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partial autocorrelation

*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, 08 Dec 2009 12:13:14 -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/08/t12602996677ioz7om3chb2nj5.htm/, Retrieved Tue, 08 Dec 2009 20:14:29 +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/08/t12602996677ioz7om3chb2nj5.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:

wsh9

Dataseries X:

» Textbox « » Textfile « » CSV «

130.7 117.2 110.8 111.4 108.2 108.8 110.2 109.5 109.5 116 111.2 112.1 114 119.1 114.1 115.1 115.4 110.8 116 119.2 126.5 127.8 131.3 140.3 137.3 143 134.5 139.9 159.3 170.4 175 175.8 180.9 180.3 169.6 172.3 184.8 177.7 184.6 211.4 215.3 215.9 244.7 259.3 289 310.9 321 315.1 333.2 314.1 284.7 273.9 216 196.4 190.9 206.4 196.3 199.5 198.9 214.4

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.433183	-3.299	0.000831
2	-0.025633	-0.1952	0.422953
3	0.134732	1.0261	0.154556
4	-0.007581	-0.0577	0.477078
5	-0.177355	-1.3507	0.091019
6	0.166381	1.2671	0.105088
7	0.01385	0.1055	0.458182
8	-0.303745	-2.3133	0.012137
9	0.24931	1.8987	0.031292
10	-0.168742	-1.2851	0.101932
11	0.011615	0.0885	0.46491
12	0.090198	0.6869	0.247434
13	-0.05869	-0.447	0.328281
14	-0.150759	-1.1481	0.127811
15	0.14197	1.0812	0.14204
16	0.064902	0.4943	0.311489
17	-0.025011	-0.1905	0.4248
18	-0.048393	-0.3686	0.356902
19	0.068792	0.5239	0.301171
20	0.012071	0.0919	0.463535
21	-0.004849	-0.0369	0.485335
22	-0.098062	-0.7468	0.229094
23	0.109848	0.8366	0.203133
24	-0.073686	-0.5612	0.28842
25	-0.055606	-0.4235	0.336755
26	0.140399	1.0692	0.144694
27	-0.036321	-0.2766	0.39153
28	0.008596	0.0655	0.474016
29	-0.100594	-0.7661	0.223362
30	0.076689	0.584	0.280727
31	-0.03824	-0.2912	0.385959
32	-0.007901	-0.0602	0.476113
33	0.072089	0.549	0.292551
34	-0.104761	-0.7978	0.21411
35	0.063968	0.4872	0.31399
36	0.023543	0.1793	0.429165
37	0.001432	0.0109	0.495667
38	-0.050315	-0.3832	0.35149
39	0.051912	0.3953	0.347018
40	-0.002566	-0.0195	0.492238
41	-0.057997	-0.4417	0.330178
42	0.102475	0.7804	0.219157
43	-0.066116	-0.5035	0.308251
44	-0.011304	-0.0861	0.465845
45	-0.012192	-0.0929	0.463169
46	0.033927	0.2584	0.398513
47	-0.068487	-0.5216	0.301974
48	0.04051	0.3085	0.379399
49	-0.0337	-0.2566	0.399179
50	-0.000585	-0.0045	0.498229
51	0.013891	0.1058	0.458057
52	0.025653	0.1954	0.422894
53	-0.007559	-0.0576	0.477145
54	-0.001459	-0.0111	0.495586
55	-0.000806	-0.0061	0.497561
56	0.005581	0.0425	0.483121
57	0.007869	0.0599	0.476208
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.433183	-3.299	0.000831
2	-0.262547	-1.9995	0.025123
3	0.009231	0.0703	0.472099
4	0.083535	0.6362	0.26358
5	-0.149272	-1.1368	0.130143
6	0.003987	0.0304	0.487941
7	0.08128	0.619	0.269166
8	-0.278706	-2.1226	0.019036
9	-0.031642	-0.241	0.405212
10	-0.19995	-1.5228	0.066625
11	-0.068332	-0.5204	0.302382
12	0.055748	0.4246	0.336364
13	-0.090016	-0.6855	0.247867
14	-0.193227	-1.4716	0.073271
15	-0.118316	-0.9011	0.185639
16	0.013668	0.1041	0.458728
17	0.185152	1.4101	0.081929
18	-0.14438	-1.0996	0.138032
19	-0.062974	-0.4796	0.31666
20	0.084743	0.6454	0.260613
21	0.047099	0.3587	0.360564
22	-0.216508	-1.6489	0.05229
23	-0.090537	-0.6895	0.246626
24	-0.031479	-0.2397	0.405691
25	0.003693	0.0281	0.48883
26	0.067306	0.5126	0.305094
27	0.028858	0.2198	0.413409
28	0.073439	0.5593	0.289057
29	-0.114745	-0.8739	0.192896
30	-0.067182	-0.5116	0.305423
31	0.030704	0.2338	0.407969
32	-0.20249	-1.5421	0.064242
33	0.071802	0.5468	0.293297
34	0.035515	0.2705	0.393879
35	-0.027684	-0.2108	0.416878
36	0.013377	0.1019	0.459602
37	-0.020887	-0.1591	0.437082
38	0.03165	0.241	0.405188
39	-0.046918	-0.3573	0.361077
40	-0.024952	-0.19	0.424975
41	0.127048	0.9676	0.168638
42	0.007461	0.0568	0.477442
43	-0.126937	-0.9667	0.168848
44	-0.02445	-0.1862	0.426466
45	-0.034681	-0.2641	0.39631
46	-0.031925	-0.2431	0.40438
47	-0.074349	-0.5662	0.286713
48	0.017951	0.1367	0.445867
49	-0.005044	-0.0384	0.484744
50	0.003653	0.0278	0.488951
51	-0.07049	-0.5368	0.296717
52	-0.027023	-0.2058	0.418833
53	-0.096568	-0.7354	0.232517
54	-0.046557	-0.3546	0.3621
55	0.058038	0.442	0.330065
56	-0.076395	-0.5818	0.281476
57	-0.076145	-0.5799	0.282112
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/08/t12602996677ioz7om3chb2nj5/1hng21260299590.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t12602996677ioz7om3chb2nj5/1hng21260299590.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t12602996677ioz7om3chb2nj5/2flay1260299590.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t12602996677ioz7om3chb2nj5/2flay1260299590.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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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