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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Thu, 22 Dec 2011 13:40:24 -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/22/t1324579274xmw8706xbrrnbtv.htm/, Retrieved Mon, 29 Apr 2024 23:17:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159843, Retrieved Mon, 29 Apr 2024 23:17:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

122

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       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [ACF van Y(t) (d=0...] [2009-11-26 00:58:58] [9717cb857c153ca3061376906953b329]
-   P           [(Partial) Autocorrelation Function] [ACF van Y(t) (d=1...] [2009-11-26 17:32:24] [9717cb857c153ca3061376906953b329]
-   P             [(Partial) Autocorrelation Function] [ACF van Y(t) (d=1...] [2009-11-26 17:41:56] [9717cb857c153ca3061376906953b329]
- RMP               [ARIMA Backward Selection] [ARIMA Backward Se...] [2009-12-03 01:42:16] [9717cb857c153ca3061376906953b329]
-                     [ARIMA Backward Selection] [Paper Arima backw...] [2011-12-20 17:11:29] [abc1cbe561c2c4615f632bb3153b1275]
- RMP                     [ARIMA Forecasting] [Paper Arima forec...] [2011-12-22 18:40:24] [c98b04636162cea751932dfe577607eb] [Current]
- R PD                      [ARIMA Forecasting] [Arima Forecasting...] [2011-12-23 19:41:16] [7156a20ff7d97880b6dc50f7239ba03b] 

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Dataseries X:

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	9 seconds
R Server	'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 & 9 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159843&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159843&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159843&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	9 seconds
R Server	'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[70])
58	278506	-	-	-	-	-	-	-
59	269826	-	-	-	-	-	-	-
60	265861	-	-	-	-	-	-	-
61	269034	-	-	-	-	-	-	-
62	264176	-	-	-	-	-	-	-
63	255198	-	-	-	-	-	-	-
64	253353	-	-	-	-	-	-	-
65	246057	-	-	-	-	-	-	-
66	235372	-	-	-	-	-	-	-
67	258556	-	-	-	-	-	-	-
68	260993	-	-	-	-	-	-	-
69	254663	-	-	-	-	-	-	-
70	250643	-	-	-	-	-	-	-
71	243422	240000.5531	234450.9062	245550.2	0.1135	1e-04	0	1e-04
72	247105	236201.5084	228824.5183	243578.4985	0.0019	0.0275	0	1e-04
73	248541	236564.9273	227828.2225	245301.6321	0.0036	0.009	0	8e-04
74	245039	231619.3729	221016.6531	242222.0927	0.0066	9e-04	0	2e-04
75	237080	223968.1318	211704.4583	236231.8053	0.0181	4e-04	0	0
76	237085	218067.5179	204097.7085	232037.3273	0.0038	0.0038	0	0
77	225554	210283.3154	194521.9571	226044.6737	0.0288	4e-04	0	0
78	226839	203239.1108	185683.8885	220794.3331	0.0042	0.0064	2e-04	0
79	247934	223995.2021	204596.5876	243393.8165	0.0078	0.3869	2e-04	0.0035
80	248333	225175.9639	203891.2866	246460.6412	0.0165	0.0181	5e-04	0.0095
81	246969	220572.4742	197366.7643	243778.184	0.0129	0.0095	0.002	0.0055
82	245098	213632.9354	188465.8154	238800.0555	0.0071	0.0047	0.002	0.002
83	246263	202679.1701	174792.7616	230565.5786	0.0011	0.0014	0.0021	4e-04
84	255765	199456.3363	168989.1164	229923.5562	1e-04	0.0013	0.0011	5e-04
85	264319	197807.4597	164805.8882	230809.0313	0	3e-04	0.0013	9e-04
86	268347	192749.1718	157034.3706	228463.9729	0	0	0.0021	7e-04
87	273046	184985.9018	146551.6641	223420.1395	0	0	0.0039	4e-04
88	273963	177798.0419	136593.416	219002.6679	0	0	0.0024	3e-04
89	267430	169691.8947	125658.3146	213725.4747	0	0	0.0065	2e-04
90	271993	162917.5134	116016.066	209818.9608	0	0	0.0038	1e-04
91	292710	182528.7454	132711.6658	232345.8251	0	2e-04	0.005	0.0037
92	295881	182893.3154	130114.5412	235672.0895	0	0	0.0075	0.0059
93	293299	178291.4478	122507.8997	234074.9959	0	0	0.0079	0.0055
94	288576	169936.0737	111106.2368	228765.9106	0	0	0.0061	0.0036

\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[70]) \tabularnewline
58 & 278506 & - & - & - & - & - & - & - \tabularnewline
59 & 269826 & - & - & - & - & - & - & - \tabularnewline
60 & 265861 & - & - & - & - & - & - & - \tabularnewline
61 & 269034 & - & - & - & - & - & - & - \tabularnewline
62 & 264176 & - & - & - & - & - & - & - \tabularnewline
63 & 255198 & - & - & - & - & - & - & - \tabularnewline
64 & 253353 & - & - & - & - & - & - & - \tabularnewline
65 & 246057 & - & - & - & - & - & - & - \tabularnewline
66 & 235372 & - & - & - & - & - & - & - \tabularnewline
67 & 258556 & - & - & - & - & - & - & - \tabularnewline
68 & 260993 & - & - & - & - & - & - & - \tabularnewline
69 & 254663 & - & - & - & - & - & - & - \tabularnewline
70 & 250643 & - & - & - & - & - & - & - \tabularnewline
71 & 243422 & 240000.5531 & 234450.9062 & 245550.2 & 0.1135 & 1e-04 & 0 & 1e-04 \tabularnewline
72 & 247105 & 236201.5084 & 228824.5183 & 243578.4985 & 0.0019 & 0.0275 & 0 & 1e-04 \tabularnewline
73 & 248541 & 236564.9273 & 227828.2225 & 245301.6321 & 0.0036 & 0.009 & 0 & 8e-04 \tabularnewline
74 & 245039 & 231619.3729 & 221016.6531 & 242222.0927 & 0.0066 & 9e-04 & 0 & 2e-04 \tabularnewline
75 & 237080 & 223968.1318 & 211704.4583 & 236231.8053 & 0.0181 & 4e-04 & 0 & 0 \tabularnewline
76 & 237085 & 218067.5179 & 204097.7085 & 232037.3273 & 0.0038 & 0.0038 & 0 & 0 \tabularnewline
77 & 225554 & 210283.3154 & 194521.9571 & 226044.6737 & 0.0288 & 4e-04 & 0 & 0 \tabularnewline
78 & 226839 & 203239.1108 & 185683.8885 & 220794.3331 & 0.0042 & 0.0064 & 2e-04 & 0 \tabularnewline
79 & 247934 & 223995.2021 & 204596.5876 & 243393.8165 & 0.0078 & 0.3869 & 2e-04 & 0.0035 \tabularnewline
80 & 248333 & 225175.9639 & 203891.2866 & 246460.6412 & 0.0165 & 0.0181 & 5e-04 & 0.0095 \tabularnewline
81 & 246969 & 220572.4742 & 197366.7643 & 243778.184 & 0.0129 & 0.0095 & 0.002 & 0.0055 \tabularnewline
82 & 245098 & 213632.9354 & 188465.8154 & 238800.0555 & 0.0071 & 0.0047 & 0.002 & 0.002 \tabularnewline
83 & 246263 & 202679.1701 & 174792.7616 & 230565.5786 & 0.0011 & 0.0014 & 0.0021 & 4e-04 \tabularnewline
84 & 255765 & 199456.3363 & 168989.1164 & 229923.5562 & 1e-04 & 0.0013 & 0.0011 & 5e-04 \tabularnewline
85 & 264319 & 197807.4597 & 164805.8882 & 230809.0313 & 0 & 3e-04 & 0.0013 & 9e-04 \tabularnewline
86 & 268347 & 192749.1718 & 157034.3706 & 228463.9729 & 0 & 0 & 0.0021 & 7e-04 \tabularnewline
87 & 273046 & 184985.9018 & 146551.6641 & 223420.1395 & 0 & 0 & 0.0039 & 4e-04 \tabularnewline
88 & 273963 & 177798.0419 & 136593.416 & 219002.6679 & 0 & 0 & 0.0024 & 3e-04 \tabularnewline
89 & 267430 & 169691.8947 & 125658.3146 & 213725.4747 & 0 & 0 & 0.0065 & 2e-04 \tabularnewline
90 & 271993 & 162917.5134 & 116016.066 & 209818.9608 & 0 & 0 & 0.0038 & 1e-04 \tabularnewline
91 & 292710 & 182528.7454 & 132711.6658 & 232345.8251 & 0 & 2e-04 & 0.005 & 0.0037 \tabularnewline
92 & 295881 & 182893.3154 & 130114.5412 & 235672.0895 & 0 & 0 & 0.0075 & 0.0059 \tabularnewline
93 & 293299 & 178291.4478 & 122507.8997 & 234074.9959 & 0 & 0 & 0.0079 & 0.0055 \tabularnewline
94 & 288576 & 169936.0737 & 111106.2368 & 228765.9106 & 0 & 0 & 0.0061 & 0.0036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159843&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[70])[/C][/ROW]
[ROW][C]58[/C][C]278506[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]269826[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]265861[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]269034[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]264176[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]63[/C][C]255198[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]64[/C][C]253353[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]65[/C][C]246057[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]66[/C][C]235372[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]67[/C][C]258556[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]68[/C][C]260993[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]69[/C][C]254663[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]70[/C][C]250643[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]71[/C][C]243422[/C][C]240000.5531[/C][C]234450.9062[/C][C]245550.2[/C][C]0.1135[/C][C]1e-04[/C][C]0[/C][C]1e-04[/C][/ROW]
[ROW][C]72[/C][C]247105[/C][C]236201.5084[/C][C]228824.5183[/C][C]243578.4985[/C][C]0.0019[/C][C]0.0275[/C][C]0[/C][C]1e-04[/C][/ROW]
[ROW][C]73[/C][C]248541[/C][C]236564.9273[/C][C]227828.2225[/C][C]245301.6321[/C][C]0.0036[/C][C]0.009[/C][C]0[/C][C]8e-04[/C][/ROW]
[ROW][C]74[/C][C]245039[/C][C]231619.3729[/C][C]221016.6531[/C][C]242222.0927[/C][C]0.0066[/C][C]9e-04[/C][C]0[/C][C]2e-04[/C][/ROW]
[ROW][C]75[/C][C]237080[/C][C]223968.1318[/C][C]211704.4583[/C][C]236231.8053[/C][C]0.0181[/C][C]4e-04[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]237085[/C][C]218067.5179[/C][C]204097.7085[/C][C]232037.3273[/C][C]0.0038[/C][C]0.0038[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]77[/C][C]225554[/C][C]210283.3154[/C][C]194521.9571[/C][C]226044.6737[/C][C]0.0288[/C][C]4e-04[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]226839[/C][C]203239.1108[/C][C]185683.8885[/C][C]220794.3331[/C][C]0.0042[/C][C]0.0064[/C][C]2e-04[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]247934[/C][C]223995.2021[/C][C]204596.5876[/C][C]243393.8165[/C][C]0.0078[/C][C]0.3869[/C][C]2e-04[/C][C]0.0035[/C][/ROW]
[ROW][C]80[/C][C]248333[/C][C]225175.9639[/C][C]203891.2866[/C][C]246460.6412[/C][C]0.0165[/C][C]0.0181[/C][C]5e-04[/C][C]0.0095[/C][/ROW]
[ROW][C]81[/C][C]246969[/C][C]220572.4742[/C][C]197366.7643[/C][C]243778.184[/C][C]0.0129[/C][C]0.0095[/C][C]0.002[/C][C]0.0055[/C][/ROW]
[ROW][C]82[/C][C]245098[/C][C]213632.9354[/C][C]188465.8154[/C][C]238800.0555[/C][C]0.0071[/C][C]0.0047[/C][C]0.002[/C][C]0.002[/C][/ROW]
[ROW][C]83[/C][C]246263[/C][C]202679.1701[/C][C]174792.7616[/C][C]230565.5786[/C][C]0.0011[/C][C]0.0014[/C][C]0.0021[/C][C]4e-04[/C][/ROW]
[ROW][C]84[/C][C]255765[/C][C]199456.3363[/C][C]168989.1164[/C][C]229923.5562[/C][C]1e-04[/C][C]0.0013[/C][C]0.0011[/C][C]5e-04[/C][/ROW]
[ROW][C]85[/C][C]264319[/C][C]197807.4597[/C][C]164805.8882[/C][C]230809.0313[/C][C]0[/C][C]3e-04[/C][C]0.0013[/C][C]9e-04[/C][/ROW]
[ROW][C]86[/C][C]268347[/C][C]192749.1718[/C][C]157034.3706[/C][C]228463.9729[/C][C]0[/C][C]0[/C][C]0.0021[/C][C]7e-04[/C][/ROW]
[ROW][C]87[/C][C]273046[/C][C]184985.9018[/C][C]146551.6641[/C][C]223420.1395[/C][C]0[/C][C]0[/C][C]0.0039[/C][C]4e-04[/C][/ROW]
[ROW][C]88[/C][C]273963[/C][C]177798.0419[/C][C]136593.416[/C][C]219002.6679[/C][C]0[/C][C]0[/C][C]0.0024[/C][C]3e-04[/C][/ROW]
[ROW][C]89[/C][C]267430[/C][C]169691.8947[/C][C]125658.3146[/C][C]213725.4747[/C][C]0[/C][C]0[/C][C]0.0065[/C][C]2e-04[/C][/ROW]
[ROW][C]90[/C][C]271993[/C][C]162917.5134[/C][C]116016.066[/C][C]209818.9608[/C][C]0[/C][C]0[/C][C]0.0038[/C][C]1e-04[/C][/ROW]
[ROW][C]91[/C][C]292710[/C][C]182528.7454[/C][C]132711.6658[/C][C]232345.8251[/C][C]0[/C][C]2e-04[/C][C]0.005[/C][C]0.0037[/C][/ROW]
[ROW][C]92[/C][C]295881[/C][C]182893.3154[/C][C]130114.5412[/C][C]235672.0895[/C][C]0[/C][C]0[/C][C]0.0075[/C][C]0.0059[/C][/ROW]
[ROW][C]93[/C][C]293299[/C][C]178291.4478[/C][C]122507.8997[/C][C]234074.9959[/C][C]0[/C][C]0[/C][C]0.0079[/C][C]0.0055[/C][/ROW]
[ROW][C]94[/C][C]288576[/C][C]169936.0737[/C][C]111106.2368[/C][C]228765.9106[/C][C]0[/C][C]0[/C][C]0.0061[/C][C]0.0036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159843&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159843&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[70])
58	278506	-	-	-	-	-	-	-
59	269826	-	-	-	-	-	-	-
60	265861	-	-	-	-	-	-	-
61	269034	-	-	-	-	-	-	-
62	264176	-	-	-	-	-	-	-
63	255198	-	-	-	-	-	-	-
64	253353	-	-	-	-	-	-	-
65	246057	-	-	-	-	-	-	-
66	235372	-	-	-	-	-	-	-
67	258556	-	-	-	-	-	-	-
68	260993	-	-	-	-	-	-	-
69	254663	-	-	-	-	-	-	-
70	250643	-	-	-	-	-	-	-
71	243422	240000.5531	234450.9062	245550.2	0.1135	1e-04	0	1e-04
72	247105	236201.5084	228824.5183	243578.4985	0.0019	0.0275	0	1e-04
73	248541	236564.9273	227828.2225	245301.6321	0.0036	0.009	0	8e-04
74	245039	231619.3729	221016.6531	242222.0927	0.0066	9e-04	0	2e-04
75	237080	223968.1318	211704.4583	236231.8053	0.0181	4e-04	0	0
76	237085	218067.5179	204097.7085	232037.3273	0.0038	0.0038	0	0
77	225554	210283.3154	194521.9571	226044.6737	0.0288	4e-04	0	0
78	226839	203239.1108	185683.8885	220794.3331	0.0042	0.0064	2e-04	0
79	247934	223995.2021	204596.5876	243393.8165	0.0078	0.3869	2e-04	0.0035
80	248333	225175.9639	203891.2866	246460.6412	0.0165	0.0181	5e-04	0.0095
81	246969	220572.4742	197366.7643	243778.184	0.0129	0.0095	0.002	0.0055
82	245098	213632.9354	188465.8154	238800.0555	0.0071	0.0047	0.002	0.002
83	246263	202679.1701	174792.7616	230565.5786	0.0011	0.0014	0.0021	4e-04
84	255765	199456.3363	168989.1164	229923.5562	1e-04	0.0013	0.0011	5e-04
85	264319	197807.4597	164805.8882	230809.0313	0	3e-04	0.0013	9e-04
86	268347	192749.1718	157034.3706	228463.9729	0	0	0.0021	7e-04
87	273046	184985.9018	146551.6641	223420.1395	0	0	0.0039	4e-04
88	273963	177798.0419	136593.416	219002.6679	0	0	0.0024	3e-04
89	267430	169691.8947	125658.3146	213725.4747	0	0	0.0065	2e-04
90	271993	162917.5134	116016.066	209818.9608	0	0	0.0038	1e-04
91	292710	182528.7454	132711.6658	232345.8251	0	2e-04	0.005	0.0037
92	295881	182893.3154	130114.5412	235672.0895	0	0	0.0075	0.0059
93	293299	178291.4478	122507.8997	234074.9959	0	0	0.0079	0.0055
94	288576	169936.0737	111106.2368	228765.9106	0	0	0.0061	0.0036

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
71	0.0118	0.0143	0	11706298.9032	0	0
72	0.0159	0.0462	0.0302	118886129.1823	65296214.0427	8080.6073
73	0.0188	0.0506	0.037	143426316.1911	91339581.4255	9557.1743
74	0.0234	0.0579	0.0422	180086392.3925	113526284.1673	10654.8714
75	0.0279	0.0585	0.0455	171921086.721	125205244.678	11189.5149
76	0.0327	0.0872	0.0525	361664626.6312	164615141.6702	12830.2432
77	0.0382	0.0726	0.0553	233193806.7326	174412093.822	13206.5171
78	0.0441	0.1161	0.0629	556954771.5274	222229928.5352	14907.3783
79	0.0442	0.1069	0.0678	573066045.1061	261211719.2653	16162.0456
80	0.0482	0.1028	0.0713	536248321.4784	288715379.4866	16991.6267
81	0.0537	0.1197	0.0757	696776576.6491	325811851.9559	18050.2591
82	0.0601	0.1473	0.0817	990050287.458	381165054.9144	19523.4488
83	0.0702	0.215	0.0919	1899550228.4085	497963914.414	22315.1051
84	0.0779	0.2823	0.1055	3170665603.8267	688871177.9434	26246.3555
85	0.0851	0.3362	0.1209	4423784987.0684	937865431.8851	30624.5887
86	0.0945	0.3922	0.1379	5715031635.9416	1236438319.6386	35163.0249
87	0.106	0.476	0.1578	7754580901.103	1619858471.4895	40247.4654
88	0.1182	0.5409	0.179	9247699158.1932	2043627398.5286	45206.4973
89	0.1324	0.576	0.1999	9552737237.265	2438843705.8305	49384.6505
90	0.1469	0.6695	0.2234	11897461766.4086	2911774608.8594	53960.8618
91	0.1392	0.6036	0.2415	12139908856.4179	3351209573.0288	57889.6327
92	0.1472	0.6178	0.2586	12766216880.2991	3779164450.632	61474.9091
93	0.1596	0.6451	0.2754	13226737062.5615	4189928477.2377	64729.6569
94	0.1766	0.6981	0.293	14075432112.8382	4601824462.0544	67836.7486

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
71 & 0.0118 & 0.0143 & 0 & 11706298.9032 & 0 & 0 \tabularnewline
72 & 0.0159 & 0.0462 & 0.0302 & 118886129.1823 & 65296214.0427 & 8080.6073 \tabularnewline
73 & 0.0188 & 0.0506 & 0.037 & 143426316.1911 & 91339581.4255 & 9557.1743 \tabularnewline
74 & 0.0234 & 0.0579 & 0.0422 & 180086392.3925 & 113526284.1673 & 10654.8714 \tabularnewline
75 & 0.0279 & 0.0585 & 0.0455 & 171921086.721 & 125205244.678 & 11189.5149 \tabularnewline
76 & 0.0327 & 0.0872 & 0.0525 & 361664626.6312 & 164615141.6702 & 12830.2432 \tabularnewline
77 & 0.0382 & 0.0726 & 0.0553 & 233193806.7326 & 174412093.822 & 13206.5171 \tabularnewline
78 & 0.0441 & 0.1161 & 0.0629 & 556954771.5274 & 222229928.5352 & 14907.3783 \tabularnewline
79 & 0.0442 & 0.1069 & 0.0678 & 573066045.1061 & 261211719.2653 & 16162.0456 \tabularnewline
80 & 0.0482 & 0.1028 & 0.0713 & 536248321.4784 & 288715379.4866 & 16991.6267 \tabularnewline
81 & 0.0537 & 0.1197 & 0.0757 & 696776576.6491 & 325811851.9559 & 18050.2591 \tabularnewline
82 & 0.0601 & 0.1473 & 0.0817 & 990050287.458 & 381165054.9144 & 19523.4488 \tabularnewline
83 & 0.0702 & 0.215 & 0.0919 & 1899550228.4085 & 497963914.414 & 22315.1051 \tabularnewline
84 & 0.0779 & 0.2823 & 0.1055 & 3170665603.8267 & 688871177.9434 & 26246.3555 \tabularnewline
85 & 0.0851 & 0.3362 & 0.1209 & 4423784987.0684 & 937865431.8851 & 30624.5887 \tabularnewline
86 & 0.0945 & 0.3922 & 0.1379 & 5715031635.9416 & 1236438319.6386 & 35163.0249 \tabularnewline
87 & 0.106 & 0.476 & 0.1578 & 7754580901.103 & 1619858471.4895 & 40247.4654 \tabularnewline
88 & 0.1182 & 0.5409 & 0.179 & 9247699158.1932 & 2043627398.5286 & 45206.4973 \tabularnewline
89 & 0.1324 & 0.576 & 0.1999 & 9552737237.265 & 2438843705.8305 & 49384.6505 \tabularnewline
90 & 0.1469 & 0.6695 & 0.2234 & 11897461766.4086 & 2911774608.8594 & 53960.8618 \tabularnewline
91 & 0.1392 & 0.6036 & 0.2415 & 12139908856.4179 & 3351209573.0288 & 57889.6327 \tabularnewline
92 & 0.1472 & 0.6178 & 0.2586 & 12766216880.2991 & 3779164450.632 & 61474.9091 \tabularnewline
93 & 0.1596 & 0.6451 & 0.2754 & 13226737062.5615 & 4189928477.2377 & 64729.6569 \tabularnewline
94 & 0.1766 & 0.6981 & 0.293 & 14075432112.8382 & 4601824462.0544 & 67836.7486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159843&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]71[/C][C]0.0118[/C][C]0.0143[/C][C]0[/C][C]11706298.9032[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]0.0159[/C][C]0.0462[/C][C]0.0302[/C][C]118886129.1823[/C][C]65296214.0427[/C][C]8080.6073[/C][/ROW]
[ROW][C]73[/C][C]0.0188[/C][C]0.0506[/C][C]0.037[/C][C]143426316.1911[/C][C]91339581.4255[/C][C]9557.1743[/C][/ROW]
[ROW][C]74[/C][C]0.0234[/C][C]0.0579[/C][C]0.0422[/C][C]180086392.3925[/C][C]113526284.1673[/C][C]10654.8714[/C][/ROW]
[ROW][C]75[/C][C]0.0279[/C][C]0.0585[/C][C]0.0455[/C][C]171921086.721[/C][C]125205244.678[/C][C]11189.5149[/C][/ROW]
[ROW][C]76[/C][C]0.0327[/C][C]0.0872[/C][C]0.0525[/C][C]361664626.6312[/C][C]164615141.6702[/C][C]12830.2432[/C][/ROW]
[ROW][C]77[/C][C]0.0382[/C][C]0.0726[/C][C]0.0553[/C][C]233193806.7326[/C][C]174412093.822[/C][C]13206.5171[/C][/ROW]
[ROW][C]78[/C][C]0.0441[/C][C]0.1161[/C][C]0.0629[/C][C]556954771.5274[/C][C]222229928.5352[/C][C]14907.3783[/C][/ROW]
[ROW][C]79[/C][C]0.0442[/C][C]0.1069[/C][C]0.0678[/C][C]573066045.1061[/C][C]261211719.2653[/C][C]16162.0456[/C][/ROW]
[ROW][C]80[/C][C]0.0482[/C][C]0.1028[/C][C]0.0713[/C][C]536248321.4784[/C][C]288715379.4866[/C][C]16991.6267[/C][/ROW]
[ROW][C]81[/C][C]0.0537[/C][C]0.1197[/C][C]0.0757[/C][C]696776576.6491[/C][C]325811851.9559[/C][C]18050.2591[/C][/ROW]
[ROW][C]82[/C][C]0.0601[/C][C]0.1473[/C][C]0.0817[/C][C]990050287.458[/C][C]381165054.9144[/C][C]19523.4488[/C][/ROW]
[ROW][C]83[/C][C]0.0702[/C][C]0.215[/C][C]0.0919[/C][C]1899550228.4085[/C][C]497963914.414[/C][C]22315.1051[/C][/ROW]
[ROW][C]84[/C][C]0.0779[/C][C]0.2823[/C][C]0.1055[/C][C]3170665603.8267[/C][C]688871177.9434[/C][C]26246.3555[/C][/ROW]
[ROW][C]85[/C][C]0.0851[/C][C]0.3362[/C][C]0.1209[/C][C]4423784987.0684[/C][C]937865431.8851[/C][C]30624.5887[/C][/ROW]
[ROW][C]86[/C][C]0.0945[/C][C]0.3922[/C][C]0.1379[/C][C]5715031635.9416[/C][C]1236438319.6386[/C][C]35163.0249[/C][/ROW]
[ROW][C]87[/C][C]0.106[/C][C]0.476[/C][C]0.1578[/C][C]7754580901.103[/C][C]1619858471.4895[/C][C]40247.4654[/C][/ROW]
[ROW][C]88[/C][C]0.1182[/C][C]0.5409[/C][C]0.179[/C][C]9247699158.1932[/C][C]2043627398.5286[/C][C]45206.4973[/C][/ROW]
[ROW][C]89[/C][C]0.1324[/C][C]0.576[/C][C]0.1999[/C][C]9552737237.265[/C][C]2438843705.8305[/C][C]49384.6505[/C][/ROW]
[ROW][C]90[/C][C]0.1469[/C][C]0.6695[/C][C]0.2234[/C][C]11897461766.4086[/C][C]2911774608.8594[/C][C]53960.8618[/C][/ROW]
[ROW][C]91[/C][C]0.1392[/C][C]0.6036[/C][C]0.2415[/C][C]12139908856.4179[/C][C]3351209573.0288[/C][C]57889.6327[/C][/ROW]
[ROW][C]92[/C][C]0.1472[/C][C]0.6178[/C][C]0.2586[/C][C]12766216880.2991[/C][C]3779164450.632[/C][C]61474.9091[/C][/ROW]
[ROW][C]93[/C][C]0.1596[/C][C]0.6451[/C][C]0.2754[/C][C]13226737062.5615[/C][C]4189928477.2377[/C][C]64729.6569[/C][/ROW]
[ROW][C]94[/C][C]0.1766[/C][C]0.6981[/C][C]0.293[/C][C]14075432112.8382[/C][C]4601824462.0544[/C][C]67836.7486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159843&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159843&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
71	0.0118	0.0143	0	11706298.9032	0	0
72	0.0159	0.0462	0.0302	118886129.1823	65296214.0427	8080.6073
73	0.0188	0.0506	0.037	143426316.1911	91339581.4255	9557.1743
74	0.0234	0.0579	0.0422	180086392.3925	113526284.1673	10654.8714
75	0.0279	0.0585	0.0455	171921086.721	125205244.678	11189.5149
76	0.0327	0.0872	0.0525	361664626.6312	164615141.6702	12830.2432
77	0.0382	0.0726	0.0553	233193806.7326	174412093.822	13206.5171
78	0.0441	0.1161	0.0629	556954771.5274	222229928.5352	14907.3783
79	0.0442	0.1069	0.0678	573066045.1061	261211719.2653	16162.0456
80	0.0482	0.1028	0.0713	536248321.4784	288715379.4866	16991.6267
81	0.0537	0.1197	0.0757	696776576.6491	325811851.9559	18050.2591
82	0.0601	0.1473	0.0817	990050287.458	381165054.9144	19523.4488
83	0.0702	0.215	0.0919	1899550228.4085	497963914.414	22315.1051
84	0.0779	0.2823	0.1055	3170665603.8267	688871177.9434	26246.3555
85	0.0851	0.3362	0.1209	4423784987.0684	937865431.8851	30624.5887
86	0.0945	0.3922	0.1379	5715031635.9416	1236438319.6386	35163.0249
87	0.106	0.476	0.1578	7754580901.103	1619858471.4895	40247.4654
88	0.1182	0.5409	0.179	9247699158.1932	2043627398.5286	45206.4973
89	0.1324	0.576	0.1999	9552737237.265	2438843705.8305	49384.6505
90	0.1469	0.6695	0.2234	11897461766.4086	2911774608.8594	53960.8618
91	0.1392	0.6036	0.2415	12139908856.4179	3351209573.0288	57889.6327
92	0.1472	0.6178	0.2586	12766216880.2991	3779164450.632	61474.9091
93	0.1596	0.6451	0.2754	13226737062.5615	4189928477.2377	64729.6569
94	0.1766	0.6981	0.293	14075432112.8382	4601824462.0544	67836.7486

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

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