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*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: Thu, 10 Dec 2009 08:24:47 -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/10/t1260458826j1hoghyi2u7178k.htm/, Retrieved Thu, 10 Dec 2009 16:27:08 +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/10/t1260458826j1hoghyi2u7178k.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 «

62,7 62,3 61,9 62 62,3 62,8 62,4 62,3 62,7 62,7 62,9 63 62,2 62,3 62,8 62,8 62,8 62,2 62,6 62,8 62,5 62,4 62,3 61,9 61,7 62 62,1 61,7 61,8 61,8 61,8 61,3 61,3 61,3 61,2 61,4 62,2 62,9 63,1 63,5 63,6 64,4 64,1 65,1 65,8 65,9 65,4 65,5 64,8 63,2 62,7 62,1 61,9 60,6 60,7 59,8 59 58,3 59,3 59 59,1

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.913266	7.1328	0
2	0.801727	6.2617	0
3	0.674909	5.2712	1e-06
4	0.507052	3.9602	9.9e-05
5	0.319153	2.4927	0.007705
6	0.14948	1.1675	0.123781
7	-0.00714	-0.0558	0.477855
8	-0.177056	-1.3829	0.085876
9	-0.316896	-2.475	0.008058
10	-0.43016	-3.3597	0.000675
11	-0.514347	-4.0172	8.2e-05
12	-0.591847	-4.6225	1e-05
13	-0.589474	-4.6039	1.1e-05
14	-0.542751	-4.239	3.9e-05
15	-0.483714	-3.7779	0.000181
16	-0.415143	-3.2424	0.000962
17	-0.325663	-2.5435	0.006763
18	-0.243056	-1.8983	0.031193
19	-0.179551	-1.4023	0.082942
20	-0.106513	-0.8319	0.204358
21	-0.037343	-0.2917	0.385769
22	0.029687	0.2319	0.408711
23	0.073504	0.5741	0.284009
24	0.11555	0.9025	0.185177
25	0.149825	1.1702	0.123242
26	0.155443	1.214	0.114704
27	0.14784	1.1547	0.126365
28	0.147584	1.1527	0.126772
29	0.142223	1.1108	0.135507
30	0.127168	0.9932	0.162264
31	0.117131	0.9148	0.181943
32	0.113895	0.8895	0.188601
33	0.10289	0.8036	0.212374
34	0.077336	0.604	0.274037
35	0.060172	0.47	0.320032
36	0.05065	0.3956	0.346893
37	0.023239	0.1815	0.428287
38	-0.000584	-0.0046	0.498188
39	-0.013339	-0.1042	0.458683
40	-0.026521	-0.2071	0.418297
41	-0.042609	-0.3328	0.370217
42	-0.045865	-0.3582	0.360709
43	-0.045639	-0.3565	0.361365
44	-0.054797	-0.428	0.335087
45	-0.055223	-0.4313	0.333882
46	-0.051592	-0.4029	0.344199
47	-0.039167	-0.3059	0.380359
48	-0.043971	-0.3434	0.366231
49	-0.04837	-0.3778	0.353451
50	-0.032844	-0.2565	0.399205
51	-0.022012	-0.1719	0.432035
52	-0.013897	-0.1085	0.456962
53	-0.001747	-0.0136	0.49458
54	0.000978	0.0076	0.496965
55	0.000797	0.0062	0.497528
56	0.007084	0.0553	0.478029
57	0.00557	0.0435	0.482721
58	0.001258	0.0098	0.496097
59	-0.008298	-0.0648	0.474268
60	-0.008285	-0.0647	0.474309

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.913266	7.1328	0
2	-0.194813	-1.5215	0.066646
3	-0.137843	-1.0766	0.142953
4	-0.317901	-2.4829	0.007899
5	-0.207619	-1.6216	0.055028
6	0.006663	0.052	0.479335
7	-0.020683	-0.1615	0.436102
8	-0.238288	-1.8611	0.033776
9	-0.038732	-0.3025	0.381647
10	-0.095764	-0.7479	0.228686
11	0.024136	0.1885	0.425553
12	-0.20952	-1.6364	0.053452
13	0.303274	2.3686	0.010518
14	0.058974	0.4606	0.323362
15	-0.004894	-0.0382	0.484817
16	-0.250413	-1.9558	0.027537
17	-0.04437	-0.3465	0.365064
18	-0.130044	-1.0157	0.156898
19	-0.000952	-0.0074	0.497045
20	-0.096939	-0.7571	0.225948
21	0.052454	0.4097	0.341738
22	0.021741	0.1698	0.432863
23	-0.053809	-0.4203	0.337886
24	-0.152523	-1.1912	0.119086
25	0.149752	1.1696	0.123356
26	-0.058217	-0.4547	0.325472
27	0.041736	0.326	0.372782
28	-0.090083	-0.7036	0.242187
29	0.050485	0.3943	0.347367
30	-0.086937	-0.679	0.249854
31	-0.037749	-0.2948	0.384562
32	-0.024264	-0.1895	0.425163
33	0.072022	0.5625	0.287915
34	-0.076214	-0.5953	0.276938
35	0.012479	0.0975	0.46134
36	-0.032902	-0.257	0.399031
37	-0.029957	-0.234	0.407895
38	-0.050308	-0.3929	0.347876
39	-0.037718	-0.2946	0.384654
40	0.043818	0.3422	0.366678
41	0.065215	0.5093	0.306174
42	0.020944	0.1636	0.435304
43	-0.089713	-0.7007	0.243082
44	-0.02029	-0.1585	0.437304
45	0.023855	0.1863	0.426409
46	-0.038828	-0.3033	0.381362
47	0.029191	0.228	0.410208
48	-0.086316	-0.6741	0.251382
49	-0.071689	-0.5599	0.288796
50	0.090064	0.7034	0.242235
51	-0.025391	-0.1983	0.421732
52	0.081553	0.6369	0.263271
53	-0.051116	-0.3992	0.345561
54	-0.074	-0.578	0.282709
55	0.031401	0.2453	0.403543
56	0.029773	0.2325	0.408452
57	-0.078271	-0.6113	0.271631
58	-0.059699	-0.4663	0.321344
59	-0.016028	-0.1252	0.450397
60	0.073562	0.5745	0.283858

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458826j1hoghyi2u7178k/1o11r1260458685.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458826j1hoghyi2u7178k/1o11r1260458685.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458826j1hoghyi2u7178k/2nmga1260458685.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260458826j1hoghyi2u7178k/2nmga1260458685.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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