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ARIMA Forecasting

Date of computation

Fri, 21 Dec 2012 15:57:01 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356123451h25jpxmrxyi8ft1.htm/, Retrieved Fri, 01 Nov 2024 01:04:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204282, Retrieved Fri, 01 Nov 2024 01:04:47 +0000

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User-defined keywords

Estimated Impact

106

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               [ARIMA Forecasting] [paper arima 7] [2012-12-11 15:33:37] [dbae308bdff61c0f4902cc85498d0d35]
-  M                  [ARIMA Forecasting] [] [2012-12-21 20:57:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204282&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]2 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=204282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204282&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	2 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[63])
51	9946	-	-	-	-	-	-	-
52	9701	-	-	-	-	-	-	-
53	9049	-	-	-	-	-	-	-
54	10190	-	-	-	-	-	-	-
55	9706	-	-	-	-	-	-	-
56	9765	-	-	-	-	-	-	-
57	9893	-	-	-	-	-	-	-
58	9994	-	-	-	-	-	-	-
59	10433	-	-	-	-	-	-	-
60	10073	-	-	-	-	-	-	-
61	10112	-	-	-	-	-	-	-
62	9266	-	-	-	-	-	-	-
63	9820	-	-	-	-	-	-	-
64	10097	9912.8067	9376.3581	10449.2554	0.2505	0.6327	0.7805	0.6327
65	9115	9130.0378	8584.6792	9675.3964	0.4784	3e-04	0.6146	0.0066
66	10411	10157.5307	9603.8933	10711.1682	0.1848	0.9999	0.4542	0.8839
67	9678	9769.0794	9207.7494	10330.4094	0.3752	0.0125	0.5872	0.4294
68	10408	9851.1633	9282.6875	10419.639	0.0274	0.7248	0.6168	0.5428
69	10153	9869.8299	9294.7204	10444.9395	0.1673	0.0333	0.4685	0.5674
70	10368	10241.7467	9660.484	10823.0094	0.3352	0.6176	0.7983	0.9225
71	10581	10358.0396	9771.0769	10945.0022	0.2283	0.4867	0.4012	0.9638
72	10597	10012.0025	9419.7682	10604.2369	0.0264	0.0298	0.42	0.7374
73	10680	10082.9333	9489.4282	10676.4384	0.0243	0.0448	0.4618	0.8074
74	9738	9313.9358	8715.6738	9912.1977	0.0824	0	0.5624	0.0487
75	9556	9783.0436	9180.332	10385.7552	0.2302	0.5582	0.4522	0.4522

\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[63]) \tabularnewline
51 & 9946 & - & - & - & - & - & - & - \tabularnewline
52 & 9701 & - & - & - & - & - & - & - \tabularnewline
53 & 9049 & - & - & - & - & - & - & - \tabularnewline
54 & 10190 & - & - & - & - & - & - & - \tabularnewline
55 & 9706 & - & - & - & - & - & - & - \tabularnewline
56 & 9765 & - & - & - & - & - & - & - \tabularnewline
57 & 9893 & - & - & - & - & - & - & - \tabularnewline
58 & 9994 & - & - & - & - & - & - & - \tabularnewline
59 & 10433 & - & - & - & - & - & - & - \tabularnewline
60 & 10073 & - & - & - & - & - & - & - \tabularnewline
61 & 10112 & - & - & - & - & - & - & - \tabularnewline
62 & 9266 & - & - & - & - & - & - & - \tabularnewline
63 & 9820 & - & - & - & - & - & - & - \tabularnewline
64 & 10097 & 9912.8067 & 9376.3581 & 10449.2554 & 0.2505 & 0.6327 & 0.7805 & 0.6327 \tabularnewline
65 & 9115 & 9130.0378 & 8584.6792 & 9675.3964 & 0.4784 & 3e-04 & 0.6146 & 0.0066 \tabularnewline
66 & 10411 & 10157.5307 & 9603.8933 & 10711.1682 & 0.1848 & 0.9999 & 0.4542 & 0.8839 \tabularnewline
67 & 9678 & 9769.0794 & 9207.7494 & 10330.4094 & 0.3752 & 0.0125 & 0.5872 & 0.4294 \tabularnewline
68 & 10408 & 9851.1633 & 9282.6875 & 10419.639 & 0.0274 & 0.7248 & 0.6168 & 0.5428 \tabularnewline
69 & 10153 & 9869.8299 & 9294.7204 & 10444.9395 & 0.1673 & 0.0333 & 0.4685 & 0.5674 \tabularnewline
70 & 10368 & 10241.7467 & 9660.484 & 10823.0094 & 0.3352 & 0.6176 & 0.7983 & 0.9225 \tabularnewline
71 & 10581 & 10358.0396 & 9771.0769 & 10945.0022 & 0.2283 & 0.4867 & 0.4012 & 0.9638 \tabularnewline
72 & 10597 & 10012.0025 & 9419.7682 & 10604.2369 & 0.0264 & 0.0298 & 0.42 & 0.7374 \tabularnewline
73 & 10680 & 10082.9333 & 9489.4282 & 10676.4384 & 0.0243 & 0.0448 & 0.4618 & 0.8074 \tabularnewline
74 & 9738 & 9313.9358 & 8715.6738 & 9912.1977 & 0.0824 & 0 & 0.5624 & 0.0487 \tabularnewline
75 & 9556 & 9783.0436 & 9180.332 & 10385.7552 & 0.2302 & 0.5582 & 0.4522 & 0.4522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204282&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[63])[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9912.8067[/C][C]9376.3581[/C][C]10449.2554[/C][C]0.2505[/C][C]0.6327[/C][C]0.7805[/C][C]0.6327[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9130.0378[/C][C]8584.6792[/C][C]9675.3964[/C][C]0.4784[/C][C]3e-04[/C][C]0.6146[/C][C]0.0066[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10157.5307[/C][C]9603.8933[/C][C]10711.1682[/C][C]0.1848[/C][C]0.9999[/C][C]0.4542[/C][C]0.8839[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9769.0794[/C][C]9207.7494[/C][C]10330.4094[/C][C]0.3752[/C][C]0.0125[/C][C]0.5872[/C][C]0.4294[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9851.1633[/C][C]9282.6875[/C][C]10419.639[/C][C]0.0274[/C][C]0.7248[/C][C]0.6168[/C][C]0.5428[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]9869.8299[/C][C]9294.7204[/C][C]10444.9395[/C][C]0.1673[/C][C]0.0333[/C][C]0.4685[/C][C]0.5674[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10241.7467[/C][C]9660.484[/C][C]10823.0094[/C][C]0.3352[/C][C]0.6176[/C][C]0.7983[/C][C]0.9225[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10358.0396[/C][C]9771.0769[/C][C]10945.0022[/C][C]0.2283[/C][C]0.4867[/C][C]0.4012[/C][C]0.9638[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10012.0025[/C][C]9419.7682[/C][C]10604.2369[/C][C]0.0264[/C][C]0.0298[/C][C]0.42[/C][C]0.7374[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10082.9333[/C][C]9489.4282[/C][C]10676.4384[/C][C]0.0243[/C][C]0.0448[/C][C]0.4618[/C][C]0.8074[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9313.9358[/C][C]8715.6738[/C][C]9912.1977[/C][C]0.0824[/C][C]0[/C][C]0.5624[/C][C]0.0487[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]9783.0436[/C][C]9180.332[/C][C]10385.7552[/C][C]0.2302[/C][C]0.5582[/C][C]0.4522[/C][C]0.4522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204282&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[63])
51	9946	-	-	-	-	-	-	-
52	9701	-	-	-	-	-	-	-
53	9049	-	-	-	-	-	-	-
54	10190	-	-	-	-	-	-	-
55	9706	-	-	-	-	-	-	-
56	9765	-	-	-	-	-	-	-
57	9893	-	-	-	-	-	-	-
58	9994	-	-	-	-	-	-	-
59	10433	-	-	-	-	-	-	-
60	10073	-	-	-	-	-	-	-
61	10112	-	-	-	-	-	-	-
62	9266	-	-	-	-	-	-	-
63	9820	-	-	-	-	-	-	-
64	10097	9912.8067	9376.3581	10449.2554	0.2505	0.6327	0.7805	0.6327
65	9115	9130.0378	8584.6792	9675.3964	0.4784	3e-04	0.6146	0.0066
66	10411	10157.5307	9603.8933	10711.1682	0.1848	0.9999	0.4542	0.8839
67	9678	9769.0794	9207.7494	10330.4094	0.3752	0.0125	0.5872	0.4294
68	10408	9851.1633	9282.6875	10419.639	0.0274	0.7248	0.6168	0.5428
69	10153	9869.8299	9294.7204	10444.9395	0.1673	0.0333	0.4685	0.5674
70	10368	10241.7467	9660.484	10823.0094	0.3352	0.6176	0.7983	0.9225
71	10581	10358.0396	9771.0769	10945.0022	0.2283	0.4867	0.4012	0.9638
72	10597	10012.0025	9419.7682	10604.2369	0.0264	0.0298	0.42	0.7374
73	10680	10082.9333	9489.4282	10676.4384	0.0243	0.0448	0.4618	0.8074
74	9738	9313.9358	8715.6738	9912.1977	0.0824	0	0.5624	0.0487
75	9556	9783.0436	9180.332	10385.7552	0.2302	0.5582	0.4522	0.4522

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
64	0.0276	0.0186	0	33927.1554	0	0
65	0.0305	-0.0016	0.0101	226.1353	17076.6453	130.6776
66	0.0278	0.025	0.0151	64246.6649	32799.9852	181.1077
67	0.0293	-0.0093	0.0136	8295.4549	26673.8526	163.3213
68	0.0294	0.0565	0.0222	310067.146	83352.5113	288.7083
69	0.0297	0.0287	0.0233	80185.2845	82824.6402	287.7927
70	0.029	0.0123	0.0217	15939.8985	73269.6771	270.6837
71	0.0289	0.0215	0.0217	49711.3533	70324.8866	265.1884
72	0.0302	0.0584	0.0258	342222.0556	100535.6831	317.0736
73	0.03	0.0592	0.0291	356488.6306	126130.9779	355.1492
74	0.0328	0.0455	0.0306	179830.4573	131012.7487	361.9568
75	0.0314	-0.0232	0.03	51548.7974	124390.7528	352.6907

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
64 & 0.0276 & 0.0186 & 0 & 33927.1554 & 0 & 0 \tabularnewline
65 & 0.0305 & -0.0016 & 0.0101 & 226.1353 & 17076.6453 & 130.6776 \tabularnewline
66 & 0.0278 & 0.025 & 0.0151 & 64246.6649 & 32799.9852 & 181.1077 \tabularnewline
67 & 0.0293 & -0.0093 & 0.0136 & 8295.4549 & 26673.8526 & 163.3213 \tabularnewline
68 & 0.0294 & 0.0565 & 0.0222 & 310067.146 & 83352.5113 & 288.7083 \tabularnewline
69 & 0.0297 & 0.0287 & 0.0233 & 80185.2845 & 82824.6402 & 287.7927 \tabularnewline
70 & 0.029 & 0.0123 & 0.0217 & 15939.8985 & 73269.6771 & 270.6837 \tabularnewline
71 & 0.0289 & 0.0215 & 0.0217 & 49711.3533 & 70324.8866 & 265.1884 \tabularnewline
72 & 0.0302 & 0.0584 & 0.0258 & 342222.0556 & 100535.6831 & 317.0736 \tabularnewline
73 & 0.03 & 0.0592 & 0.0291 & 356488.6306 & 126130.9779 & 355.1492 \tabularnewline
74 & 0.0328 & 0.0455 & 0.0306 & 179830.4573 & 131012.7487 & 361.9568 \tabularnewline
75 & 0.0314 & -0.0232 & 0.03 & 51548.7974 & 124390.7528 & 352.6907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204282&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]64[/C][C]0.0276[/C][C]0.0186[/C][C]0[/C][C]33927.1554[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]0.0305[/C][C]-0.0016[/C][C]0.0101[/C][C]226.1353[/C][C]17076.6453[/C][C]130.6776[/C][/ROW]
[ROW][C]66[/C][C]0.0278[/C][C]0.025[/C][C]0.0151[/C][C]64246.6649[/C][C]32799.9852[/C][C]181.1077[/C][/ROW]
[ROW][C]67[/C][C]0.0293[/C][C]-0.0093[/C][C]0.0136[/C][C]8295.4549[/C][C]26673.8526[/C][C]163.3213[/C][/ROW]
[ROW][C]68[/C][C]0.0294[/C][C]0.0565[/C][C]0.0222[/C][C]310067.146[/C][C]83352.5113[/C][C]288.7083[/C][/ROW]
[ROW][C]69[/C][C]0.0297[/C][C]0.0287[/C][C]0.0233[/C][C]80185.2845[/C][C]82824.6402[/C][C]287.7927[/C][/ROW]
[ROW][C]70[/C][C]0.029[/C][C]0.0123[/C][C]0.0217[/C][C]15939.8985[/C][C]73269.6771[/C][C]270.6837[/C][/ROW]
[ROW][C]71[/C][C]0.0289[/C][C]0.0215[/C][C]0.0217[/C][C]49711.3533[/C][C]70324.8866[/C][C]265.1884[/C][/ROW]
[ROW][C]72[/C][C]0.0302[/C][C]0.0584[/C][C]0.0258[/C][C]342222.0556[/C][C]100535.6831[/C][C]317.0736[/C][/ROW]
[ROW][C]73[/C][C]0.03[/C][C]0.0592[/C][C]0.0291[/C][C]356488.6306[/C][C]126130.9779[/C][C]355.1492[/C][/ROW]
[ROW][C]74[/C][C]0.0328[/C][C]0.0455[/C][C]0.0306[/C][C]179830.4573[/C][C]131012.7487[/C][C]361.9568[/C][/ROW]
[ROW][C]75[/C][C]0.0314[/C][C]-0.0232[/C][C]0.03[/C][C]51548.7974[/C][C]124390.7528[/C][C]352.6907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204282&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204282&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
64	0.0276	0.0186	0	33927.1554	0	0
65	0.0305	-0.0016	0.0101	226.1353	17076.6453	130.6776
66	0.0278	0.025	0.0151	64246.6649	32799.9852	181.1077
67	0.0293	-0.0093	0.0136	8295.4549	26673.8526	163.3213
68	0.0294	0.0565	0.0222	310067.146	83352.5113	288.7083
69	0.0297	0.0287	0.0233	80185.2845	82824.6402	287.7927
70	0.029	0.0123	0.0217	15939.8985	73269.6771	270.6837
71	0.0289	0.0215	0.0217	49711.3533	70324.8866	265.1884
72	0.0302	0.0584	0.0258	342222.0556	100535.6831	317.0736
73	0.03	0.0592	0.0291	356488.6306	126130.9779	355.1492
74	0.0328	0.0455	0.0306	179830.4573	131012.7487	361.9568
75	0.0314	-0.0232	0.03	51548.7974	124390.7528	352.6907

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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