119
30	-0.077575	-0.6537	0.257721
31	-0.063225	-0.5327	0.297937
32	0.008185	0.069	0.472604
33	-0.087793	-0.7398	0.230944
34	0.011671	0.0983	0.46097
35	-0.241147	-2.0319	0.022951
36	-0.062077	-0.5231	0.301276
37	-0.006844	-0.0577	0.477086
38	-0.078752	-0.6636	0.254554
39	0.009244	0.0779	0.469066
40	0.009149	0.0771	0.469383
41	-0.021405	-0.1804	0.428691
42	0.044992	0.3791	0.35287
43	-0.067338	-0.5674	0.286115
44	-0.016179	-0.1363	0.445975
45	-0.032528	-0.2741	0.392406
46	0.053214	0.4484	0.327619
47	0.057014	0.4804	0.316206
48	0.014056	0.1184	0.453028
49	-0.005419	-0.0457	0.481855
50	-0.04387	-0.3697	0.356371
51	-0.071253	-0.6004	0.27508
52	-0.108681	-0.9158	0.181445
53	-0.032051	-0.2701	0.393945
54	-0.045575	-0.384	0.351054
55	-0.00217	-0.0183	0.492732
56	0.016707	0.1408	0.444224
57	-0.037921	-0.3195	0.375132
58	-0.015361	-0.1294	0.448689
59	0.105574	0.8896	0.188347
60	-0.07655	-0.645	0.260496

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240553vy6fijcu9xxrr4o/1xey91261240511.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240553vy6fijcu9xxrr4o/1xey91261240511.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240553vy6fijcu9xxrr4o/277pr1261240511.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240553vy6fijcu9xxrr4o/277pr1261240511.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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