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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Wed, 21 Dec 2011 05:55:20 -0500

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/2011/Dec/21/t132446493783uvv6awvwdhb41.htm/, Retrieved Tue, 07 May 2024 17:14:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158481, Retrieved Tue, 07 May 2024 17:14:06 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

101

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

-     [Univariate Data Series] [web traffic] [2010-10-19 15:13:07] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Traffic] [2010-11-29 09:57:15] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Traffic] [2010-11-29 11:05:08] [b98453cac15ba1066b407e146608df68]
- RMP       [ARIMA Forecasting] [Traffic] [2010-11-29 21:10:32] [b98453cac15ba1066b407e146608df68]
- R PD        [ARIMA Forecasting] [] [2011-12-06 10:39:07] [aba4febe8a2e49e81bdc61a6c01f5c21]
-   PD          [ARIMA Forecasting] [] [2011-12-20 15:47:34] [aba4febe8a2e49e81bdc61a6c01f5c21]
- R               [ARIMA Forecasting] [ARIMA Forecasting CV] [2011-12-20 15:48:10] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMPD              [ARIMA Backward Selection] [paper arima backw...] [2011-12-21 10:36:30] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM                    [ARIMA Forecasting] [paper arima forec...] [2011-12-21 10:55:20] [3627de22d386f4cb93d383ef7c1ade7f] [Current]

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Dataseries X:

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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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158481&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158481&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.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[140])
128	481	-	-	-	-	-	-	-
129	1626	-	-	-	-	-	-	-
130	884	-	-	-	-	-	-	-
131	1187	-	-	-	-	-	-	-
132	488	-	-	-	-	-	-	-
133	403	-	-	-	-	-	-	-
134	977	-	-	-	-	-	-	-
135	1525	-	-	-	-	-	-	-
136	551	-	-	-	-	-	-	-
137	1807	-	-	-	-	-	-	-
138	723	-	-	-	-	-	-	-
139	632	-	-	-	-	-	-	-
140	898	-	-	-	-	-	-	-
141	621	702.7884	-181.1175	1586.6942	0.428	0.3326	0.0203	0.3326
142	1606	660.823	-249.4767	1571.1228	0.0209	0.5342	0.3154	0.3048
143	811	710.1628	-273.9603	1694.2859	0.4204	0.0372	0.1711	0.3542
144	716	626.9402	-454.4631	1708.3434	0.4359	0.3693	0.5994	0.3116
145	1001	727.404	-398.7157	1853.5237	0.317	0.5079	0.7138	0.3833
146	732	616.097	-565.3037	1797.4977	0.4238	0.2616	0.2747	0.32
147	1024	539.0414	-690.9902	1769.073	0.2198	0.3792	0.0581	0.2837
148	831	592.105	-676.9631	1861.173	0.3561	0.2524	0.5253	0.3183
149	0	460.0698	-847.0456	1767.1851	0.2451	0.289	0.0217	0.2557
150	85	545.1323	-795.462	1885.7267	0.2506	0.7873	0.3974	0.303
151	0	557.1987	-813.308	1927.7054	0.2128	0.7503	0.4574	0.313
152	0	471.4278	-926.6434	1869.4989	0.2543	0.7457	0.2749	0.2749
153	0	574.4439	-840.1802	1989.0681	0.213	0.787	0.4743	0.327
154	0	488.048	-947.2274	1923.3234	0.2526	0.7474	0.0634	0.2878
155	773	497.7273	-955.0163	1950.471	0.3552	0.7491	0.3363	0.2946
156	1128	418.9782	-1048.9982	1886.9546	0.1719	0.3182	0.3458	0.2612
157	0	389.7934	-1093.0504	1872.6373	0.3032	0.1646	0.2096	0.2509
158	0	436.3382	-1059.7313	1932.4076	0.2838	0.7162	0.3492	0.2726
159	74	479.0694	-1029.1384	1987.2773	0.2993	0.7332	0.2394	0.2931
160	259	368.5913	-1150.8808	1888.0634	0.4438	0.648	0.2754	0.2473
161	69	483.5934	-1046.1482	2013.335	0.2976	0.6132	0.7322	0.2977
162	301	361.782	-1177.4228	1900.9868	0.4692	0.6454	0.6377	0.2474
163	0	340.1037	-1207.8173	1888.0247	0.3334	0.5197	0.6666	0.24
164	668	358.6755	-1197.2553	1914.6062	0.3484	0.6743	0.6743	0.2484

\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[140]) \tabularnewline
128 & 481 & - & - & - & - & - & - & - \tabularnewline
129 & 1626 & - & - & - & - & - & - & - \tabularnewline
130 & 884 & - & - & - & - & - & - & - \tabularnewline
131 & 1187 & - & - & - & - & - & - & - \tabularnewline
132 & 488 & - & - & - & - & - & - & - \tabularnewline
133 & 403 & - & - & - & - & - & - & - \tabularnewline
134 & 977 & - & - & - & - & - & - & - \tabularnewline
135 & 1525 & - & - & - & - & - & - & - \tabularnewline
136 & 551 & - & - & - & - & - & - & - \tabularnewline
137 & 1807 & - & - & - & - & - & - & - \tabularnewline
138 & 723 & - & - & - & - & - & - & - \tabularnewline
139 & 632 & - & - & - & - & - & - & - \tabularnewline
140 & 898 & - & - & - & - & - & - & - \tabularnewline
141 & 621 & 702.7884 & -181.1175 & 1586.6942 & 0.428 & 0.3326 & 0.0203 & 0.3326 \tabularnewline
142 & 1606 & 660.823 & -249.4767 & 1571.1228 & 0.0209 & 0.5342 & 0.3154 & 0.3048 \tabularnewline
143 & 811 & 710.1628 & -273.9603 & 1694.2859 & 0.4204 & 0.0372 & 0.1711 & 0.3542 \tabularnewline
144 & 716 & 626.9402 & -454.4631 & 1708.3434 & 0.4359 & 0.3693 & 0.5994 & 0.3116 \tabularnewline
145 & 1001 & 727.404 & -398.7157 & 1853.5237 & 0.317 & 0.5079 & 0.7138 & 0.3833 \tabularnewline
146 & 732 & 616.097 & -565.3037 & 1797.4977 & 0.4238 & 0.2616 & 0.2747 & 0.32 \tabularnewline
147 & 1024 & 539.0414 & -690.9902 & 1769.073 & 0.2198 & 0.3792 & 0.0581 & 0.2837 \tabularnewline
148 & 831 & 592.105 & -676.9631 & 1861.173 & 0.3561 & 0.2524 & 0.5253 & 0.3183 \tabularnewline
149 & 0 & 460.0698 & -847.0456 & 1767.1851 & 0.2451 & 0.289 & 0.0217 & 0.2557 \tabularnewline
150 & 85 & 545.1323 & -795.462 & 1885.7267 & 0.2506 & 0.7873 & 0.3974 & 0.303 \tabularnewline
151 & 0 & 557.1987 & -813.308 & 1927.7054 & 0.2128 & 0.7503 & 0.4574 & 0.313 \tabularnewline
152 & 0 & 471.4278 & -926.6434 & 1869.4989 & 0.2543 & 0.7457 & 0.2749 & 0.2749 \tabularnewline
153 & 0 & 574.4439 & -840.1802 & 1989.0681 & 0.213 & 0.787 & 0.4743 & 0.327 \tabularnewline
154 & 0 & 488.048 & -947.2274 & 1923.3234 & 0.2526 & 0.7474 & 0.0634 & 0.2878 \tabularnewline
155 & 773 & 497.7273 & -955.0163 & 1950.471 & 0.3552 & 0.7491 & 0.3363 & 0.2946 \tabularnewline
156 & 1128 & 418.9782 & -1048.9982 & 1886.9546 & 0.1719 & 0.3182 & 0.3458 & 0.2612 \tabularnewline
157 & 0 & 389.7934 & -1093.0504 & 1872.6373 & 0.3032 & 0.1646 & 0.2096 & 0.2509 \tabularnewline
158 & 0 & 436.3382 & -1059.7313 & 1932.4076 & 0.2838 & 0.7162 & 0.3492 & 0.2726 \tabularnewline
159 & 74 & 479.0694 & -1029.1384 & 1987.2773 & 0.2993 & 0.7332 & 0.2394 & 0.2931 \tabularnewline
160 & 259 & 368.5913 & -1150.8808 & 1888.0634 & 0.4438 & 0.648 & 0.2754 & 0.2473 \tabularnewline
161 & 69 & 483.5934 & -1046.1482 & 2013.335 & 0.2976 & 0.6132 & 0.7322 & 0.2977 \tabularnewline
162 & 301 & 361.782 & -1177.4228 & 1900.9868 & 0.4692 & 0.6454 & 0.6377 & 0.2474 \tabularnewline
163 & 0 & 340.1037 & -1207.8173 & 1888.0247 & 0.3334 & 0.5197 & 0.6666 & 0.24 \tabularnewline
164 & 668 & 358.6755 & -1197.2553 & 1914.6062 & 0.3484 & 0.6743 & 0.6743 & 0.2484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158481&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[140])[/C][/ROW]
[ROW][C]128[/C][C]481[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]129[/C][C]1626[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]130[/C][C]884[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]131[/C][C]1187[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]132[/C][C]488[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]133[/C][C]403[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]134[/C][C]977[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]135[/C][C]1525[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]136[/C][C]551[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]137[/C][C]1807[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]138[/C][C]723[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]139[/C][C]632[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]140[/C][C]898[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]141[/C][C]621[/C][C]702.7884[/C][C]-181.1175[/C][C]1586.6942[/C][C]0.428[/C][C]0.3326[/C][C]0.0203[/C][C]0.3326[/C][/ROW]
[ROW][C]142[/C][C]1606[/C][C]660.823[/C][C]-249.4767[/C][C]1571.1228[/C][C]0.0209[/C][C]0.5342[/C][C]0.3154[/C][C]0.3048[/C][/ROW]
[ROW][C]143[/C][C]811[/C][C]710.1628[/C][C]-273.9603[/C][C]1694.2859[/C][C]0.4204[/C][C]0.0372[/C][C]0.1711[/C][C]0.3542[/C][/ROW]
[ROW][C]144[/C][C]716[/C][C]626.9402[/C][C]-454.4631[/C][C]1708.3434[/C][C]0.4359[/C][C]0.3693[/C][C]0.5994[/C][C]0.3116[/C][/ROW]
[ROW][C]145[/C][C]1001[/C][C]727.404[/C][C]-398.7157[/C][C]1853.5237[/C][C]0.317[/C][C]0.5079[/C][C]0.7138[/C][C]0.3833[/C][/ROW]
[ROW][C]146[/C][C]732[/C][C]616.097[/C][C]-565.3037[/C][C]1797.4977[/C][C]0.4238[/C][C]0.2616[/C][C]0.2747[/C][C]0.32[/C][/ROW]
[ROW][C]147[/C][C]1024[/C][C]539.0414[/C][C]-690.9902[/C][C]1769.073[/C][C]0.2198[/C][C]0.3792[/C][C]0.0581[/C][C]0.2837[/C][/ROW]
[ROW][C]148[/C][C]831[/C][C]592.105[/C][C]-676.9631[/C][C]1861.173[/C][C]0.3561[/C][C]0.2524[/C][C]0.5253[/C][C]0.3183[/C][/ROW]
[ROW][C]149[/C][C]0[/C][C]460.0698[/C][C]-847.0456[/C][C]1767.1851[/C][C]0.2451[/C][C]0.289[/C][C]0.0217[/C][C]0.2557[/C][/ROW]
[ROW][C]150[/C][C]85[/C][C]545.1323[/C][C]-795.462[/C][C]1885.7267[/C][C]0.2506[/C][C]0.7873[/C][C]0.3974[/C][C]0.303[/C][/ROW]
[ROW][C]151[/C][C]0[/C][C]557.1987[/C][C]-813.308[/C][C]1927.7054[/C][C]0.2128[/C][C]0.7503[/C][C]0.4574[/C][C]0.313[/C][/ROW]
[ROW][C]152[/C][C]0[/C][C]471.4278[/C][C]-926.6434[/C][C]1869.4989[/C][C]0.2543[/C][C]0.7457[/C][C]0.2749[/C][C]0.2749[/C][/ROW]
[ROW][C]153[/C][C]0[/C][C]574.4439[/C][C]-840.1802[/C][C]1989.0681[/C][C]0.213[/C][C]0.787[/C][C]0.4743[/C][C]0.327[/C][/ROW]
[ROW][C]154[/C][C]0[/C][C]488.048[/C][C]-947.2274[/C][C]1923.3234[/C][C]0.2526[/C][C]0.7474[/C][C]0.0634[/C][C]0.2878[/C][/ROW]
[ROW][C]155[/C][C]773[/C][C]497.7273[/C][C]-955.0163[/C][C]1950.471[/C][C]0.3552[/C][C]0.7491[/C][C]0.3363[/C][C]0.2946[/C][/ROW]
[ROW][C]156[/C][C]1128[/C][C]418.9782[/C][C]-1048.9982[/C][C]1886.9546[/C][C]0.1719[/C][C]0.3182[/C][C]0.3458[/C][C]0.2612[/C][/ROW]
[ROW][C]157[/C][C]0[/C][C]389.7934[/C][C]-1093.0504[/C][C]1872.6373[/C][C]0.3032[/C][C]0.1646[/C][C]0.2096[/C][C]0.2509[/C][/ROW]
[ROW][C]158[/C][C]0[/C][C]436.3382[/C][C]-1059.7313[/C][C]1932.4076[/C][C]0.2838[/C][C]0.7162[/C][C]0.3492[/C][C]0.2726[/C][/ROW]
[ROW][C]159[/C][C]74[/C][C]479.0694[/C][C]-1029.1384[/C][C]1987.2773[/C][C]0.2993[/C][C]0.7332[/C][C]0.2394[/C][C]0.2931[/C][/ROW]
[ROW][C]160[/C][C]259[/C][C]368.5913[/C][C]-1150.8808[/C][C]1888.0634[/C][C]0.4438[/C][C]0.648[/C][C]0.2754[/C][C]0.2473[/C][/ROW]
[ROW][C]161[/C][C]69[/C][C]483.5934[/C][C]-1046.1482[/C][C]2013.335[/C][C]0.2976[/C][C]0.6132[/C][C]0.7322[/C][C]0.2977[/C][/ROW]
[ROW][C]162[/C][C]301[/C][C]361.782[/C][C]-1177.4228[/C][C]1900.9868[/C][C]0.4692[/C][C]0.6454[/C][C]0.6377[/C][C]0.2474[/C][/ROW]
[ROW][C]163[/C][C]0[/C][C]340.1037[/C][C]-1207.8173[/C][C]1888.0247[/C][C]0.3334[/C][C]0.5197[/C][C]0.6666[/C][C]0.24[/C][/ROW]
[ROW][C]164[/C][C]668[/C][C]358.6755[/C][C]-1197.2553[/C][C]1914.6062[/C][C]0.3484[/C][C]0.6743[/C][C]0.6743[/C][C]0.2484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158481&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[140])
128	481	-	-	-	-	-	-	-
129	1626	-	-	-	-	-	-	-
130	884	-	-	-	-	-	-	-
131	1187	-	-	-	-	-	-	-
132	488	-	-	-	-	-	-	-
133	403	-	-	-	-	-	-	-
134	977	-	-	-	-	-	-	-
135	1525	-	-	-	-	-	-	-
136	551	-	-	-	-	-	-	-
137	1807	-	-	-	-	-	-	-
138	723	-	-	-	-	-	-	-
139	632	-	-	-	-	-	-	-
140	898	-	-	-	-	-	-	-
141	621	702.7884	-181.1175	1586.6942	0.428	0.3326	0.0203	0.3326
142	1606	660.823	-249.4767	1571.1228	0.0209	0.5342	0.3154	0.3048
143	811	710.1628	-273.9603	1694.2859	0.4204	0.0372	0.1711	0.3542
144	716	626.9402	-454.4631	1708.3434	0.4359	0.3693	0.5994	0.3116
145	1001	727.404	-398.7157	1853.5237	0.317	0.5079	0.7138	0.3833
146	732	616.097	-565.3037	1797.4977	0.4238	0.2616	0.2747	0.32
147	1024	539.0414	-690.9902	1769.073	0.2198	0.3792	0.0581	0.2837
148	831	592.105	-676.9631	1861.173	0.3561	0.2524	0.5253	0.3183
149	0	460.0698	-847.0456	1767.1851	0.2451	0.289	0.0217	0.2557
150	85	545.1323	-795.462	1885.7267	0.2506	0.7873	0.3974	0.303
151	0	557.1987	-813.308	1927.7054	0.2128	0.7503	0.4574	0.313
152	0	471.4278	-926.6434	1869.4989	0.2543	0.7457	0.2749	0.2749
153	0	574.4439	-840.1802	1989.0681	0.213	0.787	0.4743	0.327
154	0	488.048	-947.2274	1923.3234	0.2526	0.7474	0.0634	0.2878
155	773	497.7273	-955.0163	1950.471	0.3552	0.7491	0.3363	0.2946
156	1128	418.9782	-1048.9982	1886.9546	0.1719	0.3182	0.3458	0.2612
157	0	389.7934	-1093.0504	1872.6373	0.3032	0.1646	0.2096	0.2509
158	0	436.3382	-1059.7313	1932.4076	0.2838	0.7162	0.3492	0.2726
159	74	479.0694	-1029.1384	1987.2773	0.2993	0.7332	0.2394	0.2931
160	259	368.5913	-1150.8808	1888.0634	0.4438	0.648	0.2754	0.2473
161	69	483.5934	-1046.1482	2013.335	0.2976	0.6132	0.7322	0.2977
162	301	361.782	-1177.4228	1900.9868	0.4692	0.6454	0.6377	0.2474
163	0	340.1037	-1207.8173	1888.0247	0.3334	0.5197	0.6666	0.24
164	668	358.6755	-1197.2553	1914.6062	0.3484	0.6743	0.6743	0.2484

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
141	0.6417	-0.1164	0	6689.3373	0	0
142	0.7028	1.4303	0.7733	893359.4952	450024.4163	670.8386
143	0.707	0.142	0.5629	10168.1456	303405.6594	550.8227
144	0.88	0.1421	0.4577	7931.656	229537.1585	479.1004
145	0.7899	0.3761	0.4414	74854.7813	198600.6831	445.6464
146	0.9783	0.1881	0.3992	13433.5025	167739.4863	409.5601
147	1.1642	0.8997	0.4707	235184.884	177374.5431	421.1586
148	1.0935	0.4035	0.4623	57070.8409	162336.5804	402.9101
149	1.4496	-1	0.522	211664.1876	167817.4256	409.6553
150	1.2547	-0.8441	0.5542	211721.7661	172207.8597	414.9793
151	1.2549	-1	0.5947	310470.3786	184777.1796	429.8572
152	1.5131	-1	0.6285	222244.1384	187899.4261	433.4737
153	1.2564	-1	0.6571	329985.8382	198829.1501	445.9026
154	1.5004	-1	0.6816	238190.8293	201640.6986	449.0442
155	1.4892	0.5531	0.673	75775.0377	193249.6546	439.6017
156	1.7876	1.6923	0.7367	502711.9533	212591.0482	461.076
157	1.9409	-1	0.7522	151938.924	209023.2762	457.1906
158	1.7493	-1	0.766	190390.9944	207988.1495	456.0572
159	1.6062	-0.8455	0.7702	164081.2592	205677.2605	453.5165
160	2.1033	-0.2973	0.7465	12010.2528	195993.9101	442.712
161	1.6139	-0.8573	0.7518	171887.6916	194845.9949	441.4136
162	2.1707	-0.168	0.7253	3694.4545	186157.2886	431.4595
163	2.3221	-1	0.7372	115670.5427	183092.6474	427.8933
164	2.2133	0.8624	0.7424	95681.6762	179450.5236	423.616

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
141 & 0.6417 & -0.1164 & 0 & 6689.3373 & 0 & 0 \tabularnewline
142 & 0.7028 & 1.4303 & 0.7733 & 893359.4952 & 450024.4163 & 670.8386 \tabularnewline
143 & 0.707 & 0.142 & 0.5629 & 10168.1456 & 303405.6594 & 550.8227 \tabularnewline
144 & 0.88 & 0.1421 & 0.4577 & 7931.656 & 229537.1585 & 479.1004 \tabularnewline
145 & 0.7899 & 0.3761 & 0.4414 & 74854.7813 & 198600.6831 & 445.6464 \tabularnewline
146 & 0.9783 & 0.1881 & 0.3992 & 13433.5025 & 167739.4863 & 409.5601 \tabularnewline
147 & 1.1642 & 0.8997 & 0.4707 & 235184.884 & 177374.5431 & 421.1586 \tabularnewline
148 & 1.0935 & 0.4035 & 0.4623 & 57070.8409 & 162336.5804 & 402.9101 \tabularnewline
149 & 1.4496 & -1 & 0.522 & 211664.1876 & 167817.4256 & 409.6553 \tabularnewline
150 & 1.2547 & -0.8441 & 0.5542 & 211721.7661 & 172207.8597 & 414.9793 \tabularnewline
151 & 1.2549 & -1 & 0.5947 & 310470.3786 & 184777.1796 & 429.8572 \tabularnewline
152 & 1.5131 & -1 & 0.6285 & 222244.1384 & 187899.4261 & 433.4737 \tabularnewline
153 & 1.2564 & -1 & 0.6571 & 329985.8382 & 198829.1501 & 445.9026 \tabularnewline
154 & 1.5004 & -1 & 0.6816 & 238190.8293 & 201640.6986 & 449.0442 \tabularnewline
155 & 1.4892 & 0.5531 & 0.673 & 75775.0377 & 193249.6546 & 439.6017 \tabularnewline
156 & 1.7876 & 1.6923 & 0.7367 & 502711.9533 & 212591.0482 & 461.076 \tabularnewline
157 & 1.9409 & -1 & 0.7522 & 151938.924 & 209023.2762 & 457.1906 \tabularnewline
158 & 1.7493 & -1 & 0.766 & 190390.9944 & 207988.1495 & 456.0572 \tabularnewline
159 & 1.6062 & -0.8455 & 0.7702 & 164081.2592 & 205677.2605 & 453.5165 \tabularnewline
160 & 2.1033 & -0.2973 & 0.7465 & 12010.2528 & 195993.9101 & 442.712 \tabularnewline
161 & 1.6139 & -0.8573 & 0.7518 & 171887.6916 & 194845.9949 & 441.4136 \tabularnewline
162 & 2.1707 & -0.168 & 0.7253 & 3694.4545 & 186157.2886 & 431.4595 \tabularnewline
163 & 2.3221 & -1 & 0.7372 & 115670.5427 & 183092.6474 & 427.8933 \tabularnewline
164 & 2.2133 & 0.8624 & 0.7424 & 95681.6762 & 179450.5236 & 423.616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158481&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]141[/C][C]0.6417[/C][C]-0.1164[/C][C]0[/C][C]6689.3373[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]142[/C][C]0.7028[/C][C]1.4303[/C][C]0.7733[/C][C]893359.4952[/C][C]450024.4163[/C][C]670.8386[/C][/ROW]
[ROW][C]143[/C][C]0.707[/C][C]0.142[/C][C]0.5629[/C][C]10168.1456[/C][C]303405.6594[/C][C]550.8227[/C][/ROW]
[ROW][C]144[/C][C]0.88[/C][C]0.1421[/C][C]0.4577[/C][C]7931.656[/C][C]229537.1585[/C][C]479.1004[/C][/ROW]
[ROW][C]145[/C][C]0.7899[/C][C]0.3761[/C][C]0.4414[/C][C]74854.7813[/C][C]198600.6831[/C][C]445.6464[/C][/ROW]
[ROW][C]146[/C][C]0.9783[/C][C]0.1881[/C][C]0.3992[/C][C]13433.5025[/C][C]167739.4863[/C][C]409.5601[/C][/ROW]
[ROW][C]147[/C][C]1.1642[/C][C]0.8997[/C][C]0.4707[/C][C]235184.884[/C][C]177374.5431[/C][C]421.1586[/C][/ROW]
[ROW][C]148[/C][C]1.0935[/C][C]0.4035[/C][C]0.4623[/C][C]57070.8409[/C][C]162336.5804[/C][C]402.9101[/C][/ROW]
[ROW][C]149[/C][C]1.4496[/C][C]-1[/C][C]0.522[/C][C]211664.1876[/C][C]167817.4256[/C][C]409.6553[/C][/ROW]
[ROW][C]150[/C][C]1.2547[/C][C]-0.8441[/C][C]0.5542[/C][C]211721.7661[/C][C]172207.8597[/C][C]414.9793[/C][/ROW]
[ROW][C]151[/C][C]1.2549[/C][C]-1[/C][C]0.5947[/C][C]310470.3786[/C][C]184777.1796[/C][C]429.8572[/C][/ROW]
[ROW][C]152[/C][C]1.5131[/C][C]-1[/C][C]0.6285[/C][C]222244.1384[/C][C]187899.4261[/C][C]433.4737[/C][/ROW]
[ROW][C]153[/C][C]1.2564[/C][C]-1[/C][C]0.6571[/C][C]329985.8382[/C][C]198829.1501[/C][C]445.9026[/C][/ROW]
[ROW][C]154[/C][C]1.5004[/C][C]-1[/C][C]0.6816[/C][C]238190.8293[/C][C]201640.6986[/C][C]449.0442[/C][/ROW]
[ROW][C]155[/C][C]1.4892[/C][C]0.5531[/C][C]0.673[/C][C]75775.0377[/C][C]193249.6546[/C][C]439.6017[/C][/ROW]
[ROW][C]156[/C][C]1.7876[/C][C]1.6923[/C][C]0.7367[/C][C]502711.9533[/C][C]212591.0482[/C][C]461.076[/C][/ROW]
[ROW][C]157[/C][C]1.9409[/C][C]-1[/C][C]0.7522[/C][C]151938.924[/C][C]209023.2762[/C][C]457.1906[/C][/ROW]
[ROW][C]158[/C][C]1.7493[/C][C]-1[/C][C]0.766[/C][C]190390.9944[/C][C]207988.1495[/C][C]456.0572[/C][/ROW]
[ROW][C]159[/C][C]1.6062[/C][C]-0.8455[/C][C]0.7702[/C][C]164081.2592[/C][C]205677.2605[/C][C]453.5165[/C][/ROW]
[ROW][C]160[/C][C]2.1033[/C][C]-0.2973[/C][C]0.7465[/C][C]12010.2528[/C][C]195993.9101[/C][C]442.712[/C][/ROW]
[ROW][C]161[/C][C]1.6139[/C][C]-0.8573[/C][C]0.7518[/C][C]171887.6916[/C][C]194845.9949[/C][C]441.4136[/C][/ROW]
[ROW][C]162[/C][C]2.1707[/C][C]-0.168[/C][C]0.7253[/C][C]3694.4545[/C][C]186157.2886[/C][C]431.4595[/C][/ROW]
[ROW][C]163[/C][C]2.3221[/C][C]-1[/C][C]0.7372[/C][C]115670.5427[/C][C]183092.6474[/C][C]427.8933[/C][/ROW]
[ROW][C]164[/C][C]2.2133[/C][C]0.8624[/C][C]0.7424[/C][C]95681.6762[/C][C]179450.5236[/C][C]423.616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158481&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
141	0.6417	-0.1164	0	6689.3373	0	0
142	0.7028	1.4303	0.7733	893359.4952	450024.4163	670.8386
143	0.707	0.142	0.5629	10168.1456	303405.6594	550.8227
144	0.88	0.1421	0.4577	7931.656	229537.1585	479.1004
145	0.7899	0.3761	0.4414	74854.7813	198600.6831	445.6464
146	0.9783	0.1881	0.3992	13433.5025	167739.4863	409.5601
147	1.1642	0.8997	0.4707	235184.884	177374.5431	421.1586
148	1.0935	0.4035	0.4623	57070.8409	162336.5804	402.9101
149	1.4496	-1	0.522	211664.1876	167817.4256	409.6553
150	1.2547	-0.8441	0.5542	211721.7661	172207.8597	414.9793
151	1.2549	-1	0.5947	310470.3786	184777.1796	429.8572
152	1.5131	-1	0.6285	222244.1384	187899.4261	433.4737
153	1.2564	-1	0.6571	329985.8382	198829.1501	445.9026
154	1.5004	-1	0.6816	238190.8293	201640.6986	449.0442
155	1.4892	0.5531	0.673	75775.0377	193249.6546	439.6017
156	1.7876	1.6923	0.7367	502711.9533	212591.0482	461.076
157	1.9409	-1	0.7522	151938.924	209023.2762	457.1906
158	1.7493	-1	0.766	190390.9944	207988.1495	456.0572
159	1.6062	-0.8455	0.7702	164081.2592	205677.2605	453.5165
160	2.1033	-0.2973	0.7465	12010.2528	195993.9101	442.712
161	1.6139	-0.8573	0.7518	171887.6916	194845.9949	441.4136
162	2.1707	-0.168	0.7253	3694.4545	186157.2886	431.4595
163	2.3221	-1	0.7372	115670.5427	183092.6474	427.8933
164	2.2133	0.8624	0.7424	95681.6762	179450.5236	423.616

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; 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