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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Wed, 30 Dec 2009 06:38:43 -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/30/t1262180557ghfp8nrduj88p5a.htm/, Retrieved Sun, 28 Apr 2024 19:37:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71275, Retrieved Sun, 28 Apr 2024 19:37:30 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-     [Spectral Analysis] [Spectraalanalyse ...] [2008-12-11 17:29:14] [12d343c4448a5f9e527bb31caeac580b]
- RMPD  [ARIMA Backward Selection] [Paper ARIMA Backw...] [2009-12-27 11:47:45] [83058a88a37d754675a5cd22dab372fc]
- RMP       [ARIMA Forecasting] [Paper ARIMA Forec...] [2009-12-30 13:38:43] [eba9f01697e64705b70041e6f338cb22] [Current]
- R           [ARIMA Forecasting] [Paper ARIMA Forec...] [2009-12-30 14:04:28] [83058a88a37d754675a5cd22dab372fc] 
-               [ARIMA Forecasting] [paper arima 33] [2010-12-18 14:48:34] [d87a19cd5db53e12ea62bda70b3bb267] 
-   PD        [ARIMA Forecasting] [paper arima forec...] [2010-12-18 13:46:38] [d87a19cd5db53e12ea62bda70b3bb267] 
-             [ARIMA Forecasting] [paper arima 26] [2010-12-18 14:40:42] [d87a19cd5db53e12ea62bda70b3bb267] 

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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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71275&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]4 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=71275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71275&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	4 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[190])
178	258.37	-	-	-	-	-	-	-
179	258.22	-	-	-	-	-	-	-
180	258.59	-	-	-	-	-	-	-
181	257.45	-	-	-	-	-	-	-
182	257.45	-	-	-	-	-	-	-
183	256.73	-	-	-	-	-	-	-
184	258.82	-	-	-	-	-	-	-
185	257.99	-	-	-	-	-	-	-
186	262.85	-	-	-	-	-	-	-
187	262.58	-	-	-	-	-	-	-
188	261.55	-	-	-	-	-	-	-
189	261.25	-	-	-	-	-	-	-
190	259.78	-	-	-	-	-	-	-
191	256.26	259.784	254.0673	265.764	0.124	0.5005	0.6959	0.5005
192	254.29	260.1901	252.5713	268.2829	0.0765	0.8294	0.6508	0.5396
193	248.5	259.3232	249.7811	269.6234	0.0197	0.8309	0.6392	0.4654
194	241.88	259.5327	247.9076	272.3018	0.0034	0.9548	0.6254	0.4849
195	238.53	259.6815	246.1932	274.7333	0.0029	0.9898	0.6496	0.4949
196	232.24	259.8257	244.4804	277.2264	9e-04	0.9918	0.5451	0.5021
197	232.46	259.6751	242.5432	279.4111	0.0034	0.9968	0.5665	0.4958
198	225.79	260.8315	241.7694	283.1567	0.001	0.9936	0.4297	0.5368
199	221.63	260.9154	240.0704	285.7245	0.001	0.9972	0.4477	0.5357
200	219.62	261.1297	238.4918	288.5159	0.0015	0.9977	0.488	0.5385
201	215.94	261.1363	236.7462	291.1291	0.0016	0.9967	0.497	0.5353
202	211.81	260.7761	234.7087	293.3572	0.0016	0.9965	0.5239	0.5239
203	205.57	260.3818	232.2713	296.2333	0.0014	0.996	0.5891	0.5131
204	201.25	260.4862	230.3322	299.7248	0.0015	0.997	0.6215	0.5141
205	194.7	259.542	227.5666	301.9722	0.0014	0.9965	0.695	0.4956
206	187.94	259.3382	225.3716	305.3603	0.0012	0.997	0.7714	0.4925
207	185.61	259.1267	223.2009	308.8361	0.0019	0.9975	0.7916	0.4897
208	181.15	258.8937	221.0257	312.4203	0.0022	0.9964	0.8355	0.4871
209	186.5	258.4222	218.6963	315.784	0.007	0.9959	0.8125	0.4815
210	183.21	258.9807	217.1152	320.8486	0.0082	0.9892	0.8535	0.4899
211	182.61	258.6943	214.9468	324.7999	0.012	0.9874	0.8641	0.4872
212	187.09	258.51	212.8657	329.0722	0.0236	0.9825	0.86	0.4859
213	189.1	258.165	210.6931	333.2507	0.0357	0.9682	0.8648	0.4832
214	191.25	257.5367	208.3545	337.1122	0.0513	0.9541	0.87	0.478
215	190.74	256.8844	205.8339	341.6096	0.063	0.9355	0.8824	0.4733
216	190.79	256.6187	203.6251	346.8996	0.0765	0.9237	0.8853	0.4726

\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[190]) \tabularnewline
178 & 258.37 & - & - & - & - & - & - & - \tabularnewline
179 & 258.22 & - & - & - & - & - & - & - \tabularnewline
180 & 258.59 & - & - & - & - & - & - & - \tabularnewline
181 & 257.45 & - & - & - & - & - & - & - \tabularnewline
182 & 257.45 & - & - & - & - & - & - & - \tabularnewline
183 & 256.73 & - & - & - & - & - & - & - \tabularnewline
184 & 258.82 & - & - & - & - & - & - & - \tabularnewline
185 & 257.99 & - & - & - & - & - & - & - \tabularnewline
186 & 262.85 & - & - & - & - & - & - & - \tabularnewline
187 & 262.58 & - & - & - & - & - & - & - \tabularnewline
188 & 261.55 & - & - & - & - & - & - & - \tabularnewline
189 & 261.25 & - & - & - & - & - & - & - \tabularnewline
190 & 259.78 & - & - & - & - & - & - & - \tabularnewline
191 & 256.26 & 259.784 & 254.0673 & 265.764 & 0.124 & 0.5005 & 0.6959 & 0.5005 \tabularnewline
192 & 254.29 & 260.1901 & 252.5713 & 268.2829 & 0.0765 & 0.8294 & 0.6508 & 0.5396 \tabularnewline
193 & 248.5 & 259.3232 & 249.7811 & 269.6234 & 0.0197 & 0.8309 & 0.6392 & 0.4654 \tabularnewline
194 & 241.88 & 259.5327 & 247.9076 & 272.3018 & 0.0034 & 0.9548 & 0.6254 & 0.4849 \tabularnewline
195 & 238.53 & 259.6815 & 246.1932 & 274.7333 & 0.0029 & 0.9898 & 0.6496 & 0.4949 \tabularnewline
196 & 232.24 & 259.8257 & 244.4804 & 277.2264 & 9e-04 & 0.9918 & 0.5451 & 0.5021 \tabularnewline
197 & 232.46 & 259.6751 & 242.5432 & 279.4111 & 0.0034 & 0.9968 & 0.5665 & 0.4958 \tabularnewline
198 & 225.79 & 260.8315 & 241.7694 & 283.1567 & 0.001 & 0.9936 & 0.4297 & 0.5368 \tabularnewline
199 & 221.63 & 260.9154 & 240.0704 & 285.7245 & 0.001 & 0.9972 & 0.4477 & 0.5357 \tabularnewline
200 & 219.62 & 261.1297 & 238.4918 & 288.5159 & 0.0015 & 0.9977 & 0.488 & 0.5385 \tabularnewline
201 & 215.94 & 261.1363 & 236.7462 & 291.1291 & 0.0016 & 0.9967 & 0.497 & 0.5353 \tabularnewline
202 & 211.81 & 260.7761 & 234.7087 & 293.3572 & 0.0016 & 0.9965 & 0.5239 & 0.5239 \tabularnewline
203 & 205.57 & 260.3818 & 232.2713 & 296.2333 & 0.0014 & 0.996 & 0.5891 & 0.5131 \tabularnewline
204 & 201.25 & 260.4862 & 230.3322 & 299.7248 & 0.0015 & 0.997 & 0.6215 & 0.5141 \tabularnewline
205 & 194.7 & 259.542 & 227.5666 & 301.9722 & 0.0014 & 0.9965 & 0.695 & 0.4956 \tabularnewline
206 & 187.94 & 259.3382 & 225.3716 & 305.3603 & 0.0012 & 0.997 & 0.7714 & 0.4925 \tabularnewline
207 & 185.61 & 259.1267 & 223.2009 & 308.8361 & 0.0019 & 0.9975 & 0.7916 & 0.4897 \tabularnewline
208 & 181.15 & 258.8937 & 221.0257 & 312.4203 & 0.0022 & 0.9964 & 0.8355 & 0.4871 \tabularnewline
209 & 186.5 & 258.4222 & 218.6963 & 315.784 & 0.007 & 0.9959 & 0.8125 & 0.4815 \tabularnewline
210 & 183.21 & 258.9807 & 217.1152 & 320.8486 & 0.0082 & 0.9892 & 0.8535 & 0.4899 \tabularnewline
211 & 182.61 & 258.6943 & 214.9468 & 324.7999 & 0.012 & 0.9874 & 0.8641 & 0.4872 \tabularnewline
212 & 187.09 & 258.51 & 212.8657 & 329.0722 & 0.0236 & 0.9825 & 0.86 & 0.4859 \tabularnewline
213 & 189.1 & 258.165 & 210.6931 & 333.2507 & 0.0357 & 0.9682 & 0.8648 & 0.4832 \tabularnewline
214 & 191.25 & 257.5367 & 208.3545 & 337.1122 & 0.0513 & 0.9541 & 0.87 & 0.478 \tabularnewline
215 & 190.74 & 256.8844 & 205.8339 & 341.6096 & 0.063 & 0.9355 & 0.8824 & 0.4733 \tabularnewline
216 & 190.79 & 256.6187 & 203.6251 & 346.8996 & 0.0765 & 0.9237 & 0.8853 & 0.4726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71275&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[190])[/C][/ROW]
[ROW][C]178[/C][C]258.37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]179[/C][C]258.22[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]180[/C][C]258.59[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]181[/C][C]257.45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]182[/C][C]257.45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]183[/C][C]256.73[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]184[/C][C]258.82[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]185[/C][C]257.99[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]186[/C][C]262.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]187[/C][C]262.58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]188[/C][C]261.55[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]189[/C][C]261.25[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]190[/C][C]259.78[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]191[/C][C]256.26[/C][C]259.784[/C][C]254.0673[/C][C]265.764[/C][C]0.124[/C][C]0.5005[/C][C]0.6959[/C][C]0.5005[/C][/ROW]
[ROW][C]192[/C][C]254.29[/C][C]260.1901[/C][C]252.5713[/C][C]268.2829[/C][C]0.0765[/C][C]0.8294[/C][C]0.6508[/C][C]0.5396[/C][/ROW]
[ROW][C]193[/C][C]248.5[/C][C]259.3232[/C][C]249.7811[/C][C]269.6234[/C][C]0.0197[/C][C]0.8309[/C][C]0.6392[/C][C]0.4654[/C][/ROW]
[ROW][C]194[/C][C]241.88[/C][C]259.5327[/C][C]247.9076[/C][C]272.3018[/C][C]0.0034[/C][C]0.9548[/C][C]0.6254[/C][C]0.4849[/C][/ROW]
[ROW][C]195[/C][C]238.53[/C][C]259.6815[/C][C]246.1932[/C][C]274.7333[/C][C]0.0029[/C][C]0.9898[/C][C]0.6496[/C][C]0.4949[/C][/ROW]
[ROW][C]196[/C][C]232.24[/C][C]259.8257[/C][C]244.4804[/C][C]277.2264[/C][C]9e-04[/C][C]0.9918[/C][C]0.5451[/C][C]0.5021[/C][/ROW]
[ROW][C]197[/C][C]232.46[/C][C]259.6751[/C][C]242.5432[/C][C]279.4111[/C][C]0.0034[/C][C]0.9968[/C][C]0.5665[/C][C]0.4958[/C][/ROW]
[ROW][C]198[/C][C]225.79[/C][C]260.8315[/C][C]241.7694[/C][C]283.1567[/C][C]0.001[/C][C]0.9936[/C][C]0.4297[/C][C]0.5368[/C][/ROW]
[ROW][C]199[/C][C]221.63[/C][C]260.9154[/C][C]240.0704[/C][C]285.7245[/C][C]0.001[/C][C]0.9972[/C][C]0.4477[/C][C]0.5357[/C][/ROW]
[ROW][C]200[/C][C]219.62[/C][C]261.1297[/C][C]238.4918[/C][C]288.5159[/C][C]0.0015[/C][C]0.9977[/C][C]0.488[/C][C]0.5385[/C][/ROW]
[ROW][C]201[/C][C]215.94[/C][C]261.1363[/C][C]236.7462[/C][C]291.1291[/C][C]0.0016[/C][C]0.9967[/C][C]0.497[/C][C]0.5353[/C][/ROW]
[ROW][C]202[/C][C]211.81[/C][C]260.7761[/C][C]234.7087[/C][C]293.3572[/C][C]0.0016[/C][C]0.9965[/C][C]0.5239[/C][C]0.5239[/C][/ROW]
[ROW][C]203[/C][C]205.57[/C][C]260.3818[/C][C]232.2713[/C][C]296.2333[/C][C]0.0014[/C][C]0.996[/C][C]0.5891[/C][C]0.5131[/C][/ROW]
[ROW][C]204[/C][C]201.25[/C][C]260.4862[/C][C]230.3322[/C][C]299.7248[/C][C]0.0015[/C][C]0.997[/C][C]0.6215[/C][C]0.5141[/C][/ROW]
[ROW][C]205[/C][C]194.7[/C][C]259.542[/C][C]227.5666[/C][C]301.9722[/C][C]0.0014[/C][C]0.9965[/C][C]0.695[/C][C]0.4956[/C][/ROW]
[ROW][C]206[/C][C]187.94[/C][C]259.3382[/C][C]225.3716[/C][C]305.3603[/C][C]0.0012[/C][C]0.997[/C][C]0.7714[/C][C]0.4925[/C][/ROW]
[ROW][C]207[/C][C]185.61[/C][C]259.1267[/C][C]223.2009[/C][C]308.8361[/C][C]0.0019[/C][C]0.9975[/C][C]0.7916[/C][C]0.4897[/C][/ROW]
[ROW][C]208[/C][C]181.15[/C][C]258.8937[/C][C]221.0257[/C][C]312.4203[/C][C]0.0022[/C][C]0.9964[/C][C]0.8355[/C][C]0.4871[/C][/ROW]
[ROW][C]209[/C][C]186.5[/C][C]258.4222[/C][C]218.6963[/C][C]315.784[/C][C]0.007[/C][C]0.9959[/C][C]0.8125[/C][C]0.4815[/C][/ROW]
[ROW][C]210[/C][C]183.21[/C][C]258.9807[/C][C]217.1152[/C][C]320.8486[/C][C]0.0082[/C][C]0.9892[/C][C]0.8535[/C][C]0.4899[/C][/ROW]
[ROW][C]211[/C][C]182.61[/C][C]258.6943[/C][C]214.9468[/C][C]324.7999[/C][C]0.012[/C][C]0.9874[/C][C]0.8641[/C][C]0.4872[/C][/ROW]
[ROW][C]212[/C][C]187.09[/C][C]258.51[/C][C]212.8657[/C][C]329.0722[/C][C]0.0236[/C][C]0.9825[/C][C]0.86[/C][C]0.4859[/C][/ROW]
[ROW][C]213[/C][C]189.1[/C][C]258.165[/C][C]210.6931[/C][C]333.2507[/C][C]0.0357[/C][C]0.9682[/C][C]0.8648[/C][C]0.4832[/C][/ROW]
[ROW][C]214[/C][C]191.25[/C][C]257.5367[/C][C]208.3545[/C][C]337.1122[/C][C]0.0513[/C][C]0.9541[/C][C]0.87[/C][C]0.478[/C][/ROW]
[ROW][C]215[/C][C]190.74[/C][C]256.8844[/C][C]205.8339[/C][C]341.6096[/C][C]0.063[/C][C]0.9355[/C][C]0.8824[/C][C]0.4733[/C][/ROW]
[ROW][C]216[/C][C]190.79[/C][C]256.6187[/C][C]203.6251[/C][C]346.8996[/C][C]0.0765[/C][C]0.9237[/C][C]0.8853[/C][C]0.4726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71275&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[190])
178	258.37	-	-	-	-	-	-	-
179	258.22	-	-	-	-	-	-	-
180	258.59	-	-	-	-	-	-	-
181	257.45	-	-	-	-	-	-	-
182	257.45	-	-	-	-	-	-	-
183	256.73	-	-	-	-	-	-	-
184	258.82	-	-	-	-	-	-	-
185	257.99	-	-	-	-	-	-	-
186	262.85	-	-	-	-	-	-	-
187	262.58	-	-	-	-	-	-	-
188	261.55	-	-	-	-	-	-	-
189	261.25	-	-	-	-	-	-	-
190	259.78	-	-	-	-	-	-	-
191	256.26	259.784	254.0673	265.764	0.124	0.5005	0.6959	0.5005
192	254.29	260.1901	252.5713	268.2829	0.0765	0.8294	0.6508	0.5396
193	248.5	259.3232	249.7811	269.6234	0.0197	0.8309	0.6392	0.4654
194	241.88	259.5327	247.9076	272.3018	0.0034	0.9548	0.6254	0.4849
195	238.53	259.6815	246.1932	274.7333	0.0029	0.9898	0.6496	0.4949
196	232.24	259.8257	244.4804	277.2264	9e-04	0.9918	0.5451	0.5021
197	232.46	259.6751	242.5432	279.4111	0.0034	0.9968	0.5665	0.4958
198	225.79	260.8315	241.7694	283.1567	0.001	0.9936	0.4297	0.5368
199	221.63	260.9154	240.0704	285.7245	0.001	0.9972	0.4477	0.5357
200	219.62	261.1297	238.4918	288.5159	0.0015	0.9977	0.488	0.5385
201	215.94	261.1363	236.7462	291.1291	0.0016	0.9967	0.497	0.5353
202	211.81	260.7761	234.7087	293.3572	0.0016	0.9965	0.5239	0.5239
203	205.57	260.3818	232.2713	296.2333	0.0014	0.996	0.5891	0.5131
204	201.25	260.4862	230.3322	299.7248	0.0015	0.997	0.6215	0.5141
205	194.7	259.542	227.5666	301.9722	0.0014	0.9965	0.695	0.4956
206	187.94	259.3382	225.3716	305.3603	0.0012	0.997	0.7714	0.4925
207	185.61	259.1267	223.2009	308.8361	0.0019	0.9975	0.7916	0.4897
208	181.15	258.8937	221.0257	312.4203	0.0022	0.9964	0.8355	0.4871
209	186.5	258.4222	218.6963	315.784	0.007	0.9959	0.8125	0.4815
210	183.21	258.9807	217.1152	320.8486	0.0082	0.9892	0.8535	0.4899
211	182.61	258.6943	214.9468	324.7999	0.012	0.9874	0.8641	0.4872
212	187.09	258.51	212.8657	329.0722	0.0236	0.9825	0.86	0.4859
213	189.1	258.165	210.6931	333.2507	0.0357	0.9682	0.8648	0.4832
214	191.25	257.5367	208.3545	337.1122	0.0513	0.9541	0.87	0.478
215	190.74	256.8844	205.8339	341.6096	0.063	0.9355	0.8824	0.4733
216	190.79	256.6187	203.6251	346.8996	0.0765	0.9237	0.8853	0.4726

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
191	0.0117	-0.0136	0	12.4189	0	0
192	0.0159	-0.0227	0.0181	34.8117	23.6153	4.8596
193	0.0203	-0.0417	0.026	117.1421	54.7909	7.4021
194	0.0251	-0.068	0.0365	311.6195	118.998	10.9086
195	0.0296	-0.0815	0.0455	447.384	184.6752	13.5895
196	0.0342	-0.1062	0.0556	760.9716	280.7246	16.7548
197	0.0388	-0.1048	0.0626	740.6613	346.4299	18.6126
198	0.0437	-0.1343	0.0716	1227.904	456.6141	21.3685
199	0.0485	-0.1506	0.0804	1543.3417	577.3616	24.0284
200	0.0535	-0.159	0.0882	1723.0537	691.9309	26.3046
201	0.0586	-0.1731	0.0959	2042.7076	814.7287	28.5435
202	0.0637	-0.1878	0.1036	2397.6816	946.6415	30.7675
203	0.0702	-0.2105	0.1118	3004.333	1104.9254	33.2404
204	0.0769	-0.2274	0.1201	3508.9311	1276.6401	35.7301
205	0.0834	-0.2498	0.1287	4204.4845	1471.8298	38.3644
206	0.0905	-0.2753	0.1379	5097.7052	1698.447	41.2122
207	0.0979	-0.2837	0.1465	5404.6989	1916.4618	43.7774
208	0.1055	-0.3003	0.155	6044.0844	2145.7742	46.3225
209	0.1132	-0.2783	0.1615	5172.8002	2305.0913	48.0114
210	0.1219	-0.2926	0.1681	5741.1936	2476.8964	49.7684
211	0.1304	-0.2941	0.1741	5788.816	2634.6069	51.3284
212	0.1393	-0.2763	0.1787	5100.8132	2746.7072	52.409
213	0.1484	-0.2675	0.1826	4769.9725	2834.6752	53.2417
214	0.1576	-0.2574	0.1857	4393.9211	2899.6438	53.8483
215	0.1683	-0.2575	0.1886	4375.0769	2958.6611	54.3936
216	0.1795	-0.2565	0.1912	4333.4217	3011.5365	54.8775

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
191 & 0.0117 & -0.0136 & 0 & 12.4189 & 0 & 0 \tabularnewline
192 & 0.0159 & -0.0227 & 0.0181 & 34.8117 & 23.6153 & 4.8596 \tabularnewline
193 & 0.0203 & -0.0417 & 0.026 & 117.1421 & 54.7909 & 7.4021 \tabularnewline
194 & 0.0251 & -0.068 & 0.0365 & 311.6195 & 118.998 & 10.9086 \tabularnewline
195 & 0.0296 & -0.0815 & 0.0455 & 447.384 & 184.6752 & 13.5895 \tabularnewline
196 & 0.0342 & -0.1062 & 0.0556 & 760.9716 & 280.7246 & 16.7548 \tabularnewline
197 & 0.0388 & -0.1048 & 0.0626 & 740.6613 & 346.4299 & 18.6126 \tabularnewline
198 & 0.0437 & -0.1343 & 0.0716 & 1227.904 & 456.6141 & 21.3685 \tabularnewline
199 & 0.0485 & -0.1506 & 0.0804 & 1543.3417 & 577.3616 & 24.0284 \tabularnewline
200 & 0.0535 & -0.159 & 0.0882 & 1723.0537 & 691.9309 & 26.3046 \tabularnewline
201 & 0.0586 & -0.1731 & 0.0959 & 2042.7076 & 814.7287 & 28.5435 \tabularnewline
202 & 0.0637 & -0.1878 & 0.1036 & 2397.6816 & 946.6415 & 30.7675 \tabularnewline
203 & 0.0702 & -0.2105 & 0.1118 & 3004.333 & 1104.9254 & 33.2404 \tabularnewline
204 & 0.0769 & -0.2274 & 0.1201 & 3508.9311 & 1276.6401 & 35.7301 \tabularnewline
205 & 0.0834 & -0.2498 & 0.1287 & 4204.4845 & 1471.8298 & 38.3644 \tabularnewline
206 & 0.0905 & -0.2753 & 0.1379 & 5097.7052 & 1698.447 & 41.2122 \tabularnewline
207 & 0.0979 & -0.2837 & 0.1465 & 5404.6989 & 1916.4618 & 43.7774 \tabularnewline
208 & 0.1055 & -0.3003 & 0.155 & 6044.0844 & 2145.7742 & 46.3225 \tabularnewline
209 & 0.1132 & -0.2783 & 0.1615 & 5172.8002 & 2305.0913 & 48.0114 \tabularnewline
210 & 0.1219 & -0.2926 & 0.1681 & 5741.1936 & 2476.8964 & 49.7684 \tabularnewline
211 & 0.1304 & -0.2941 & 0.1741 & 5788.816 & 2634.6069 & 51.3284 \tabularnewline
212 & 0.1393 & -0.2763 & 0.1787 & 5100.8132 & 2746.7072 & 52.409 \tabularnewline
213 & 0.1484 & -0.2675 & 0.1826 & 4769.9725 & 2834.6752 & 53.2417 \tabularnewline
214 & 0.1576 & -0.2574 & 0.1857 & 4393.9211 & 2899.6438 & 53.8483 \tabularnewline
215 & 0.1683 & -0.2575 & 0.1886 & 4375.0769 & 2958.6611 & 54.3936 \tabularnewline
216 & 0.1795 & -0.2565 & 0.1912 & 4333.4217 & 3011.5365 & 54.8775 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71275&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]191[/C][C]0.0117[/C][C]-0.0136[/C][C]0[/C][C]12.4189[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]192[/C][C]0.0159[/C][C]-0.0227[/C][C]0.0181[/C][C]34.8117[/C][C]23.6153[/C][C]4.8596[/C][/ROW]
[ROW][C]193[/C][C]0.0203[/C][C]-0.0417[/C][C]0.026[/C][C]117.1421[/C][C]54.7909[/C][C]7.4021[/C][/ROW]
[ROW][C]194[/C][C]0.0251[/C][C]-0.068[/C][C]0.0365[/C][C]311.6195[/C][C]118.998[/C][C]10.9086[/C][/ROW]
[ROW][C]195[/C][C]0.0296[/C][C]-0.0815[/C][C]0.0455[/C][C]447.384[/C][C]184.6752[/C][C]13.5895[/C][/ROW]
[ROW][C]196[/C][C]0.0342[/C][C]-0.1062[/C][C]0.0556[/C][C]760.9716[/C][C]280.7246[/C][C]16.7548[/C][/ROW]
[ROW][C]197[/C][C]0.0388[/C][C]-0.1048[/C][C]0.0626[/C][C]740.6613[/C][C]346.4299[/C][C]18.6126[/C][/ROW]
[ROW][C]198[/C][C]0.0437[/C][C]-0.1343[/C][C]0.0716[/C][C]1227.904[/C][C]456.6141[/C][C]21.3685[/C][/ROW]
[ROW][C]199[/C][C]0.0485[/C][C]-0.1506[/C][C]0.0804[/C][C]1543.3417[/C][C]577.3616[/C][C]24.0284[/C][/ROW]
[ROW][C]200[/C][C]0.0535[/C][C]-0.159[/C][C]0.0882[/C][C]1723.0537[/C][C]691.9309[/C][C]26.3046[/C][/ROW]
[ROW][C]201[/C][C]0.0586[/C][C]-0.1731[/C][C]0.0959[/C][C]2042.7076[/C][C]814.7287[/C][C]28.5435[/C][/ROW]
[ROW][C]202[/C][C]0.0637[/C][C]-0.1878[/C][C]0.1036[/C][C]2397.6816[/C][C]946.6415[/C][C]30.7675[/C][/ROW]
[ROW][C]203[/C][C]0.0702[/C][C]-0.2105[/C][C]0.1118[/C][C]3004.333[/C][C]1104.9254[/C][C]33.2404[/C][/ROW]
[ROW][C]204[/C][C]0.0769[/C][C]-0.2274[/C][C]0.1201[/C][C]3508.9311[/C][C]1276.6401[/C][C]35.7301[/C][/ROW]
[ROW][C]205[/C][C]0.0834[/C][C]-0.2498[/C][C]0.1287[/C][C]4204.4845[/C][C]1471.8298[/C][C]38.3644[/C][/ROW]
[ROW][C]206[/C][C]0.0905[/C][C]-0.2753[/C][C]0.1379[/C][C]5097.7052[/C][C]1698.447[/C][C]41.2122[/C][/ROW]
[ROW][C]207[/C][C]0.0979[/C][C]-0.2837[/C][C]0.1465[/C][C]5404.6989[/C][C]1916.4618[/C][C]43.7774[/C][/ROW]
[ROW][C]208[/C][C]0.1055[/C][C]-0.3003[/C][C]0.155[/C][C]6044.0844[/C][C]2145.7742[/C][C]46.3225[/C][/ROW]
[ROW][C]209[/C][C]0.1132[/C][C]-0.2783[/C][C]0.1615[/C][C]5172.8002[/C][C]2305.0913[/C][C]48.0114[/C][/ROW]
[ROW][C]210[/C][C]0.1219[/C][C]-0.2926[/C][C]0.1681[/C][C]5741.1936[/C][C]2476.8964[/C][C]49.7684[/C][/ROW]
[ROW][C]211[/C][C]0.1304[/C][C]-0.2941[/C][C]0.1741[/C][C]5788.816[/C][C]2634.6069[/C][C]51.3284[/C][/ROW]
[ROW][C]212[/C][C]0.1393[/C][C]-0.2763[/C][C]0.1787[/C][C]5100.8132[/C][C]2746.7072[/C][C]52.409[/C][/ROW]
[ROW][C]213[/C][C]0.1484[/C][C]-0.2675[/C][C]0.1826[/C][C]4769.9725[/C][C]2834.6752[/C][C]53.2417[/C][/ROW]
[ROW][C]214[/C][C]0.1576[/C][C]-0.2574[/C][C]0.1857[/C][C]4393.9211[/C][C]2899.6438[/C][C]53.8483[/C][/ROW]
[ROW][C]215[/C][C]0.1683[/C][C]-0.2575[/C][C]0.1886[/C][C]4375.0769[/C][C]2958.6611[/C][C]54.3936[/C][/ROW]
[ROW][C]216[/C][C]0.1795[/C][C]-0.2565[/C][C]0.1912[/C][C]4333.4217[/C][C]3011.5365[/C][C]54.8775[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71275&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
191	0.0117	-0.0136	0	12.4189	0	0
192	0.0159	-0.0227	0.0181	34.8117	23.6153	4.8596
193	0.0203	-0.0417	0.026	117.1421	54.7909	7.4021
194	0.0251	-0.068	0.0365	311.6195	118.998	10.9086
195	0.0296	-0.0815	0.0455	447.384	184.6752	13.5895
196	0.0342	-0.1062	0.0556	760.9716	280.7246	16.7548
197	0.0388	-0.1048	0.0626	740.6613	346.4299	18.6126
198	0.0437	-0.1343	0.0716	1227.904	456.6141	21.3685
199	0.0485	-0.1506	0.0804	1543.3417	577.3616	24.0284
200	0.0535	-0.159	0.0882	1723.0537	691.9309	26.3046
201	0.0586	-0.1731	0.0959	2042.7076	814.7287	28.5435
202	0.0637	-0.1878	0.1036	2397.6816	946.6415	30.7675
203	0.0702	-0.2105	0.1118	3004.333	1104.9254	33.2404
204	0.0769	-0.2274	0.1201	3508.9311	1276.6401	35.7301
205	0.0834	-0.2498	0.1287	4204.4845	1471.8298	38.3644
206	0.0905	-0.2753	0.1379	5097.7052	1698.447	41.2122
207	0.0979	-0.2837	0.1465	5404.6989	1916.4618	43.7774
208	0.1055	-0.3003	0.155	6044.0844	2145.7742	46.3225
209	0.1132	-0.2783	0.1615	5172.8002	2305.0913	48.0114
210	0.1219	-0.2926	0.1681	5741.1936	2476.8964	49.7684
211	0.1304	-0.2941	0.1741	5788.816	2634.6069	51.3284
212	0.1393	-0.2763	0.1787	5100.8132	2746.7072	52.409
213	0.1484	-0.2675	0.1826	4769.9725	2834.6752	53.2417
214	0.1576	-0.2574	0.1857	4393.9211	2899.6438	53.8483
215	0.1683	-0.2575	0.1886	4375.0769	2958.6611	54.3936
216	0.1795	-0.2565	0.1912	4333.4217	3011.5365	54.8775

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0 ; par2 = -1.0 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 0 ; par2 = -1.0 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

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

par1 <- 26
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