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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 24 Dec 2010 09:39:58 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t12931834741r7dpdx60zr3val.htm/, Retrieved Tue, 30 Apr 2024 02:18:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114663, Retrieved Tue, 30 Apr 2024 02:18:44 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

192

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
F   PD      [ARIMA Forecasting] [ARIMA model faill...] [2010-12-03 14:08:17] [95e8426e0df851c9330605aa1e892ab5]
-   P         [ARIMA Forecasting] [verbetering forec...] [2010-12-13 18:37:08] [bd591a1ebb67d263a02e7adae3fa1a4d]
-   PD          [ARIMA Forecasting] [Forecast] [2010-12-21 10:29:11] [bd591a1ebb67d263a02e7adae3fa1a4d]
-    D              [ARIMA Forecasting] [forecast 1] [2010-12-24 09:39:58] [09489ba95453d3f5c9e6f2eaeda915af] [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	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 9 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114663&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114663&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114663&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	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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[56])
44	99.8	-	-	-	-	-	-	-
45	116.8	-	-	-	-	-	-	-
46	115.7	-	-	-	-	-	-	-
47	99.4	-	-	-	-	-	-	-
48	94.3	-	-	-	-	-	-	-
49	91	-	-	-	-	-	-	-
50	93.2	-	-	-	-	-	-	-
51	103.1	-	-	-	-	-	-	-
52	94.1	-	-	-	-	-	-	-
53	91.8	-	-	-	-	-	-	-
54	102.7	-	-	-	-	-	-	-
55	82.6	-	-	-	-	-	-	-
56	89.1	-	-	-	-	-	-	-
57	104.5	104.3227	95.4883	113.1571	0.4843	0.9996	0.0028	0.9996
58	105.1	107.1734	98.2511	116.0957	0.3244	0.7215	0.0305	1
59	95.1	94.8436	84.7362	104.951	0.4802	0.0234	0.1885	0.8673
60	88.7	87.6305	75.1938	100.0673	0.4331	0.1196	0.1466	0.4084
61	86.3	89.1867	76.3605	102.0129	0.3296	0.5296	0.3909	0.5053
62	91.8	90.4628	76.0801	104.8456	0.4277	0.7147	0.3546	0.5737
63	111.5	98.4817	82.7989	114.1646	0.0519	0.7982	0.2819	0.8795
64	99.7	92.9491	76.577	109.3212	0.2095	0.0132	0.4452	0.6775
65	97.5	90.3316	72.5785	108.0846	0.2143	0.1505	0.4356	0.5541
66	111.7	100.0103	81.3046	118.7159	0.1103	0.6037	0.389	0.8735
67	86.2	78.1833	58.6315	97.7352	0.2108	4e-04	0.329	0.1369
68	95.4	85.532	64.8533	106.2107	0.1748	0.4748	0.3676	0.3676

\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[56]) \tabularnewline
44 & 99.8 & - & - & - & - & - & - & - \tabularnewline
45 & 116.8 & - & - & - & - & - & - & - \tabularnewline
46 & 115.7 & - & - & - & - & - & - & - \tabularnewline
47 & 99.4 & - & - & - & - & - & - & - \tabularnewline
48 & 94.3 & - & - & - & - & - & - & - \tabularnewline
49 & 91 & - & - & - & - & - & - & - \tabularnewline
50 & 93.2 & - & - & - & - & - & - & - \tabularnewline
51 & 103.1 & - & - & - & - & - & - & - \tabularnewline
52 & 94.1 & - & - & - & - & - & - & - \tabularnewline
53 & 91.8 & - & - & - & - & - & - & - \tabularnewline
54 & 102.7 & - & - & - & - & - & - & - \tabularnewline
55 & 82.6 & - & - & - & - & - & - & - \tabularnewline
56 & 89.1 & - & - & - & - & - & - & - \tabularnewline
57 & 104.5 & 104.3227 & 95.4883 & 113.1571 & 0.4843 & 0.9996 & 0.0028 & 0.9996 \tabularnewline
58 & 105.1 & 107.1734 & 98.2511 & 116.0957 & 0.3244 & 0.7215 & 0.0305 & 1 \tabularnewline
59 & 95.1 & 94.8436 & 84.7362 & 104.951 & 0.4802 & 0.0234 & 0.1885 & 0.8673 \tabularnewline
60 & 88.7 & 87.6305 & 75.1938 & 100.0673 & 0.4331 & 0.1196 & 0.1466 & 0.4084 \tabularnewline
61 & 86.3 & 89.1867 & 76.3605 & 102.0129 & 0.3296 & 0.5296 & 0.3909 & 0.5053 \tabularnewline
62 & 91.8 & 90.4628 & 76.0801 & 104.8456 & 0.4277 & 0.7147 & 0.3546 & 0.5737 \tabularnewline
63 & 111.5 & 98.4817 & 82.7989 & 114.1646 & 0.0519 & 0.7982 & 0.2819 & 0.8795 \tabularnewline
64 & 99.7 & 92.9491 & 76.577 & 109.3212 & 0.2095 & 0.0132 & 0.4452 & 0.6775 \tabularnewline
65 & 97.5 & 90.3316 & 72.5785 & 108.0846 & 0.2143 & 0.1505 & 0.4356 & 0.5541 \tabularnewline
66 & 111.7 & 100.0103 & 81.3046 & 118.7159 & 0.1103 & 0.6037 & 0.389 & 0.8735 \tabularnewline
67 & 86.2 & 78.1833 & 58.6315 & 97.7352 & 0.2108 & 4e-04 & 0.329 & 0.1369 \tabularnewline
68 & 95.4 & 85.532 & 64.8533 & 106.2107 & 0.1748 & 0.4748 & 0.3676 & 0.3676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114663&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[56])[/C][/ROW]
[ROW][C]44[/C][C]99.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]116.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]115.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]99.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]94.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]91[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]93.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]103.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]94.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]91.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]102.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]82.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]89.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]104.5[/C][C]104.3227[/C][C]95.4883[/C][C]113.1571[/C][C]0.4843[/C][C]0.9996[/C][C]0.0028[/C][C]0.9996[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]107.1734[/C][C]98.2511[/C][C]116.0957[/C][C]0.3244[/C][C]0.7215[/C][C]0.0305[/C][C]1[/C][/ROW]
[ROW][C]59[/C][C]95.1[/C][C]94.8436[/C][C]84.7362[/C][C]104.951[/C][C]0.4802[/C][C]0.0234[/C][C]0.1885[/C][C]0.8673[/C][/ROW]
[ROW][C]60[/C][C]88.7[/C][C]87.6305[/C][C]75.1938[/C][C]100.0673[/C][C]0.4331[/C][C]0.1196[/C][C]0.1466[/C][C]0.4084[/C][/ROW]
[ROW][C]61[/C][C]86.3[/C][C]89.1867[/C][C]76.3605[/C][C]102.0129[/C][C]0.3296[/C][C]0.5296[/C][C]0.3909[/C][C]0.5053[/C][/ROW]
[ROW][C]62[/C][C]91.8[/C][C]90.4628[/C][C]76.0801[/C][C]104.8456[/C][C]0.4277[/C][C]0.7147[/C][C]0.3546[/C][C]0.5737[/C][/ROW]
[ROW][C]63[/C][C]111.5[/C][C]98.4817[/C][C]82.7989[/C][C]114.1646[/C][C]0.0519[/C][C]0.7982[/C][C]0.2819[/C][C]0.8795[/C][/ROW]
[ROW][C]64[/C][C]99.7[/C][C]92.9491[/C][C]76.577[/C][C]109.3212[/C][C]0.2095[/C][C]0.0132[/C][C]0.4452[/C][C]0.6775[/C][/ROW]
[ROW][C]65[/C][C]97.5[/C][C]90.3316[/C][C]72.5785[/C][C]108.0846[/C][C]0.2143[/C][C]0.1505[/C][C]0.4356[/C][C]0.5541[/C][/ROW]
[ROW][C]66[/C][C]111.7[/C][C]100.0103[/C][C]81.3046[/C][C]118.7159[/C][C]0.1103[/C][C]0.6037[/C][C]0.389[/C][C]0.8735[/C][/ROW]
[ROW][C]67[/C][C]86.2[/C][C]78.1833[/C][C]58.6315[/C][C]97.7352[/C][C]0.2108[/C][C]4e-04[/C][C]0.329[/C][C]0.1369[/C][/ROW]
[ROW][C]68[/C][C]95.4[/C][C]85.532[/C][C]64.8533[/C][C]106.2107[/C][C]0.1748[/C][C]0.4748[/C][C]0.3676[/C][C]0.3676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114663&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114663&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[56])
44	99.8	-	-	-	-	-	-	-
45	116.8	-	-	-	-	-	-	-
46	115.7	-	-	-	-	-	-	-
47	99.4	-	-	-	-	-	-	-
48	94.3	-	-	-	-	-	-	-
49	91	-	-	-	-	-	-	-
50	93.2	-	-	-	-	-	-	-
51	103.1	-	-	-	-	-	-	-
52	94.1	-	-	-	-	-	-	-
53	91.8	-	-	-	-	-	-	-
54	102.7	-	-	-	-	-	-	-
55	82.6	-	-	-	-	-	-	-
56	89.1	-	-	-	-	-	-	-
57	104.5	104.3227	95.4883	113.1571	0.4843	0.9996	0.0028	0.9996
58	105.1	107.1734	98.2511	116.0957	0.3244	0.7215	0.0305	1
59	95.1	94.8436	84.7362	104.951	0.4802	0.0234	0.1885	0.8673
60	88.7	87.6305	75.1938	100.0673	0.4331	0.1196	0.1466	0.4084
61	86.3	89.1867	76.3605	102.0129	0.3296	0.5296	0.3909	0.5053
62	91.8	90.4628	76.0801	104.8456	0.4277	0.7147	0.3546	0.5737
63	111.5	98.4817	82.7989	114.1646	0.0519	0.7982	0.2819	0.8795
64	99.7	92.9491	76.577	109.3212	0.2095	0.0132	0.4452	0.6775
65	97.5	90.3316	72.5785	108.0846	0.2143	0.1505	0.4356	0.5541
66	111.7	100.0103	81.3046	118.7159	0.1103	0.6037	0.389	0.8735
67	86.2	78.1833	58.6315	97.7352	0.2108	4e-04	0.329	0.1369
68	95.4	85.532	64.8533	106.2107	0.1748	0.4748	0.3676	0.3676

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
57	0.0432	0.0017	0	0.0314	0	0
58	0.0425	-0.0193	0.0105	4.299	2.1652	1.4715
59	0.0544	0.0027	0.0079	0.0657	1.4654	1.2105
60	0.0724	0.0122	0.009	1.1437	1.385	1.1769
61	0.0734	-0.0324	0.0137	8.3331	2.7746	1.6657
62	0.0811	0.0148	0.0139	1.788	2.6102	1.6156
63	0.0812	0.1322	0.0308	169.4756	26.4481	5.1428
64	0.0899	0.0726	0.036	45.5745	28.8389	5.3702
65	0.1003	0.0794	0.0408	51.3864	31.3442	5.5986
66	0.0954	0.1169	0.0484	136.65	41.8748	6.4711
67	0.1276	0.1025	0.0533	64.2669	43.9104	6.6265
68	0.1233	0.1154	0.0585	97.3768	48.3659	6.9546

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
57 & 0.0432 & 0.0017 & 0 & 0.0314 & 0 & 0 \tabularnewline
58 & 0.0425 & -0.0193 & 0.0105 & 4.299 & 2.1652 & 1.4715 \tabularnewline
59 & 0.0544 & 0.0027 & 0.0079 & 0.0657 & 1.4654 & 1.2105 \tabularnewline
60 & 0.0724 & 0.0122 & 0.009 & 1.1437 & 1.385 & 1.1769 \tabularnewline
61 & 0.0734 & -0.0324 & 0.0137 & 8.3331 & 2.7746 & 1.6657 \tabularnewline
62 & 0.0811 & 0.0148 & 0.0139 & 1.788 & 2.6102 & 1.6156 \tabularnewline
63 & 0.0812 & 0.1322 & 0.0308 & 169.4756 & 26.4481 & 5.1428 \tabularnewline
64 & 0.0899 & 0.0726 & 0.036 & 45.5745 & 28.8389 & 5.3702 \tabularnewline
65 & 0.1003 & 0.0794 & 0.0408 & 51.3864 & 31.3442 & 5.5986 \tabularnewline
66 & 0.0954 & 0.1169 & 0.0484 & 136.65 & 41.8748 & 6.4711 \tabularnewline
67 & 0.1276 & 0.1025 & 0.0533 & 64.2669 & 43.9104 & 6.6265 \tabularnewline
68 & 0.1233 & 0.1154 & 0.0585 & 97.3768 & 48.3659 & 6.9546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114663&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]57[/C][C]0.0432[/C][C]0.0017[/C][C]0[/C][C]0.0314[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]0.0425[/C][C]-0.0193[/C][C]0.0105[/C][C]4.299[/C][C]2.1652[/C][C]1.4715[/C][/ROW]
[ROW][C]59[/C][C]0.0544[/C][C]0.0027[/C][C]0.0079[/C][C]0.0657[/C][C]1.4654[/C][C]1.2105[/C][/ROW]
[ROW][C]60[/C][C]0.0724[/C][C]0.0122[/C][C]0.009[/C][C]1.1437[/C][C]1.385[/C][C]1.1769[/C][/ROW]
[ROW][C]61[/C][C]0.0734[/C][C]-0.0324[/C][C]0.0137[/C][C]8.3331[/C][C]2.7746[/C][C]1.6657[/C][/ROW]
[ROW][C]62[/C][C]0.0811[/C][C]0.0148[/C][C]0.0139[/C][C]1.788[/C][C]2.6102[/C][C]1.6156[/C][/ROW]
[ROW][C]63[/C][C]0.0812[/C][C]0.1322[/C][C]0.0308[/C][C]169.4756[/C][C]26.4481[/C][C]5.1428[/C][/ROW]
[ROW][C]64[/C][C]0.0899[/C][C]0.0726[/C][C]0.036[/C][C]45.5745[/C][C]28.8389[/C][C]5.3702[/C][/ROW]
[ROW][C]65[/C][C]0.1003[/C][C]0.0794[/C][C]0.0408[/C][C]51.3864[/C][C]31.3442[/C][C]5.5986[/C][/ROW]
[ROW][C]66[/C][C]0.0954[/C][C]0.1169[/C][C]0.0484[/C][C]136.65[/C][C]41.8748[/C][C]6.4711[/C][/ROW]
[ROW][C]67[/C][C]0.1276[/C][C]0.1025[/C][C]0.0533[/C][C]64.2669[/C][C]43.9104[/C][C]6.6265[/C][/ROW]
[ROW][C]68[/C][C]0.1233[/C][C]0.1154[/C][C]0.0585[/C][C]97.3768[/C][C]48.3659[/C][C]6.9546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114663&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114663&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
57	0.0432	0.0017	0	0.0314	0	0
58	0.0425	-0.0193	0.0105	4.299	2.1652	1.4715
59	0.0544	0.0027	0.0079	0.0657	1.4654	1.2105
60	0.0724	0.0122	0.009	1.1437	1.385	1.1769
61	0.0734	-0.0324	0.0137	8.3331	2.7746	1.6657
62	0.0811	0.0148	0.0139	1.788	2.6102	1.6156
63	0.0812	0.1322	0.0308	169.4756	26.4481	5.1428
64	0.0899	0.0726	0.036	45.5745	28.8389	5.3702
65	0.1003	0.0794	0.0408	51.3864	31.3442	5.5986
66	0.0954	0.1169	0.0484	136.65	41.8748	6.4711
67	0.1276	0.1025	0.0533	64.2669	43.9104	6.6265
68	0.1233	0.1154	0.0585	97.3768	48.3659	6.9546

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; 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