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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 14 Dec 2009 14:07:10 -0700

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/2009/Dec/14/t126082566524w41yoqbjkdmdf.htm/, Retrieved Sun, 05 May 2024 20:24:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67691, Retrieved Sun, 05 May 2024 20:24:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

151

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

-     [ARIMA Forecasting] [] [2009-12-06 10:44:58] [1e83ffa964db6f7ea6ccc4e7b5acbbff]
-   PD  [ARIMA Forecasting] [ws 10 deel 2 prblm] [2009-12-09 19:29:01] [134dc66689e3d457a82860db6471d419]
-   P     [ARIMA Forecasting] [ws 10 deel 2 arim...] [2009-12-12 09:45:03] [134dc66689e3d457a82860db6471d419]
-   P         [ARIMA Forecasting] [Paper ARIMA F IGP] [2009-12-14 21:07:10] [4f297b039e1043ebee7ff7a83b1eaaaa] [Current]
-   PD          [ARIMA Forecasting] [Paper ARIMA F ICP] [2009-12-15 20:21:11] [134dc66689e3d457a82860db6471d419] 
-   P           [ARIMA Forecasting] [Paper ARIMA F IGP 12] [2009-12-15 20:24:19] [134dc66689e3d457a82860db6471d419] 
- R PD            [ARIMA Forecasting] [Paper arima forec...] [2009-12-23 22:37:42] [62d3ced7fb1c10c35a82e9cb1d0d0e2b] 
- R PD            [ARIMA Forecasting] [Paper arima forec...] [2009-12-23 23:25:41] [62d3ced7fb1c10c35a82e9cb1d0d0e2b] 

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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	'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67691&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67691&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	'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[93])
81	217.48	-	-	-	-	-	-	-
82	209.39	-	-	-	-	-	-	-
83	211.73	-	-	-	-	-	-	-
84	221	-	-	-	-	-	-	-
85	203.11	-	-	-	-	-	-	-
86	214.71	-	-	-	-	-	-	-
87	224.19	-	-	-	-	-	-	-
88	238.04	-	-	-	-	-	-	-
89	238.36	-	-	-	-	-	-	-
90	246.24	-	-	-	-	-	-	-
91	259.87	-	-	-	-	-	-	-
92	249.97	-	-	-	-	-	-	-
93	266.48	-	-	-	-	-	-	-
94	282.98	271.0437	229.9633	326.3723	0.3362	0.5642	0.9855	0.5642
95	306.31	271.0129	213.6032	360.672	0.2202	0.3968	0.9025	0.5395
96	301.73	267.9242	200.6082	385.2695	0.2862	0.2607	0.7834	0.5096
97	314.62	265.9295	191.0772	409.1383	0.2526	0.3121	0.805	0.497
98	332.62	268.6372	185.7388	442.3999	0.2352	0.302	0.7285	0.5097
99	355.51	263.8463	177.4642	457.7288	0.1771	0.2434	0.6558	0.4894
100	370.32	260.8019	171.0102	475.9838	0.1592	0.1942	0.5821	0.4794
101	408.13	257.2099	164.9814	491.6121	0.1035	0.1721	0.5626	0.4691
102	433.58	260.6571	162.6926	529.227	0.1035	0.1409	0.5419	0.4831
103	440.51	259.5669	158.6737	553.322	0.1137	0.1228	0.4992	0.4816
104	386.29	259.2261	155.2972	580.702	0.2193	0.1345	0.5225	0.4824
105	342.84	258.7604	152.129	608.458	0.3187	0.2374	0.4827	0.4827
106	254.97	256.4332	148.077	632.9599	0.497	0.3264	0.445	0.4791
107	203.42	256.5995	145.2322	670.4733	0.4006	0.5031	0.4069	0.4813
108	170.09	259.1395	143.4583	723.7611	0.3536	0.5929	0.4287	0.4876
109	174.03	260.8217	141.5004	777.1011	0.3709	0.6347	0.4191	0.4914
110	167.85	258.5499	138.3054	807.7483	0.3731	0.6185	0.3958	0.4887
111	177.01	262.6204	137.4186	887.5256	0.3942	0.6169	0.3854	0.4952
112	188.19	265.332	136.1379	966.4284	0.4146	0.5975	0.3846	0.4987
113	211.2	268.6652	135.1167	1061.9439	0.4435	0.5788	0.3652	0.5022
114	240.91	265.4635	132.1616	1096.1416	0.4769	0.5509	0.3458	0.499
115	230.26	266.4612	130.5995	1181.0779	0.4691	0.5218	0.3546	0.5
116	251.25	266.7759	128.9128	1265.8861	0.4879	0.5286	0.4073	0.5002
117	241.66	267.2081	127.3363	1361.1928	0.4817	0.5114	0.4461	0.5005

\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[93]) \tabularnewline
81 & 217.48 & - & - & - & - & - & - & - \tabularnewline
82 & 209.39 & - & - & - & - & - & - & - \tabularnewline
83 & 211.73 & - & - & - & - & - & - & - \tabularnewline
84 & 221 & - & - & - & - & - & - & - \tabularnewline
85 & 203.11 & - & - & - & - & - & - & - \tabularnewline
86 & 214.71 & - & - & - & - & - & - & - \tabularnewline
87 & 224.19 & - & - & - & - & - & - & - \tabularnewline
88 & 238.04 & - & - & - & - & - & - & - \tabularnewline
89 & 238.36 & - & - & - & - & - & - & - \tabularnewline
90 & 246.24 & - & - & - & - & - & - & - \tabularnewline
91 & 259.87 & - & - & - & - & - & - & - \tabularnewline
92 & 249.97 & - & - & - & - & - & - & - \tabularnewline
93 & 266.48 & - & - & - & - & - & - & - \tabularnewline
94 & 282.98 & 271.0437 & 229.9633 & 326.3723 & 0.3362 & 0.5642 & 0.9855 & 0.5642 \tabularnewline
95 & 306.31 & 271.0129 & 213.6032 & 360.672 & 0.2202 & 0.3968 & 0.9025 & 0.5395 \tabularnewline
96 & 301.73 & 267.9242 & 200.6082 & 385.2695 & 0.2862 & 0.2607 & 0.7834 & 0.5096 \tabularnewline
97 & 314.62 & 265.9295 & 191.0772 & 409.1383 & 0.2526 & 0.3121 & 0.805 & 0.497 \tabularnewline
98 & 332.62 & 268.6372 & 185.7388 & 442.3999 & 0.2352 & 0.302 & 0.7285 & 0.5097 \tabularnewline
99 & 355.51 & 263.8463 & 177.4642 & 457.7288 & 0.1771 & 0.2434 & 0.6558 & 0.4894 \tabularnewline
100 & 370.32 & 260.8019 & 171.0102 & 475.9838 & 0.1592 & 0.1942 & 0.5821 & 0.4794 \tabularnewline
101 & 408.13 & 257.2099 & 164.9814 & 491.6121 & 0.1035 & 0.1721 & 0.5626 & 0.4691 \tabularnewline
102 & 433.58 & 260.6571 & 162.6926 & 529.227 & 0.1035 & 0.1409 & 0.5419 & 0.4831 \tabularnewline
103 & 440.51 & 259.5669 & 158.6737 & 553.322 & 0.1137 & 0.1228 & 0.4992 & 0.4816 \tabularnewline
104 & 386.29 & 259.2261 & 155.2972 & 580.702 & 0.2193 & 0.1345 & 0.5225 & 0.4824 \tabularnewline
105 & 342.84 & 258.7604 & 152.129 & 608.458 & 0.3187 & 0.2374 & 0.4827 & 0.4827 \tabularnewline
106 & 254.97 & 256.4332 & 148.077 & 632.9599 & 0.497 & 0.3264 & 0.445 & 0.4791 \tabularnewline
107 & 203.42 & 256.5995 & 145.2322 & 670.4733 & 0.4006 & 0.5031 & 0.4069 & 0.4813 \tabularnewline
108 & 170.09 & 259.1395 & 143.4583 & 723.7611 & 0.3536 & 0.5929 & 0.4287 & 0.4876 \tabularnewline
109 & 174.03 & 260.8217 & 141.5004 & 777.1011 & 0.3709 & 0.6347 & 0.4191 & 0.4914 \tabularnewline
110 & 167.85 & 258.5499 & 138.3054 & 807.7483 & 0.3731 & 0.6185 & 0.3958 & 0.4887 \tabularnewline
111 & 177.01 & 262.6204 & 137.4186 & 887.5256 & 0.3942 & 0.6169 & 0.3854 & 0.4952 \tabularnewline
112 & 188.19 & 265.332 & 136.1379 & 966.4284 & 0.4146 & 0.5975 & 0.3846 & 0.4987 \tabularnewline
113 & 211.2 & 268.6652 & 135.1167 & 1061.9439 & 0.4435 & 0.5788 & 0.3652 & 0.5022 \tabularnewline
114 & 240.91 & 265.4635 & 132.1616 & 1096.1416 & 0.4769 & 0.5509 & 0.3458 & 0.499 \tabularnewline
115 & 230.26 & 266.4612 & 130.5995 & 1181.0779 & 0.4691 & 0.5218 & 0.3546 & 0.5 \tabularnewline
116 & 251.25 & 266.7759 & 128.9128 & 1265.8861 & 0.4879 & 0.5286 & 0.4073 & 0.5002 \tabularnewline
117 & 241.66 & 267.2081 & 127.3363 & 1361.1928 & 0.4817 & 0.5114 & 0.4461 & 0.5005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67691&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[93])[/C][/ROW]
[ROW][C]81[/C][C]217.48[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]209.39[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]211.73[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]221[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]203.11[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]214.71[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]87[/C][C]224.19[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]88[/C][C]238.04[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]89[/C][C]238.36[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]90[/C][C]246.24[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]91[/C][C]259.87[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]92[/C][C]249.97[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]93[/C][C]266.48[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]94[/C][C]282.98[/C][C]271.0437[/C][C]229.9633[/C][C]326.3723[/C][C]0.3362[/C][C]0.5642[/C][C]0.9855[/C][C]0.5642[/C][/ROW]
[ROW][C]95[/C][C]306.31[/C][C]271.0129[/C][C]213.6032[/C][C]360.672[/C][C]0.2202[/C][C]0.3968[/C][C]0.9025[/C][C]0.5395[/C][/ROW]
[ROW][C]96[/C][C]301.73[/C][C]267.9242[/C][C]200.6082[/C][C]385.2695[/C][C]0.2862[/C][C]0.2607[/C][C]0.7834[/C][C]0.5096[/C][/ROW]
[ROW][C]97[/C][C]314.62[/C][C]265.9295[/C][C]191.0772[/C][C]409.1383[/C][C]0.2526[/C][C]0.3121[/C][C]0.805[/C][C]0.497[/C][/ROW]
[ROW][C]98[/C][C]332.62[/C][C]268.6372[/C][C]185.7388[/C][C]442.3999[/C][C]0.2352[/C][C]0.302[/C][C]0.7285[/C][C]0.5097[/C][/ROW]
[ROW][C]99[/C][C]355.51[/C][C]263.8463[/C][C]177.4642[/C][C]457.7288[/C][C]0.1771[/C][C]0.2434[/C][C]0.6558[/C][C]0.4894[/C][/ROW]
[ROW][C]100[/C][C]370.32[/C][C]260.8019[/C][C]171.0102[/C][C]475.9838[/C][C]0.1592[/C][C]0.1942[/C][C]0.5821[/C][C]0.4794[/C][/ROW]
[ROW][C]101[/C][C]408.13[/C][C]257.2099[/C][C]164.9814[/C][C]491.6121[/C][C]0.1035[/C][C]0.1721[/C][C]0.5626[/C][C]0.4691[/C][/ROW]
[ROW][C]102[/C][C]433.58[/C][C]260.6571[/C][C]162.6926[/C][C]529.227[/C][C]0.1035[/C][C]0.1409[/C][C]0.5419[/C][C]0.4831[/C][/ROW]
[ROW][C]103[/C][C]440.51[/C][C]259.5669[/C][C]158.6737[/C][C]553.322[/C][C]0.1137[/C][C]0.1228[/C][C]0.4992[/C][C]0.4816[/C][/ROW]
[ROW][C]104[/C][C]386.29[/C][C]259.2261[/C][C]155.2972[/C][C]580.702[/C][C]0.2193[/C][C]0.1345[/C][C]0.5225[/C][C]0.4824[/C][/ROW]
[ROW][C]105[/C][C]342.84[/C][C]258.7604[/C][C]152.129[/C][C]608.458[/C][C]0.3187[/C][C]0.2374[/C][C]0.4827[/C][C]0.4827[/C][/ROW]
[ROW][C]106[/C][C]254.97[/C][C]256.4332[/C][C]148.077[/C][C]632.9599[/C][C]0.497[/C][C]0.3264[/C][C]0.445[/C][C]0.4791[/C][/ROW]
[ROW][C]107[/C][C]203.42[/C][C]256.5995[/C][C]145.2322[/C][C]670.4733[/C][C]0.4006[/C][C]0.5031[/C][C]0.4069[/C][C]0.4813[/C][/ROW]
[ROW][C]108[/C][C]170.09[/C][C]259.1395[/C][C]143.4583[/C][C]723.7611[/C][C]0.3536[/C][C]0.5929[/C][C]0.4287[/C][C]0.4876[/C][/ROW]
[ROW][C]109[/C][C]174.03[/C][C]260.8217[/C][C]141.5004[/C][C]777.1011[/C][C]0.3709[/C][C]0.6347[/C][C]0.4191[/C][C]0.4914[/C][/ROW]
[ROW][C]110[/C][C]167.85[/C][C]258.5499[/C][C]138.3054[/C][C]807.7483[/C][C]0.3731[/C][C]0.6185[/C][C]0.3958[/C][C]0.4887[/C][/ROW]
[ROW][C]111[/C][C]177.01[/C][C]262.6204[/C][C]137.4186[/C][C]887.5256[/C][C]0.3942[/C][C]0.6169[/C][C]0.3854[/C][C]0.4952[/C][/ROW]
[ROW][C]112[/C][C]188.19[/C][C]265.332[/C][C]136.1379[/C][C]966.4284[/C][C]0.4146[/C][C]0.5975[/C][C]0.3846[/C][C]0.4987[/C][/ROW]
[ROW][C]113[/C][C]211.2[/C][C]268.6652[/C][C]135.1167[/C][C]1061.9439[/C][C]0.4435[/C][C]0.5788[/C][C]0.3652[/C][C]0.5022[/C][/ROW]
[ROW][C]114[/C][C]240.91[/C][C]265.4635[/C][C]132.1616[/C][C]1096.1416[/C][C]0.4769[/C][C]0.5509[/C][C]0.3458[/C][C]0.499[/C][/ROW]
[ROW][C]115[/C][C]230.26[/C][C]266.4612[/C][C]130.5995[/C][C]1181.0779[/C][C]0.4691[/C][C]0.5218[/C][C]0.3546[/C][C]0.5[/C][/ROW]
[ROW][C]116[/C][C]251.25[/C][C]266.7759[/C][C]128.9128[/C][C]1265.8861[/C][C]0.4879[/C][C]0.5286[/C][C]0.4073[/C][C]0.5002[/C][/ROW]
[ROW][C]117[/C][C]241.66[/C][C]267.2081[/C][C]127.3363[/C][C]1361.1928[/C][C]0.4817[/C][C]0.5114[/C][C]0.4461[/C][C]0.5005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67691&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[93])
81	217.48	-	-	-	-	-	-	-
82	209.39	-	-	-	-	-	-	-
83	211.73	-	-	-	-	-	-	-
84	221	-	-	-	-	-	-	-
85	203.11	-	-	-	-	-	-	-
86	214.71	-	-	-	-	-	-	-
87	224.19	-	-	-	-	-	-	-
88	238.04	-	-	-	-	-	-	-
89	238.36	-	-	-	-	-	-	-
90	246.24	-	-	-	-	-	-	-
91	259.87	-	-	-	-	-	-	-
92	249.97	-	-	-	-	-	-	-
93	266.48	-	-	-	-	-	-	-
94	282.98	271.0437	229.9633	326.3723	0.3362	0.5642	0.9855	0.5642
95	306.31	271.0129	213.6032	360.672	0.2202	0.3968	0.9025	0.5395
96	301.73	267.9242	200.6082	385.2695	0.2862	0.2607	0.7834	0.5096
97	314.62	265.9295	191.0772	409.1383	0.2526	0.3121	0.805	0.497
98	332.62	268.6372	185.7388	442.3999	0.2352	0.302	0.7285	0.5097
99	355.51	263.8463	177.4642	457.7288	0.1771	0.2434	0.6558	0.4894
100	370.32	260.8019	171.0102	475.9838	0.1592	0.1942	0.5821	0.4794
101	408.13	257.2099	164.9814	491.6121	0.1035	0.1721	0.5626	0.4691
102	433.58	260.6571	162.6926	529.227	0.1035	0.1409	0.5419	0.4831
103	440.51	259.5669	158.6737	553.322	0.1137	0.1228	0.4992	0.4816
104	386.29	259.2261	155.2972	580.702	0.2193	0.1345	0.5225	0.4824
105	342.84	258.7604	152.129	608.458	0.3187	0.2374	0.4827	0.4827
106	254.97	256.4332	148.077	632.9599	0.497	0.3264	0.445	0.4791
107	203.42	256.5995	145.2322	670.4733	0.4006	0.5031	0.4069	0.4813
108	170.09	259.1395	143.4583	723.7611	0.3536	0.5929	0.4287	0.4876
109	174.03	260.8217	141.5004	777.1011	0.3709	0.6347	0.4191	0.4914
110	167.85	258.5499	138.3054	807.7483	0.3731	0.6185	0.3958	0.4887
111	177.01	262.6204	137.4186	887.5256	0.3942	0.6169	0.3854	0.4952
112	188.19	265.332	136.1379	966.4284	0.4146	0.5975	0.3846	0.4987
113	211.2	268.6652	135.1167	1061.9439	0.4435	0.5788	0.3652	0.5022
114	240.91	265.4635	132.1616	1096.1416	0.4769	0.5509	0.3458	0.499
115	230.26	266.4612	130.5995	1181.0779	0.4691	0.5218	0.3546	0.5
116	251.25	266.7759	128.9128	1265.8861	0.4879	0.5286	0.4073	0.5002
117	241.66	267.2081	127.3363	1361.1928	0.4817	0.5114	0.4461	0.5005

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
94	0.1041	0.044	0.0018	142.4764	5.9365	2.4365
95	0.1688	0.1302	0.0054	1245.8858	51.9119	7.205
96	0.2235	0.1262	0.0053	1142.8345	47.6181	6.9006
97	0.2748	0.1831	0.0076	2370.7629	98.7818	9.9389
98	0.33	0.2382	0.0099	4093.7986	170.5749	13.0604
99	0.3749	0.3474	0.0145	8402.2301	350.0929	18.7108
100	0.421	0.4199	0.0175	11994.2195	499.7591	22.3553
101	0.465	0.5868	0.0244	22776.8758	949.0365	30.8064
102	0.5257	0.6634	0.0276	29902.3131	1245.9297	35.2977
103	0.5774	0.6971	0.029	32740.4092	1364.1837	36.9349
104	0.6327	0.4902	0.0204	16145.2253	672.7177	25.9368
105	0.6895	0.3249	0.0135	7069.3761	294.5573	17.1627
106	0.7491	-0.0057	2e-04	2.1411	0.0892	0.2987
107	0.8229	-0.2072	0.0086	2828.0559	117.8357	10.8552
108	0.9148	-0.3436	0.0143	7929.8214	330.4092	18.1772
109	1.0099	-0.3328	0.0139	7532.7948	313.8664	17.7163
110	1.0837	-0.3508	0.0146	8226.4755	342.7698	18.514
111	1.214	-0.326	0.0136	7329.1457	305.3811	17.4752
112	1.3481	-0.2907	0.0121	5950.8935	247.9539	15.7466
113	1.5065	-0.2139	0.0089	3302.2478	137.5937	11.73
114	1.5965	-0.0925	0.0039	602.8733	25.1197	5.012
115	1.7513	-0.1359	0.0057	1310.5304	54.6054	7.3895
116	1.9108	-0.0582	0.0024	241.0528	10.0439	3.1692
117	2.0888	-0.0956	0.004	652.7029	27.196	5.215

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
94 & 0.1041 & 0.044 & 0.0018 & 142.4764 & 5.9365 & 2.4365 \tabularnewline
95 & 0.1688 & 0.1302 & 0.0054 & 1245.8858 & 51.9119 & 7.205 \tabularnewline
96 & 0.2235 & 0.1262 & 0.0053 & 1142.8345 & 47.6181 & 6.9006 \tabularnewline
97 & 0.2748 & 0.1831 & 0.0076 & 2370.7629 & 98.7818 & 9.9389 \tabularnewline
98 & 0.33 & 0.2382 & 0.0099 & 4093.7986 & 170.5749 & 13.0604 \tabularnewline
99 & 0.3749 & 0.3474 & 0.0145 & 8402.2301 & 350.0929 & 18.7108 \tabularnewline
100 & 0.421 & 0.4199 & 0.0175 & 11994.2195 & 499.7591 & 22.3553 \tabularnewline
101 & 0.465 & 0.5868 & 0.0244 & 22776.8758 & 949.0365 & 30.8064 \tabularnewline
102 & 0.5257 & 0.6634 & 0.0276 & 29902.3131 & 1245.9297 & 35.2977 \tabularnewline
103 & 0.5774 & 0.6971 & 0.029 & 32740.4092 & 1364.1837 & 36.9349 \tabularnewline
104 & 0.6327 & 0.4902 & 0.0204 & 16145.2253 & 672.7177 & 25.9368 \tabularnewline
105 & 0.6895 & 0.3249 & 0.0135 & 7069.3761 & 294.5573 & 17.1627 \tabularnewline
106 & 0.7491 & -0.0057 & 2e-04 & 2.1411 & 0.0892 & 0.2987 \tabularnewline
107 & 0.8229 & -0.2072 & 0.0086 & 2828.0559 & 117.8357 & 10.8552 \tabularnewline
108 & 0.9148 & -0.3436 & 0.0143 & 7929.8214 & 330.4092 & 18.1772 \tabularnewline
109 & 1.0099 & -0.3328 & 0.0139 & 7532.7948 & 313.8664 & 17.7163 \tabularnewline
110 & 1.0837 & -0.3508 & 0.0146 & 8226.4755 & 342.7698 & 18.514 \tabularnewline
111 & 1.214 & -0.326 & 0.0136 & 7329.1457 & 305.3811 & 17.4752 \tabularnewline
112 & 1.3481 & -0.2907 & 0.0121 & 5950.8935 & 247.9539 & 15.7466 \tabularnewline
113 & 1.5065 & -0.2139 & 0.0089 & 3302.2478 & 137.5937 & 11.73 \tabularnewline
114 & 1.5965 & -0.0925 & 0.0039 & 602.8733 & 25.1197 & 5.012 \tabularnewline
115 & 1.7513 & -0.1359 & 0.0057 & 1310.5304 & 54.6054 & 7.3895 \tabularnewline
116 & 1.9108 & -0.0582 & 0.0024 & 241.0528 & 10.0439 & 3.1692 \tabularnewline
117 & 2.0888 & -0.0956 & 0.004 & 652.7029 & 27.196 & 5.215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67691&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]94[/C][C]0.1041[/C][C]0.044[/C][C]0.0018[/C][C]142.4764[/C][C]5.9365[/C][C]2.4365[/C][/ROW]
[ROW][C]95[/C][C]0.1688[/C][C]0.1302[/C][C]0.0054[/C][C]1245.8858[/C][C]51.9119[/C][C]7.205[/C][/ROW]
[ROW][C]96[/C][C]0.2235[/C][C]0.1262[/C][C]0.0053[/C][C]1142.8345[/C][C]47.6181[/C][C]6.9006[/C][/ROW]
[ROW][C]97[/C][C]0.2748[/C][C]0.1831[/C][C]0.0076[/C][C]2370.7629[/C][C]98.7818[/C][C]9.9389[/C][/ROW]
[ROW][C]98[/C][C]0.33[/C][C]0.2382[/C][C]0.0099[/C][C]4093.7986[/C][C]170.5749[/C][C]13.0604[/C][/ROW]
[ROW][C]99[/C][C]0.3749[/C][C]0.3474[/C][C]0.0145[/C][C]8402.2301[/C][C]350.0929[/C][C]18.7108[/C][/ROW]
[ROW][C]100[/C][C]0.421[/C][C]0.4199[/C][C]0.0175[/C][C]11994.2195[/C][C]499.7591[/C][C]22.3553[/C][/ROW]
[ROW][C]101[/C][C]0.465[/C][C]0.5868[/C][C]0.0244[/C][C]22776.8758[/C][C]949.0365[/C][C]30.8064[/C][/ROW]
[ROW][C]102[/C][C]0.5257[/C][C]0.6634[/C][C]0.0276[/C][C]29902.3131[/C][C]1245.9297[/C][C]35.2977[/C][/ROW]
[ROW][C]103[/C][C]0.5774[/C][C]0.6971[/C][C]0.029[/C][C]32740.4092[/C][C]1364.1837[/C][C]36.9349[/C][/ROW]
[ROW][C]104[/C][C]0.6327[/C][C]0.4902[/C][C]0.0204[/C][C]16145.2253[/C][C]672.7177[/C][C]25.9368[/C][/ROW]
[ROW][C]105[/C][C]0.6895[/C][C]0.3249[/C][C]0.0135[/C][C]7069.3761[/C][C]294.5573[/C][C]17.1627[/C][/ROW]
[ROW][C]106[/C][C]0.7491[/C][C]-0.0057[/C][C]2e-04[/C][C]2.1411[/C][C]0.0892[/C][C]0.2987[/C][/ROW]
[ROW][C]107[/C][C]0.8229[/C][C]-0.2072[/C][C]0.0086[/C][C]2828.0559[/C][C]117.8357[/C][C]10.8552[/C][/ROW]
[ROW][C]108[/C][C]0.9148[/C][C]-0.3436[/C][C]0.0143[/C][C]7929.8214[/C][C]330.4092[/C][C]18.1772[/C][/ROW]
[ROW][C]109[/C][C]1.0099[/C][C]-0.3328[/C][C]0.0139[/C][C]7532.7948[/C][C]313.8664[/C][C]17.7163[/C][/ROW]
[ROW][C]110[/C][C]1.0837[/C][C]-0.3508[/C][C]0.0146[/C][C]8226.4755[/C][C]342.7698[/C][C]18.514[/C][/ROW]
[ROW][C]111[/C][C]1.214[/C][C]-0.326[/C][C]0.0136[/C][C]7329.1457[/C][C]305.3811[/C][C]17.4752[/C][/ROW]
[ROW][C]112[/C][C]1.3481[/C][C]-0.2907[/C][C]0.0121[/C][C]5950.8935[/C][C]247.9539[/C][C]15.7466[/C][/ROW]
[ROW][C]113[/C][C]1.5065[/C][C]-0.2139[/C][C]0.0089[/C][C]3302.2478[/C][C]137.5937[/C][C]11.73[/C][/ROW]
[ROW][C]114[/C][C]1.5965[/C][C]-0.0925[/C][C]0.0039[/C][C]602.8733[/C][C]25.1197[/C][C]5.012[/C][/ROW]
[ROW][C]115[/C][C]1.7513[/C][C]-0.1359[/C][C]0.0057[/C][C]1310.5304[/C][C]54.6054[/C][C]7.3895[/C][/ROW]
[ROW][C]116[/C][C]1.9108[/C][C]-0.0582[/C][C]0.0024[/C][C]241.0528[/C][C]10.0439[/C][C]3.1692[/C][/ROW]
[ROW][C]117[/C][C]2.0888[/C][C]-0.0956[/C][C]0.004[/C][C]652.7029[/C][C]27.196[/C][C]5.215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67691&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67691&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
94	0.1041	0.044	0.0018	142.4764	5.9365	2.4365
95	0.1688	0.1302	0.0054	1245.8858	51.9119	7.205
96	0.2235	0.1262	0.0053	1142.8345	47.6181	6.9006
97	0.2748	0.1831	0.0076	2370.7629	98.7818	9.9389
98	0.33	0.2382	0.0099	4093.7986	170.5749	13.0604
99	0.3749	0.3474	0.0145	8402.2301	350.0929	18.7108
100	0.421	0.4199	0.0175	11994.2195	499.7591	22.3553
101	0.465	0.5868	0.0244	22776.8758	949.0365	30.8064
102	0.5257	0.6634	0.0276	29902.3131	1245.9297	35.2977
103	0.5774	0.6971	0.029	32740.4092	1364.1837	36.9349
104	0.6327	0.4902	0.0204	16145.2253	672.7177	25.9368
105	0.6895	0.3249	0.0135	7069.3761	294.5573	17.1627
106	0.7491	-0.0057	2e-04	2.1411	0.0892	0.2987
107	0.8229	-0.2072	0.0086	2828.0559	117.8357	10.8552
108	0.9148	-0.3436	0.0143	7929.8214	330.4092	18.1772
109	1.0099	-0.3328	0.0139	7532.7948	313.8664	17.7163
110	1.0837	-0.3508	0.0146	8226.4755	342.7698	18.514
111	1.214	-0.326	0.0136	7329.1457	305.3811	17.4752
112	1.3481	-0.2907	0.0121	5950.8935	247.9539	15.7466
113	1.5065	-0.2139	0.0089	3302.2478	137.5937	11.73
114	1.5965	-0.0925	0.0039	602.8733	25.1197	5.012
115	1.7513	-0.1359	0.0057	1310.5304	54.6054	7.3895
116	1.9108	-0.0582	0.0024	241.0528	10.0439	3.1692
117	2.0888	-0.0956	0.004	652.7029	27.196	5.215

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = -0.7 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = -0.7 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; 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,fx))
(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.se <- array(0, dim=fx)
perf.mse <- 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$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
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 = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
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[1:12] <- 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.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[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