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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Tue, 06 Dec 2011 10:43:59 -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/06/t13231865849fei9gqib9bs8nw.htm/, Retrieved Mon, 29 Apr 2024 02:33:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151696, Retrieved Mon, 29 Apr 2024 02:33:45 +0000

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User-defined keywords

Estimated Impact

127

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP           [ARIMA Forecasting] [Births] [2010-11-29 20:53:49] [b98453cac15ba1066b407e146608df68]
- R PD              [ARIMA Forecasting] [arima forecast] [2011-12-06 15:43:59] [c897fb90cb9e1f725365d7e541ad7850] [Current]

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Dataseries X:

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Boxplots

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151696&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151696&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	'Gwilym Jenkins' @ jenkins.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[121])
109	19814	-	-	-	-	-	-	-
110	12738	-	-	-	-	-	-	-
111	31566	-	-	-	-	-	-	-
112	30111	-	-	-	-	-	-	-
113	30019	-	-	-	-	-	-	-
114	31934	-	-	-	-	-	-	-
115	25826	-	-	-	-	-	-	-
116	26835	-	-	-	-	-	-	-
117	20205	-	-	-	-	-	-	-
118	17789	-	-	-	-	-	-	-
119	20520	-	-	-	-	-	-	-
120	22518	-	-	-	-	-	-	-
121	15572	-	-	-	-	-	-	-
122	11509	11548.8178	9641.4183	13833.5657	0.4864	3e-04	0.1538	3e-04
123	25447	30204.2208	25035.626	36439.8698	0.0674	1	0.3343	1
124	24090	27017.3368	22240.0288	32820.8426	0.1614	0.7021	0.1481	0.9999
125	27786	30066.0034	24585.1734	36768.6875	0.2525	0.9597	0.5055	1
126	26195	27014.5243	21947.8782	33250.8006	0.3984	0.4042	0.061	0.9998
127	20516	23485.1275	18961.3938	29088.1155	0.1495	0.1716	0.2064	0.9972
128	22759	23630.5159	18963.1257	29446.6898	0.3845	0.853	0.1401	0.9967
129	19028	19113.1635	15247.5375	23958.8207	0.4863	0.0701	0.3294	0.924
130	16971	17078.2059	13545.8226	21531.739	0.4812	0.1954	0.3772	0.7463
131	20036	18472.1395	14569.2485	23420.5586	0.2678	0.7239	0.2086	0.8747
132	22485	21482.7553	16850.9087	27387.7677	0.3697	0.6845	0.3656	0.9751
133	18730	17002.3991	13263.0703	21795.9771	0.24	0.0125	0.7207	0.7207
134	14538	11238.6077	8687.4612	14538.9201	0.025	0	0.4362	0.005
135	27561	29392.9122	22585.1521	38252.7107	0.3426	0.9995	0.8086	0.9989
136	25985	26291.6304	20084.2557	34417.498	0.4705	0.3797	0.7023	0.9951
137	34670	29258.4075	22222.9044	38521.2658	0.1261	0.7557	0.6223	0.9981
138	32066	26288.8934	19855.6967	34806.43	0.0919	0.0269	0.5086	0.9932
139	27186	22854.299	17166.8737	30425.9815	0.1311	0.0086	0.7275	0.9703
140	29586	22995.7821	17180.1543	30780.0493	0.0485	0.1457	0.5238	0.9692
141	21359	18599.7692	13822.4371	25028.2502	0.2001	4e-04	0.4481	0.822
142	21553	16619.4722	12286.6326	22480.2731	0.0495	0.0565	0.4532	0.6369
143	19573	17975.9637	13221.6218	24439.9118	0.3141	0.139	0.2661	0.767
144	24256	20905.712	15299.2752	28566.6339	0.1957	0.6334	0.3431	0.9138
145	22380	16545.7016	12044.7752	22728.5473	0.0322	0.0073	0.2443	0.6212

\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[121]) \tabularnewline
109 & 19814 & - & - & - & - & - & - & - \tabularnewline
110 & 12738 & - & - & - & - & - & - & - \tabularnewline
111 & 31566 & - & - & - & - & - & - & - \tabularnewline
112 & 30111 & - & - & - & - & - & - & - \tabularnewline
113 & 30019 & - & - & - & - & - & - & - \tabularnewline
114 & 31934 & - & - & - & - & - & - & - \tabularnewline
115 & 25826 & - & - & - & - & - & - & - \tabularnewline
116 & 26835 & - & - & - & - & - & - & - \tabularnewline
117 & 20205 & - & - & - & - & - & - & - \tabularnewline
118 & 17789 & - & - & - & - & - & - & - \tabularnewline
119 & 20520 & - & - & - & - & - & - & - \tabularnewline
120 & 22518 & - & - & - & - & - & - & - \tabularnewline
121 & 15572 & - & - & - & - & - & - & - \tabularnewline
122 & 11509 & 11548.8178 & 9641.4183 & 13833.5657 & 0.4864 & 3e-04 & 0.1538 & 3e-04 \tabularnewline
123 & 25447 & 30204.2208 & 25035.626 & 36439.8698 & 0.0674 & 1 & 0.3343 & 1 \tabularnewline
124 & 24090 & 27017.3368 & 22240.0288 & 32820.8426 & 0.1614 & 0.7021 & 0.1481 & 0.9999 \tabularnewline
125 & 27786 & 30066.0034 & 24585.1734 & 36768.6875 & 0.2525 & 0.9597 & 0.5055 & 1 \tabularnewline
126 & 26195 & 27014.5243 & 21947.8782 & 33250.8006 & 0.3984 & 0.4042 & 0.061 & 0.9998 \tabularnewline
127 & 20516 & 23485.1275 & 18961.3938 & 29088.1155 & 0.1495 & 0.1716 & 0.2064 & 0.9972 \tabularnewline
128 & 22759 & 23630.5159 & 18963.1257 & 29446.6898 & 0.3845 & 0.853 & 0.1401 & 0.9967 \tabularnewline
129 & 19028 & 19113.1635 & 15247.5375 & 23958.8207 & 0.4863 & 0.0701 & 0.3294 & 0.924 \tabularnewline
130 & 16971 & 17078.2059 & 13545.8226 & 21531.739 & 0.4812 & 0.1954 & 0.3772 & 0.7463 \tabularnewline
131 & 20036 & 18472.1395 & 14569.2485 & 23420.5586 & 0.2678 & 0.7239 & 0.2086 & 0.8747 \tabularnewline
132 & 22485 & 21482.7553 & 16850.9087 & 27387.7677 & 0.3697 & 0.6845 & 0.3656 & 0.9751 \tabularnewline
133 & 18730 & 17002.3991 & 13263.0703 & 21795.9771 & 0.24 & 0.0125 & 0.7207 & 0.7207 \tabularnewline
134 & 14538 & 11238.6077 & 8687.4612 & 14538.9201 & 0.025 & 0 & 0.4362 & 0.005 \tabularnewline
135 & 27561 & 29392.9122 & 22585.1521 & 38252.7107 & 0.3426 & 0.9995 & 0.8086 & 0.9989 \tabularnewline
136 & 25985 & 26291.6304 & 20084.2557 & 34417.498 & 0.4705 & 0.3797 & 0.7023 & 0.9951 \tabularnewline
137 & 34670 & 29258.4075 & 22222.9044 & 38521.2658 & 0.1261 & 0.7557 & 0.6223 & 0.9981 \tabularnewline
138 & 32066 & 26288.8934 & 19855.6967 & 34806.43 & 0.0919 & 0.0269 & 0.5086 & 0.9932 \tabularnewline
139 & 27186 & 22854.299 & 17166.8737 & 30425.9815 & 0.1311 & 0.0086 & 0.7275 & 0.9703 \tabularnewline
140 & 29586 & 22995.7821 & 17180.1543 & 30780.0493 & 0.0485 & 0.1457 & 0.5238 & 0.9692 \tabularnewline
141 & 21359 & 18599.7692 & 13822.4371 & 25028.2502 & 0.2001 & 4e-04 & 0.4481 & 0.822 \tabularnewline
142 & 21553 & 16619.4722 & 12286.6326 & 22480.2731 & 0.0495 & 0.0565 & 0.4532 & 0.6369 \tabularnewline
143 & 19573 & 17975.9637 & 13221.6218 & 24439.9118 & 0.3141 & 0.139 & 0.2661 & 0.767 \tabularnewline
144 & 24256 & 20905.712 & 15299.2752 & 28566.6339 & 0.1957 & 0.6334 & 0.3431 & 0.9138 \tabularnewline
145 & 22380 & 16545.7016 & 12044.7752 & 22728.5473 & 0.0322 & 0.0073 & 0.2443 & 0.6212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151696&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[121])[/C][/ROW]
[ROW][C]109[/C][C]19814[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]110[/C][C]12738[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]111[/C][C]31566[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]112[/C][C]30111[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]113[/C][C]30019[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]114[/C][C]31934[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]115[/C][C]25826[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]116[/C][C]26835[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]117[/C][C]20205[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]118[/C][C]17789[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]119[/C][C]20520[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]120[/C][C]22518[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]121[/C][C]15572[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]122[/C][C]11509[/C][C]11548.8178[/C][C]9641.4183[/C][C]13833.5657[/C][C]0.4864[/C][C]3e-04[/C][C]0.1538[/C][C]3e-04[/C][/ROW]
[ROW][C]123[/C][C]25447[/C][C]30204.2208[/C][C]25035.626[/C][C]36439.8698[/C][C]0.0674[/C][C]1[/C][C]0.3343[/C][C]1[/C][/ROW]
[ROW][C]124[/C][C]24090[/C][C]27017.3368[/C][C]22240.0288[/C][C]32820.8426[/C][C]0.1614[/C][C]0.7021[/C][C]0.1481[/C][C]0.9999[/C][/ROW]
[ROW][C]125[/C][C]27786[/C][C]30066.0034[/C][C]24585.1734[/C][C]36768.6875[/C][C]0.2525[/C][C]0.9597[/C][C]0.5055[/C][C]1[/C][/ROW]
[ROW][C]126[/C][C]26195[/C][C]27014.5243[/C][C]21947.8782[/C][C]33250.8006[/C][C]0.3984[/C][C]0.4042[/C][C]0.061[/C][C]0.9998[/C][/ROW]
[ROW][C]127[/C][C]20516[/C][C]23485.1275[/C][C]18961.3938[/C][C]29088.1155[/C][C]0.1495[/C][C]0.1716[/C][C]0.2064[/C][C]0.9972[/C][/ROW]
[ROW][C]128[/C][C]22759[/C][C]23630.5159[/C][C]18963.1257[/C][C]29446.6898[/C][C]0.3845[/C][C]0.853[/C][C]0.1401[/C][C]0.9967[/C][/ROW]
[ROW][C]129[/C][C]19028[/C][C]19113.1635[/C][C]15247.5375[/C][C]23958.8207[/C][C]0.4863[/C][C]0.0701[/C][C]0.3294[/C][C]0.924[/C][/ROW]
[ROW][C]130[/C][C]16971[/C][C]17078.2059[/C][C]13545.8226[/C][C]21531.739[/C][C]0.4812[/C][C]0.1954[/C][C]0.3772[/C][C]0.7463[/C][/ROW]
[ROW][C]131[/C][C]20036[/C][C]18472.1395[/C][C]14569.2485[/C][C]23420.5586[/C][C]0.2678[/C][C]0.7239[/C][C]0.2086[/C][C]0.8747[/C][/ROW]
[ROW][C]132[/C][C]22485[/C][C]21482.7553[/C][C]16850.9087[/C][C]27387.7677[/C][C]0.3697[/C][C]0.6845[/C][C]0.3656[/C][C]0.9751[/C][/ROW]
[ROW][C]133[/C][C]18730[/C][C]17002.3991[/C][C]13263.0703[/C][C]21795.9771[/C][C]0.24[/C][C]0.0125[/C][C]0.7207[/C][C]0.7207[/C][/ROW]
[ROW][C]134[/C][C]14538[/C][C]11238.6077[/C][C]8687.4612[/C][C]14538.9201[/C][C]0.025[/C][C]0[/C][C]0.4362[/C][C]0.005[/C][/ROW]
[ROW][C]135[/C][C]27561[/C][C]29392.9122[/C][C]22585.1521[/C][C]38252.7107[/C][C]0.3426[/C][C]0.9995[/C][C]0.8086[/C][C]0.9989[/C][/ROW]
[ROW][C]136[/C][C]25985[/C][C]26291.6304[/C][C]20084.2557[/C][C]34417.498[/C][C]0.4705[/C][C]0.3797[/C][C]0.7023[/C][C]0.9951[/C][/ROW]
[ROW][C]137[/C][C]34670[/C][C]29258.4075[/C][C]22222.9044[/C][C]38521.2658[/C][C]0.1261[/C][C]0.7557[/C][C]0.6223[/C][C]0.9981[/C][/ROW]
[ROW][C]138[/C][C]32066[/C][C]26288.8934[/C][C]19855.6967[/C][C]34806.43[/C][C]0.0919[/C][C]0.0269[/C][C]0.5086[/C][C]0.9932[/C][/ROW]
[ROW][C]139[/C][C]27186[/C][C]22854.299[/C][C]17166.8737[/C][C]30425.9815[/C][C]0.1311[/C][C]0.0086[/C][C]0.7275[/C][C]0.9703[/C][/ROW]
[ROW][C]140[/C][C]29586[/C][C]22995.7821[/C][C]17180.1543[/C][C]30780.0493[/C][C]0.0485[/C][C]0.1457[/C][C]0.5238[/C][C]0.9692[/C][/ROW]
[ROW][C]141[/C][C]21359[/C][C]18599.7692[/C][C]13822.4371[/C][C]25028.2502[/C][C]0.2001[/C][C]4e-04[/C][C]0.4481[/C][C]0.822[/C][/ROW]
[ROW][C]142[/C][C]21553[/C][C]16619.4722[/C][C]12286.6326[/C][C]22480.2731[/C][C]0.0495[/C][C]0.0565[/C][C]0.4532[/C][C]0.6369[/C][/ROW]
[ROW][C]143[/C][C]19573[/C][C]17975.9637[/C][C]13221.6218[/C][C]24439.9118[/C][C]0.3141[/C][C]0.139[/C][C]0.2661[/C][C]0.767[/C][/ROW]
[ROW][C]144[/C][C]24256[/C][C]20905.712[/C][C]15299.2752[/C][C]28566.6339[/C][C]0.1957[/C][C]0.6334[/C][C]0.3431[/C][C]0.9138[/C][/ROW]
[ROW][C]145[/C][C]22380[/C][C]16545.7016[/C][C]12044.7752[/C][C]22728.5473[/C][C]0.0322[/C][C]0.0073[/C][C]0.2443[/C][C]0.6212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151696&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[121])
109	19814	-	-	-	-	-	-	-
110	12738	-	-	-	-	-	-	-
111	31566	-	-	-	-	-	-	-
112	30111	-	-	-	-	-	-	-
113	30019	-	-	-	-	-	-	-
114	31934	-	-	-	-	-	-	-
115	25826	-	-	-	-	-	-	-
116	26835	-	-	-	-	-	-	-
117	20205	-	-	-	-	-	-	-
118	17789	-	-	-	-	-	-	-
119	20520	-	-	-	-	-	-	-
120	22518	-	-	-	-	-	-	-
121	15572	-	-	-	-	-	-	-
122	11509	11548.8178	9641.4183	13833.5657	0.4864	3e-04	0.1538	3e-04
123	25447	30204.2208	25035.626	36439.8698	0.0674	1	0.3343	1
124	24090	27017.3368	22240.0288	32820.8426	0.1614	0.7021	0.1481	0.9999
125	27786	30066.0034	24585.1734	36768.6875	0.2525	0.9597	0.5055	1
126	26195	27014.5243	21947.8782	33250.8006	0.3984	0.4042	0.061	0.9998
127	20516	23485.1275	18961.3938	29088.1155	0.1495	0.1716	0.2064	0.9972
128	22759	23630.5159	18963.1257	29446.6898	0.3845	0.853	0.1401	0.9967
129	19028	19113.1635	15247.5375	23958.8207	0.4863	0.0701	0.3294	0.924
130	16971	17078.2059	13545.8226	21531.739	0.4812	0.1954	0.3772	0.7463
131	20036	18472.1395	14569.2485	23420.5586	0.2678	0.7239	0.2086	0.8747
132	22485	21482.7553	16850.9087	27387.7677	0.3697	0.6845	0.3656	0.9751
133	18730	17002.3991	13263.0703	21795.9771	0.24	0.0125	0.7207	0.7207
134	14538	11238.6077	8687.4612	14538.9201	0.025	0	0.4362	0.005
135	27561	29392.9122	22585.1521	38252.7107	0.3426	0.9995	0.8086	0.9989
136	25985	26291.6304	20084.2557	34417.498	0.4705	0.3797	0.7023	0.9951
137	34670	29258.4075	22222.9044	38521.2658	0.1261	0.7557	0.6223	0.9981
138	32066	26288.8934	19855.6967	34806.43	0.0919	0.0269	0.5086	0.9932
139	27186	22854.299	17166.8737	30425.9815	0.1311	0.0086	0.7275	0.9703
140	29586	22995.7821	17180.1543	30780.0493	0.0485	0.1457	0.5238	0.9692
141	21359	18599.7692	13822.4371	25028.2502	0.2001	4e-04	0.4481	0.822
142	21553	16619.4722	12286.6326	22480.2731	0.0495	0.0565	0.4532	0.6369
143	19573	17975.9637	13221.6218	24439.9118	0.3141	0.139	0.2661	0.767
144	24256	20905.712	15299.2752	28566.6339	0.1957	0.6334	0.3431	0.9138
145	22380	16545.7016	12044.7752	22728.5473	0.0322	0.0073	0.2443	0.6212

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
122	0.1009	-0.0034	0	1585.4611	0	0
123	0.1053	-0.1575	0.0805	22631149.5044	11316367.4828	3363.9809
124	0.1096	-0.1084	0.0898	8569300.6669	10400678.5441	3225.0083
125	0.1137	-0.0758	0.0863	5198415.3417	9100112.7435	3016.6393
126	0.1178	-0.0303	0.0751	671620.0451	7414414.2039	2722.9422
127	0.1217	-0.1264	0.0836	8815718.0824	7647964.8503	2765.4954
128	0.1256	-0.0369	0.077	759539.9258	6663904.1468	2581.4539
129	0.1293	-0.0045	0.0679	7252.8155	5831822.7304	2414.9167
130	0.133	-0.0063	0.0611	11493.1049	5185119.4387	2277.0857
131	0.1367	0.0847	0.0634	2445659.664	4911173.4612	2216.1168
132	0.1402	0.0467	0.0619	1004494.4916	4556020.8276	2134.4837
133	0.1438	0.1016	0.0652	2984604.8419	4425069.4955	2103.5849
134	0.1498	0.2936	0.0828	10885989.2561	4922063.3232	2218.5724
135	0.1538	-0.0623	0.0813	3355902.4537	4810194.6897	2193.2156
136	0.1577	-0.0117	0.0767	94022.2022	4495783.1905	2120.3262
137	0.1615	0.185	0.0834	29285333.8789	6045130.1085	2458.6846
138	0.1653	0.2198	0.0915	33374960.224	7652767.1741	2766.3635
139	0.169	0.1895	0.0969	18763633.9143	8270037.5486	2875.7673
140	0.1727	0.2866	0.1069	43430971.9979	10120613.0459	3181.2911
141	0.1763	0.1483	0.109	7613354.4222	9995250.1147	3161.5265
142	0.1799	0.2969	0.1179	24339696.6434	10678318.9971	3267.7697
143	0.1835	0.0888	0.1166	2550525.0541	10308873.8178	3210.7435
144	0.187	0.1603	0.1185	11224429.747	10348680.5974	3216.9365
145	0.1907	0.3526	0.1282	34039037.4965	11335778.8015	3366.8648

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
122 & 0.1009 & -0.0034 & 0 & 1585.4611 & 0 & 0 \tabularnewline
123 & 0.1053 & -0.1575 & 0.0805 & 22631149.5044 & 11316367.4828 & 3363.9809 \tabularnewline
124 & 0.1096 & -0.1084 & 0.0898 & 8569300.6669 & 10400678.5441 & 3225.0083 \tabularnewline
125 & 0.1137 & -0.0758 & 0.0863 & 5198415.3417 & 9100112.7435 & 3016.6393 \tabularnewline
126 & 0.1178 & -0.0303 & 0.0751 & 671620.0451 & 7414414.2039 & 2722.9422 \tabularnewline
127 & 0.1217 & -0.1264 & 0.0836 & 8815718.0824 & 7647964.8503 & 2765.4954 \tabularnewline
128 & 0.1256 & -0.0369 & 0.077 & 759539.9258 & 6663904.1468 & 2581.4539 \tabularnewline
129 & 0.1293 & -0.0045 & 0.0679 & 7252.8155 & 5831822.7304 & 2414.9167 \tabularnewline
130 & 0.133 & -0.0063 & 0.0611 & 11493.1049 & 5185119.4387 & 2277.0857 \tabularnewline
131 & 0.1367 & 0.0847 & 0.0634 & 2445659.664 & 4911173.4612 & 2216.1168 \tabularnewline
132 & 0.1402 & 0.0467 & 0.0619 & 1004494.4916 & 4556020.8276 & 2134.4837 \tabularnewline
133 & 0.1438 & 0.1016 & 0.0652 & 2984604.8419 & 4425069.4955 & 2103.5849 \tabularnewline
134 & 0.1498 & 0.2936 & 0.0828 & 10885989.2561 & 4922063.3232 & 2218.5724 \tabularnewline
135 & 0.1538 & -0.0623 & 0.0813 & 3355902.4537 & 4810194.6897 & 2193.2156 \tabularnewline
136 & 0.1577 & -0.0117 & 0.0767 & 94022.2022 & 4495783.1905 & 2120.3262 \tabularnewline
137 & 0.1615 & 0.185 & 0.0834 & 29285333.8789 & 6045130.1085 & 2458.6846 \tabularnewline
138 & 0.1653 & 0.2198 & 0.0915 & 33374960.224 & 7652767.1741 & 2766.3635 \tabularnewline
139 & 0.169 & 0.1895 & 0.0969 & 18763633.9143 & 8270037.5486 & 2875.7673 \tabularnewline
140 & 0.1727 & 0.2866 & 0.1069 & 43430971.9979 & 10120613.0459 & 3181.2911 \tabularnewline
141 & 0.1763 & 0.1483 & 0.109 & 7613354.4222 & 9995250.1147 & 3161.5265 \tabularnewline
142 & 0.1799 & 0.2969 & 0.1179 & 24339696.6434 & 10678318.9971 & 3267.7697 \tabularnewline
143 & 0.1835 & 0.0888 & 0.1166 & 2550525.0541 & 10308873.8178 & 3210.7435 \tabularnewline
144 & 0.187 & 0.1603 & 0.1185 & 11224429.747 & 10348680.5974 & 3216.9365 \tabularnewline
145 & 0.1907 & 0.3526 & 0.1282 & 34039037.4965 & 11335778.8015 & 3366.8648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151696&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]122[/C][C]0.1009[/C][C]-0.0034[/C][C]0[/C][C]1585.4611[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]123[/C][C]0.1053[/C][C]-0.1575[/C][C]0.0805[/C][C]22631149.5044[/C][C]11316367.4828[/C][C]3363.9809[/C][/ROW]
[ROW][C]124[/C][C]0.1096[/C][C]-0.1084[/C][C]0.0898[/C][C]8569300.6669[/C][C]10400678.5441[/C][C]3225.0083[/C][/ROW]
[ROW][C]125[/C][C]0.1137[/C][C]-0.0758[/C][C]0.0863[/C][C]5198415.3417[/C][C]9100112.7435[/C][C]3016.6393[/C][/ROW]
[ROW][C]126[/C][C]0.1178[/C][C]-0.0303[/C][C]0.0751[/C][C]671620.0451[/C][C]7414414.2039[/C][C]2722.9422[/C][/ROW]
[ROW][C]127[/C][C]0.1217[/C][C]-0.1264[/C][C]0.0836[/C][C]8815718.0824[/C][C]7647964.8503[/C][C]2765.4954[/C][/ROW]
[ROW][C]128[/C][C]0.1256[/C][C]-0.0369[/C][C]0.077[/C][C]759539.9258[/C][C]6663904.1468[/C][C]2581.4539[/C][/ROW]
[ROW][C]129[/C][C]0.1293[/C][C]-0.0045[/C][C]0.0679[/C][C]7252.8155[/C][C]5831822.7304[/C][C]2414.9167[/C][/ROW]
[ROW][C]130[/C][C]0.133[/C][C]-0.0063[/C][C]0.0611[/C][C]11493.1049[/C][C]5185119.4387[/C][C]2277.0857[/C][/ROW]
[ROW][C]131[/C][C]0.1367[/C][C]0.0847[/C][C]0.0634[/C][C]2445659.664[/C][C]4911173.4612[/C][C]2216.1168[/C][/ROW]
[ROW][C]132[/C][C]0.1402[/C][C]0.0467[/C][C]0.0619[/C][C]1004494.4916[/C][C]4556020.8276[/C][C]2134.4837[/C][/ROW]
[ROW][C]133[/C][C]0.1438[/C][C]0.1016[/C][C]0.0652[/C][C]2984604.8419[/C][C]4425069.4955[/C][C]2103.5849[/C][/ROW]
[ROW][C]134[/C][C]0.1498[/C][C]0.2936[/C][C]0.0828[/C][C]10885989.2561[/C][C]4922063.3232[/C][C]2218.5724[/C][/ROW]
[ROW][C]135[/C][C]0.1538[/C][C]-0.0623[/C][C]0.0813[/C][C]3355902.4537[/C][C]4810194.6897[/C][C]2193.2156[/C][/ROW]
[ROW][C]136[/C][C]0.1577[/C][C]-0.0117[/C][C]0.0767[/C][C]94022.2022[/C][C]4495783.1905[/C][C]2120.3262[/C][/ROW]
[ROW][C]137[/C][C]0.1615[/C][C]0.185[/C][C]0.0834[/C][C]29285333.8789[/C][C]6045130.1085[/C][C]2458.6846[/C][/ROW]
[ROW][C]138[/C][C]0.1653[/C][C]0.2198[/C][C]0.0915[/C][C]33374960.224[/C][C]7652767.1741[/C][C]2766.3635[/C][/ROW]
[ROW][C]139[/C][C]0.169[/C][C]0.1895[/C][C]0.0969[/C][C]18763633.9143[/C][C]8270037.5486[/C][C]2875.7673[/C][/ROW]
[ROW][C]140[/C][C]0.1727[/C][C]0.2866[/C][C]0.1069[/C][C]43430971.9979[/C][C]10120613.0459[/C][C]3181.2911[/C][/ROW]
[ROW][C]141[/C][C]0.1763[/C][C]0.1483[/C][C]0.109[/C][C]7613354.4222[/C][C]9995250.1147[/C][C]3161.5265[/C][/ROW]
[ROW][C]142[/C][C]0.1799[/C][C]0.2969[/C][C]0.1179[/C][C]24339696.6434[/C][C]10678318.9971[/C][C]3267.7697[/C][/ROW]
[ROW][C]143[/C][C]0.1835[/C][C]0.0888[/C][C]0.1166[/C][C]2550525.0541[/C][C]10308873.8178[/C][C]3210.7435[/C][/ROW]
[ROW][C]144[/C][C]0.187[/C][C]0.1603[/C][C]0.1185[/C][C]11224429.747[/C][C]10348680.5974[/C][C]3216.9365[/C][/ROW]
[ROW][C]145[/C][C]0.1907[/C][C]0.3526[/C][C]0.1282[/C][C]34039037.4965[/C][C]11335778.8015[/C][C]3366.8648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151696&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
122	0.1009	-0.0034	0	1585.4611	0	0
123	0.1053	-0.1575	0.0805	22631149.5044	11316367.4828	3363.9809
124	0.1096	-0.1084	0.0898	8569300.6669	10400678.5441	3225.0083
125	0.1137	-0.0758	0.0863	5198415.3417	9100112.7435	3016.6393
126	0.1178	-0.0303	0.0751	671620.0451	7414414.2039	2722.9422
127	0.1217	-0.1264	0.0836	8815718.0824	7647964.8503	2765.4954
128	0.1256	-0.0369	0.077	759539.9258	6663904.1468	2581.4539
129	0.1293	-0.0045	0.0679	7252.8155	5831822.7304	2414.9167
130	0.133	-0.0063	0.0611	11493.1049	5185119.4387	2277.0857
131	0.1367	0.0847	0.0634	2445659.664	4911173.4612	2216.1168
132	0.1402	0.0467	0.0619	1004494.4916	4556020.8276	2134.4837
133	0.1438	0.1016	0.0652	2984604.8419	4425069.4955	2103.5849
134	0.1498	0.2936	0.0828	10885989.2561	4922063.3232	2218.5724
135	0.1538	-0.0623	0.0813	3355902.4537	4810194.6897	2193.2156
136	0.1577	-0.0117	0.0767	94022.2022	4495783.1905	2120.3262
137	0.1615	0.185	0.0834	29285333.8789	6045130.1085	2458.6846
138	0.1653	0.2198	0.0915	33374960.224	7652767.1741	2766.3635
139	0.169	0.1895	0.0969	18763633.9143	8270037.5486	2875.7673
140	0.1727	0.2866	0.1069	43430971.9979	10120613.0459	3181.2911
141	0.1763	0.1483	0.109	7613354.4222	9995250.1147	3161.5265
142	0.1799	0.2969	0.1179	24339696.6434	10678318.9971	3267.7697
143	0.1835	0.0888	0.1166	2550525.0541	10308873.8178	3210.7435
144	0.187	0.1603	0.1185	11224429.747	10348680.5974	3216.9365
145	0.1907	0.3526	0.1282	34039037.4965	11335778.8015	3366.8648

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; 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