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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: Mon, 21 Dec 2009 05:47:04 -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/21/t1261399999p4y6ynye0u85m6k.htm/, Retrieved Mon, 21 Dec 2009 13:53:21 +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/2009/Dec/21/t1261399999p4y6ynye0u85m6k.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 «

3030.29 2803.47 2767.63 2882.6 2863.36 2897.06 3012.61 3142.95 3032.93 3045.78 3110.52 3013.24 2987.1 2995.55 2833.18 2848.96 2794.83 2845.26 2915.02 2892.63 2604.42 2641.65 2659.81 2638.53 2720.25 2745.88 2735.7 2811.7 2799.43 2555.28 2304.98 2214.95 2065.81 1940.49 2042 1995.37 1946.81 1765.9 1635.25 1833.42 1910.43 1959.67 1969.6 2061.41 2093.48 2120.88 2174.56 2196.72 2350.44 2440.25 2408.64 2472.81 2407.6 2454.62 2448.05 2497.84 2645.64 2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293 etc...

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	0.285105	3.097	0.001221
2	0.06967	0.7568	0.225335
3	0.211663	2.2993	0.011625
4	0.183539	1.9937	0.024243
5	0.190325	2.0675	0.020439
6	0.001905	0.0207	0.491762
7	-0.013478	-0.1464	0.441922
8	0.127828	1.3886	0.08379
9	0.060946	0.662	0.254616
10	-0.106163	-1.1532	0.125574
11	0.07039	0.7646	0.22301
12	0.033454	0.3634	0.358475
13	-0.027618	-0.3	0.382349
14	0.044674	0.4853	0.314187
15	0.009369	0.1018	0.459554
16	0.058329	0.6336	0.263778
17	-0.05359	-0.5821	0.280791
18	-0.09445	-1.026	0.153497
19	0.005601	0.0608	0.475793
20	-0.110266	-1.1978	0.116698
21	-0.101607	-1.1037	0.135977
22	-0.088895	-0.9656	0.168097
23	-0.126586	-1.3751	0.085857
24	-0.067233	-0.7303	0.233316
25	-0.047417	-0.5151	0.30373
26	-0.118045	-1.2823	0.101125
27	-0.030891	-0.3356	0.3689
28	0.026794	0.2911	0.385759
29	-0.032584	-0.354	0.362002
30	-0.020762	-0.2255	0.410978
31	-0.040721	-0.4423	0.329526
32	0.010313	0.112	0.455496
33	-0.027866	-0.3027	0.381324
34	-0.069024	-0.7498	0.227434
35	-0.122151	-1.3269	0.093552
36	-0.029426	-0.3196	0.3749
37	-0.04606	-0.5003	0.308884
38	-0.082759	-0.899	0.185245
39	-0.014083	-0.153	0.439336
40	-0.049667	-0.5395	0.295274
41	-0.032851	-0.3568	0.360921
42	-0.040479	-0.4397	0.330474
43	-0.082718	-0.8985	0.185362
44	-0.012124	-0.1317	0.447722
45	-0.051636	-0.5609	0.287961
46	-0.076565	-0.8317	0.203627
47	-0.091181	-0.9905	0.161983
48	-0.072734	-0.7901	0.215528
49	-0.099205	-1.0776	0.141696
50	-0.082394	-0.895	0.186299
51	-0.080423	-0.8736	0.192051
52	-0.103677	-1.1262	0.131179
53	-0.014348	-0.1559	0.438205
54	-0.02945	-0.3199	0.374801
55	-0.046337	-0.5033	0.30783
56	-0.010017	-0.1088	0.45677
57	-0.049563	-0.5384	0.295659
58	-0.043447	-0.472	0.318914
59	-0.016395	-0.1781	0.429477
60	0.011615	0.1262	0.449905

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.285105	3.097	0.001221
2	-0.012642	-0.1373	0.445503
3	0.212453	2.3078	0.011375
4	0.075754	0.8229	0.206112
5	0.136923	1.4874	0.069793
6	-0.134565	-1.4617	0.073234
7	-0.020989	-0.228	0.41002
8	0.073618	0.7997	0.212747
9	-0.002772	-0.0301	0.488016
10	-0.135627	-1.4733	0.071668
11	0.152378	1.6553	0.050265
12	-0.062744	-0.6816	0.248422
13	-0.013351	-0.145	0.442468
14	0.056854	0.6176	0.269018
15	0.023158	0.2516	0.400909
16	0.00689	0.0748	0.470232
17	-0.106031	-1.1518	0.125868
18	-0.025366	-0.2755	0.391691
19	-0.009301	-0.101	0.459845
20	-0.152924	-1.6612	0.049666
21	0.040136	0.436	0.33182
22	-0.059461	-0.6459	0.259794
23	-0.06878	-0.7471	0.228231
24	0.019392	0.2107	0.41676
25	0.038543	0.4187	0.338106
26	-0.068346	-0.7424	0.229651
27	0.029845	0.3242	0.37318
28	0.07788	0.846	0.199633
29	-0.008317	-0.0903	0.464081
30	-0.066954	-0.7273	0.234238
31	0.031199	0.3389	0.367642
32	0.020953	0.2276	0.410173
33	-0.105435	-1.1453	0.127199
34	0.025199	0.2737	0.392383
35	-0.111849	-1.215	0.113398
36	0.027127	0.2947	0.384381
37	-0.051615	-0.5607	0.288039
38	0.029481	0.3202	0.374675
39	0.027615	0.3	0.38236
40	-0.068246	-0.7413	0.229979
41	-0.002	-0.0217	0.491352
42	-0.008164	-0.0887	0.464742
43	-0.131479	-1.4282	0.077935
44	0.04509	0.4898	0.312593
45	-0.065947	-0.7164	0.237591
46	-0.02242	-0.2435	0.404003
47	-0.104091	-1.1307	0.130233
48	0.017094	0.1857	0.426503
49	-0.059394	-0.6452	0.260032
50	-0.028325	-0.3077	0.379432
51	-0.000611	-0.0066	0.497359
52	-0.031974	-0.3473	0.364481
53	-0.018407	-0.1999	0.420933
54	0.058691	0.6376	0.262501
55	-0.078465	-0.8523	0.197874
56	0.027407	0.2977	0.383223
57	-0.092546	-1.0053	0.158404
58	-0.033795	-0.3671	0.357099
59	-0.00668	-0.0726	0.471138
60	0.014243	0.1547	0.438655

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261399999p4y6ynye0u85m6k/1esuh1261399622.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261399999p4y6ynye0u85m6k/1esuh1261399622.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261399999p4y6ynye0u85m6k/25yb41261399622.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261399999p4y6ynye0u85m6k/25yb41261399622.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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