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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 23 Dec 2011 07:03:11 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324641836bhzs6qnsk7am88g.htm/, Retrieved Mon, 29 Apr 2024 17:55:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160326, Retrieved Mon, 29 Apr 2024 17:55:57 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

112

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Variance Reduction Matrix] [] [2011-12-06 08:04:41] [80bca13c5f9401fbb753952fd2952f4a]
- RMP   [(Partial) Autocorrelation Function] [] [2011-12-06 08:29:14] [80bca13c5f9401fbb753952fd2952f4a]
-   P     [(Partial) Autocorrelation Function] [] [2011-12-06 08:31:19] [80bca13c5f9401fbb753952fd2952f4a]
- RMP       [Variance Reduction Matrix] [] [2011-12-06 08:45:18] [80bca13c5f9401fbb753952fd2952f4a]
- RM          [ARIMA Backward Selection] [] [2011-12-06 09:03:08] [80bca13c5f9401fbb753952fd2952f4a]
- RM            [ARIMA Forecasting] [] [2011-12-06 09:14:29] [80bca13c5f9401fbb753952fd2952f4a]
-   PD              [ARIMA Forecasting] [Paper arima forec...] [2011-12-23 12:03:11] [c18e83883fa784c15a15b4fbc0636edd] [Current]

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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	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160326&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160326&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160326&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	'Herman Ole Andreas Wold' @ wold.wessa.net

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[60])
48	516141	-	-	-	-	-	-	-
49	528222	-	-	-	-	-	-	-
50	532638	-	-	-	-	-	-	-
51	536322	-	-	-	-	-	-	-
52	536535	-	-	-	-	-	-	-
53	523597	-	-	-	-	-	-	-
54	536214	-	-	-	-	-	-	-
55	586570	-	-	-	-	-	-	-
56	596594	-	-	-	-	-	-	-
57	580523	-	-	-	-	-	-	-
58	564478	-	-	-	-	-	-	-
59	557560	-	-	-	-	-	-	-
60	575093	-	-	-	-	-	-	-
61	580112	585710.9778	570111.4825	601563.8108	0.2444	0.9054	1	0.9054
62	574761	588457.9236	564865.9487	612631.4299	0.1334	0.7507	1	0.8607
63	563250	588484.7	557779.28	620182.5925	0.0593	0.8019	0.9994	0.7962
64	551531	587614.724	550191.4236	626525.1659	0.0346	0.8901	0.995	0.7359
65	537034	576853.9476	533391.1439	622375.1892	0.0432	0.8622	0.9891	0.5302
66	544686	586472.769	536202.6462	639469.4782	0.0611	0.9663	0.9685	0.6631
67	600991	641672.9443	581972.0624	704905.1926	0.1037	0.9987	0.9562	0.9805
68	604378	652612.1049	585759.4752	723845.2313	0.0922	0.9222	0.9384	0.9835
69	586111	639577.8219	567224.7303	717203.1757	0.0885	0.8129	0.932	0.9483
70	563668	622976.5567	545690.7798	706482.9922	0.082	0.8066	0.9151	0.8695
71	548604	613341.9345	530888.4096	703036.8953	0.0786	0.8611	0.8886	0.7984
72	551174	626906.2686	537473.7063	724719.8128	0.0646	0.9417	0.8504	0.8504

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[60]) \tabularnewline
48 & 516141 & - & - & - & - & - & - & - \tabularnewline
49 & 528222 & - & - & - & - & - & - & - \tabularnewline
50 & 532638 & - & - & - & - & - & - & - \tabularnewline
51 & 536322 & - & - & - & - & - & - & - \tabularnewline
52 & 536535 & - & - & - & - & - & - & - \tabularnewline
53 & 523597 & - & - & - & - & - & - & - \tabularnewline
54 & 536214 & - & - & - & - & - & - & - \tabularnewline
55 & 586570 & - & - & - & - & - & - & - \tabularnewline
56 & 596594 & - & - & - & - & - & - & - \tabularnewline
57 & 580523 & - & - & - & - & - & - & - \tabularnewline
58 & 564478 & - & - & - & - & - & - & - \tabularnewline
59 & 557560 & - & - & - & - & - & - & - \tabularnewline
60 & 575093 & - & - & - & - & - & - & - \tabularnewline
61 & 580112 & 585710.9778 & 570111.4825 & 601563.8108 & 0.2444 & 0.9054 & 1 & 0.9054 \tabularnewline
62 & 574761 & 588457.9236 & 564865.9487 & 612631.4299 & 0.1334 & 0.7507 & 1 & 0.8607 \tabularnewline
63 & 563250 & 588484.7 & 557779.28 & 620182.5925 & 0.0593 & 0.8019 & 0.9994 & 0.7962 \tabularnewline
64 & 551531 & 587614.724 & 550191.4236 & 626525.1659 & 0.0346 & 0.8901 & 0.995 & 0.7359 \tabularnewline
65 & 537034 & 576853.9476 & 533391.1439 & 622375.1892 & 0.0432 & 0.8622 & 0.9891 & 0.5302 \tabularnewline
66 & 544686 & 586472.769 & 536202.6462 & 639469.4782 & 0.0611 & 0.9663 & 0.9685 & 0.6631 \tabularnewline
67 & 600991 & 641672.9443 & 581972.0624 & 704905.1926 & 0.1037 & 0.9987 & 0.9562 & 0.9805 \tabularnewline
68 & 604378 & 652612.1049 & 585759.4752 & 723845.2313 & 0.0922 & 0.9222 & 0.9384 & 0.9835 \tabularnewline
69 & 586111 & 639577.8219 & 567224.7303 & 717203.1757 & 0.0885 & 0.8129 & 0.932 & 0.9483 \tabularnewline
70 & 563668 & 622976.5567 & 545690.7798 & 706482.9922 & 0.082 & 0.8066 & 0.9151 & 0.8695 \tabularnewline
71 & 548604 & 613341.9345 & 530888.4096 & 703036.8953 & 0.0786 & 0.8611 & 0.8886 & 0.7984 \tabularnewline
72 & 551174 & 626906.2686 & 537473.7063 & 724719.8128 & 0.0646 & 0.9417 & 0.8504 & 0.8504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160326&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[60])[/C][/ROW]
[ROW][C]48[/C][C]516141[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]528222[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]532638[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]536322[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]536535[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]523597[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]536214[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]586570[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]596594[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]580523[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]564478[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]557560[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]575093[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]580112[/C][C]585710.9778[/C][C]570111.4825[/C][C]601563.8108[/C][C]0.2444[/C][C]0.9054[/C][C]1[/C][C]0.9054[/C][/ROW]
[ROW][C]62[/C][C]574761[/C][C]588457.9236[/C][C]564865.9487[/C][C]612631.4299[/C][C]0.1334[/C][C]0.7507[/C][C]1[/C][C]0.8607[/C][/ROW]
[ROW][C]63[/C][C]563250[/C][C]588484.7[/C][C]557779.28[/C][C]620182.5925[/C][C]0.0593[/C][C]0.8019[/C][C]0.9994[/C][C]0.7962[/C][/ROW]
[ROW][C]64[/C][C]551531[/C][C]587614.724[/C][C]550191.4236[/C][C]626525.1659[/C][C]0.0346[/C][C]0.8901[/C][C]0.995[/C][C]0.7359[/C][/ROW]
[ROW][C]65[/C][C]537034[/C][C]576853.9476[/C][C]533391.1439[/C][C]622375.1892[/C][C]0.0432[/C][C]0.8622[/C][C]0.9891[/C][C]0.5302[/C][/ROW]
[ROW][C]66[/C][C]544686[/C][C]586472.769[/C][C]536202.6462[/C][C]639469.4782[/C][C]0.0611[/C][C]0.9663[/C][C]0.9685[/C][C]0.6631[/C][/ROW]
[ROW][C]67[/C][C]600991[/C][C]641672.9443[/C][C]581972.0624[/C][C]704905.1926[/C][C]0.1037[/C][C]0.9987[/C][C]0.9562[/C][C]0.9805[/C][/ROW]
[ROW][C]68[/C][C]604378[/C][C]652612.1049[/C][C]585759.4752[/C][C]723845.2313[/C][C]0.0922[/C][C]0.9222[/C][C]0.9384[/C][C]0.9835[/C][/ROW]
[ROW][C]69[/C][C]586111[/C][C]639577.8219[/C][C]567224.7303[/C][C]717203.1757[/C][C]0.0885[/C][C]0.8129[/C][C]0.932[/C][C]0.9483[/C][/ROW]
[ROW][C]70[/C][C]563668[/C][C]622976.5567[/C][C]545690.7798[/C][C]706482.9922[/C][C]0.082[/C][C]0.8066[/C][C]0.9151[/C][C]0.8695[/C][/ROW]
[ROW][C]71[/C][C]548604[/C][C]613341.9345[/C][C]530888.4096[/C][C]703036.8953[/C][C]0.0786[/C][C]0.8611[/C][C]0.8886[/C][C]0.7984[/C][/ROW]
[ROW][C]72[/C][C]551174[/C][C]626906.2686[/C][C]537473.7063[/C][C]724719.8128[/C][C]0.0646[/C][C]0.9417[/C][C]0.8504[/C][C]0.8504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160326&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160326&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[60])
48	516141	-	-	-	-	-	-	-
49	528222	-	-	-	-	-	-	-
50	532638	-	-	-	-	-	-	-
51	536322	-	-	-	-	-	-	-
52	536535	-	-	-	-	-	-	-
53	523597	-	-	-	-	-	-	-
54	536214	-	-	-	-	-	-	-
55	586570	-	-	-	-	-	-	-
56	596594	-	-	-	-	-	-	-
57	580523	-	-	-	-	-	-	-
58	564478	-	-	-	-	-	-	-
59	557560	-	-	-	-	-	-	-
60	575093	-	-	-	-	-	-	-
61	580112	585710.9778	570111.4825	601563.8108	0.2444	0.9054	1	0.9054
62	574761	588457.9236	564865.9487	612631.4299	0.1334	0.7507	1	0.8607
63	563250	588484.7	557779.28	620182.5925	0.0593	0.8019	0.9994	0.7962
64	551531	587614.724	550191.4236	626525.1659	0.0346	0.8901	0.995	0.7359
65	537034	576853.9476	533391.1439	622375.1892	0.0432	0.8622	0.9891	0.5302
66	544686	586472.769	536202.6462	639469.4782	0.0611	0.9663	0.9685	0.6631
67	600991	641672.9443	581972.0624	704905.1926	0.1037	0.9987	0.9562	0.9805
68	604378	652612.1049	585759.4752	723845.2313	0.0922	0.9222	0.9384	0.9835
69	586111	639577.8219	567224.7303	717203.1757	0.0885	0.8129	0.932	0.9483
70	563668	622976.5567	545690.7798	706482.9922	0.082	0.8066	0.9151	0.8695
71	548604	613341.9345	530888.4096	703036.8953	0.0786	0.8611	0.8886	0.7984
72	551174	626906.2686	537473.7063	724719.8128	0.0646	0.9417	0.8504	0.8504

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.0138	-0.0096	0	31348552.0423	0	0
62	0.021	-0.0233	0.0164	187605716.4302	109477134.2363	10463.1321
63	0.0275	-0.0429	0.0252	636790083.1442	285248117.2056	16889.29
64	0.0338	-0.0614	0.0343	1302035136.9868	539444872.1509	23225.9526
65	0.0403	-0.069	0.0412	1585628229.4966	748681543.62	27362.0457
66	0.0461	-0.0713	0.0462	1746134060.2392	914923629.7232	30247.7045
67	0.0503	-0.0634	0.0487	1655020590.1094	1020651766.9212	31947.641
68	0.0557	-0.0739	0.0518	2326528874.2812	1183886405.3412	34407.6504
69	0.0619	-0.0836	0.0554	2858701048.3182	1369976921.2276	37013.1993
70	0.0684	-0.0952	0.0594	3517504893.3279	1584729718.4376	39808.6639
71	0.0746	-0.1055	0.0636	4191000166.1067	1821663395.4984	42680.9489
72	0.0796	-0.1208	0.0683	5735376501.5665	2147806154.3374	46344.4296

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.0138 & -0.0096 & 0 & 31348552.0423 & 0 & 0 \tabularnewline
62 & 0.021 & -0.0233 & 0.0164 & 187605716.4302 & 109477134.2363 & 10463.1321 \tabularnewline
63 & 0.0275 & -0.0429 & 0.0252 & 636790083.1442 & 285248117.2056 & 16889.29 \tabularnewline
64 & 0.0338 & -0.0614 & 0.0343 & 1302035136.9868 & 539444872.1509 & 23225.9526 \tabularnewline
65 & 0.0403 & -0.069 & 0.0412 & 1585628229.4966 & 748681543.62 & 27362.0457 \tabularnewline
66 & 0.0461 & -0.0713 & 0.0462 & 1746134060.2392 & 914923629.7232 & 30247.7045 \tabularnewline
67 & 0.0503 & -0.0634 & 0.0487 & 1655020590.1094 & 1020651766.9212 & 31947.641 \tabularnewline
68 & 0.0557 & -0.0739 & 0.0518 & 2326528874.2812 & 1183886405.3412 & 34407.6504 \tabularnewline
69 & 0.0619 & -0.0836 & 0.0554 & 2858701048.3182 & 1369976921.2276 & 37013.1993 \tabularnewline
70 & 0.0684 & -0.0952 & 0.0594 & 3517504893.3279 & 1584729718.4376 & 39808.6639 \tabularnewline
71 & 0.0746 & -0.1055 & 0.0636 & 4191000166.1067 & 1821663395.4984 & 42680.9489 \tabularnewline
72 & 0.0796 & -0.1208 & 0.0683 & 5735376501.5665 & 2147806154.3374 & 46344.4296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160326&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]61[/C][C]0.0138[/C][C]-0.0096[/C][C]0[/C][C]31348552.0423[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.021[/C][C]-0.0233[/C][C]0.0164[/C][C]187605716.4302[/C][C]109477134.2363[/C][C]10463.1321[/C][/ROW]
[ROW][C]63[/C][C]0.0275[/C][C]-0.0429[/C][C]0.0252[/C][C]636790083.1442[/C][C]285248117.2056[/C][C]16889.29[/C][/ROW]
[ROW][C]64[/C][C]0.0338[/C][C]-0.0614[/C][C]0.0343[/C][C]1302035136.9868[/C][C]539444872.1509[/C][C]23225.9526[/C][/ROW]
[ROW][C]65[/C][C]0.0403[/C][C]-0.069[/C][C]0.0412[/C][C]1585628229.4966[/C][C]748681543.62[/C][C]27362.0457[/C][/ROW]
[ROW][C]66[/C][C]0.0461[/C][C]-0.0713[/C][C]0.0462[/C][C]1746134060.2392[/C][C]914923629.7232[/C][C]30247.7045[/C][/ROW]
[ROW][C]67[/C][C]0.0503[/C][C]-0.0634[/C][C]0.0487[/C][C]1655020590.1094[/C][C]1020651766.9212[/C][C]31947.641[/C][/ROW]
[ROW][C]68[/C][C]0.0557[/C][C]-0.0739[/C][C]0.0518[/C][C]2326528874.2812[/C][C]1183886405.3412[/C][C]34407.6504[/C][/ROW]
[ROW][C]69[/C][C]0.0619[/C][C]-0.0836[/C][C]0.0554[/C][C]2858701048.3182[/C][C]1369976921.2276[/C][C]37013.1993[/C][/ROW]
[ROW][C]70[/C][C]0.0684[/C][C]-0.0952[/C][C]0.0594[/C][C]3517504893.3279[/C][C]1584729718.4376[/C][C]39808.6639[/C][/ROW]
[ROW][C]71[/C][C]0.0746[/C][C]-0.1055[/C][C]0.0636[/C][C]4191000166.1067[/C][C]1821663395.4984[/C][C]42680.9489[/C][/ROW]
[ROW][C]72[/C][C]0.0796[/C][C]-0.1208[/C][C]0.0683[/C][C]5735376501.5665[/C][C]2147806154.3374[/C][C]46344.4296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160326&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160326&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.0138	-0.0096	0	31348552.0423	0	0
62	0.021	-0.0233	0.0164	187605716.4302	109477134.2363	10463.1321
63	0.0275	-0.0429	0.0252	636790083.1442	285248117.2056	16889.29
64	0.0338	-0.0614	0.0343	1302035136.9868	539444872.1509	23225.9526
65	0.0403	-0.069	0.0412	1585628229.4966	748681543.62	27362.0457
66	0.0461	-0.0713	0.0462	1746134060.2392	914923629.7232	30247.7045
67	0.0503	-0.0634	0.0487	1655020590.1094	1020651766.9212	31947.641
68	0.0557	-0.0739	0.0518	2326528874.2812	1183886405.3412	34407.6504
69	0.0619	-0.0836	0.0554	2858701048.3182	1369976921.2276	37013.1993
70	0.0684	-0.0952	0.0594	3517504893.3279	1584729718.4376	39808.6639
71	0.0746	-0.1055	0.0636	4191000166.1067	1821663395.4984	42680.9489
72	0.0796	-0.1208	0.0683	5735376501.5665	2147806154.3374	46344.4296

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 0.4 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 0.4 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
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,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code