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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Wed, 19 Dec 2012 09:13:54 -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/2012/Dec/19/t1355926458wi8x37z5xclipvf.htm/, Retrieved Mon, 29 Apr 2024 12:15:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201976, Retrieved Mon, 29 Apr 2024 12:15:03 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

118

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 Backward Selection] [Births] [2010-11-29 17:47:06] [b98453cac15ba1066b407e146608df68]
-   P             [ARIMA Backward Selection] [ARIMA model d=1,D...] [2012-11-22 09:43:52] [0dc867bfbaab36a894719867823e3cb9]
- R P               [ARIMA Backward Selection] [ARIMA  lambda = 0...] [2012-12-16 21:07:32] [0dc867bfbaab36a894719867823e3cb9]
- RMP                   [ARIMA Forecasting] [ARIMA  Model Fore...] [2012-12-19 14:13:54] [b7b610b08ce09537f4b16b68ce5f31b7] [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	7 seconds
R Server	'George Udny Yule' @ yule.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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201976&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201976&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	7 seconds
R Server	'George Udny Yule' @ yule.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	9705.99999999999	-	-	-	-	-	-	-
56	9764.99999999999	-	-	-	-	-	-	-
57	9893	-	-	-	-	-	-	-
58	9993.99999999999	-	-	-	-	-	-	-
59	10433	-	-	-	-	-	-	-
60	10073	-	-	-	-	-	-	-
61	10112	-	-	-	-	-	-	-
62	9266	-	-	-	-	-	-	-
63	9820	-	-	-	-	-	-	-
64	10097	9969.4531	9429.2032	10540.6568	0.3308	0.696	0.8215	0.696
65	9115	9075.2585	8577.621	9601.7667	0.4412	1e-04	0.5389	0.0028
66	10411	10176.4416	9615.845	10769.7206	0.2192	0.9998	0.4821	0.8805
67	9678	9765.5906	9210.2494	10354.4166	0.3853	0.0158	0.5786	0.4281
68	10408	9868.8604	9303.8997	10468.1271	0.0389	0.7338	0.633	0.5635
69	10153	9846.6868	9272.8254	10456.0624	0.1623	0.0355	0.4408	0.5342
70	10368	10247.3366	9644.8088	10887.5054	0.3559	0.6136	0.781	0.9046
71	10581	10352.0233	9736.0553	11006.9615	0.2466	0.4809	0.4043	0.9443
72	10597	9990.1888	9390.4498	10628.2313	0.0312	0.0348	0.3996	0.6994
73	10680	10083.5437	9476.6928	10729.2551	0.0351	0.0596	0.4656	0.7881
74	9738	9287.4555	8723.9078	9887.4073	0.0705	0	0.5279	0.0409
75	9556	9754.0222	9157.4411	10389.4688	0.2707	0.5197	0.4194	0.4194

\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 & 9705.99999999999 & - & - & - & - & - & - & - \tabularnewline
56 & 9764.99999999999 & - & - & - & - & - & - & - \tabularnewline
57 & 9893 & - & - & - & - & - & - & - \tabularnewline
58 & 9993.99999999999 & - & - & - & - & - & - & - \tabularnewline
59 & 10433 & - & - & - & - & - & - & - \tabularnewline
60 & 10073 & - & - & - & - & - & - & - \tabularnewline
61 & 10112 & - & - & - & - & - & - & - \tabularnewline
62 & 9266 & - & - & - & - & - & - & - \tabularnewline
63 & 9820 & - & - & - & - & - & - & - \tabularnewline
64 & 10097 & 9969.4531 & 9429.2032 & 10540.6568 & 0.3308 & 0.696 & 0.8215 & 0.696 \tabularnewline
65 & 9115 & 9075.2585 & 8577.621 & 9601.7667 & 0.4412 & 1e-04 & 0.5389 & 0.0028 \tabularnewline
66 & 10411 & 10176.4416 & 9615.845 & 10769.7206 & 0.2192 & 0.9998 & 0.4821 & 0.8805 \tabularnewline
67 & 9678 & 9765.5906 & 9210.2494 & 10354.4166 & 0.3853 & 0.0158 & 0.5786 & 0.4281 \tabularnewline
68 & 10408 & 9868.8604 & 9303.8997 & 10468.1271 & 0.0389 & 0.7338 & 0.633 & 0.5635 \tabularnewline
69 & 10153 & 9846.6868 & 9272.8254 & 10456.0624 & 0.1623 & 0.0355 & 0.4408 & 0.5342 \tabularnewline
70 & 10368 & 10247.3366 & 9644.8088 & 10887.5054 & 0.3559 & 0.6136 & 0.781 & 0.9046 \tabularnewline
71 & 10581 & 10352.0233 & 9736.0553 & 11006.9615 & 0.2466 & 0.4809 & 0.4043 & 0.9443 \tabularnewline
72 & 10597 & 9990.1888 & 9390.4498 & 10628.2313 & 0.0312 & 0.0348 & 0.3996 & 0.6994 \tabularnewline
73 & 10680 & 10083.5437 & 9476.6928 & 10729.2551 & 0.0351 & 0.0596 & 0.4656 & 0.7881 \tabularnewline
74 & 9738 & 9287.4555 & 8723.9078 & 9887.4073 & 0.0705 & 0 & 0.5279 & 0.0409 \tabularnewline
75 & 9556 & 9754.0222 & 9157.4411 & 10389.4688 & 0.2707 & 0.5197 & 0.4194 & 0.4194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201976&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]9705.99999999999[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]9764.99999999999[/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]9993.99999999999[/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]9969.4531[/C][C]9429.2032[/C][C]10540.6568[/C][C]0.3308[/C][C]0.696[/C][C]0.8215[/C][C]0.696[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9075.2585[/C][C]8577.621[/C][C]9601.7667[/C][C]0.4412[/C][C]1e-04[/C][C]0.5389[/C][C]0.0028[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10176.4416[/C][C]9615.845[/C][C]10769.7206[/C][C]0.2192[/C][C]0.9998[/C][C]0.4821[/C][C]0.8805[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9765.5906[/C][C]9210.2494[/C][C]10354.4166[/C][C]0.3853[/C][C]0.0158[/C][C]0.5786[/C][C]0.4281[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9868.8604[/C][C]9303.8997[/C][C]10468.1271[/C][C]0.0389[/C][C]0.7338[/C][C]0.633[/C][C]0.5635[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]9846.6868[/C][C]9272.8254[/C][C]10456.0624[/C][C]0.1623[/C][C]0.0355[/C][C]0.4408[/C][C]0.5342[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10247.3366[/C][C]9644.8088[/C][C]10887.5054[/C][C]0.3559[/C][C]0.6136[/C][C]0.781[/C][C]0.9046[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10352.0233[/C][C]9736.0553[/C][C]11006.9615[/C][C]0.2466[/C][C]0.4809[/C][C]0.4043[/C][C]0.9443[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]9990.1888[/C][C]9390.4498[/C][C]10628.2313[/C][C]0.0312[/C][C]0.0348[/C][C]0.3996[/C][C]0.6994[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10083.5437[/C][C]9476.6928[/C][C]10729.2551[/C][C]0.0351[/C][C]0.0596[/C][C]0.4656[/C][C]0.7881[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9287.4555[/C][C]8723.9078[/C][C]9887.4073[/C][C]0.0705[/C][C]0[/C][C]0.5279[/C][C]0.0409[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]9754.0222[/C][C]9157.4411[/C][C]10389.4688[/C][C]0.2707[/C][C]0.5197[/C][C]0.4194[/C][C]0.4194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201976&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	9705.99999999999	-	-	-	-	-	-	-
56	9764.99999999999	-	-	-	-	-	-	-
57	9893	-	-	-	-	-	-	-
58	9993.99999999999	-	-	-	-	-	-	-
59	10433	-	-	-	-	-	-	-
60	10073	-	-	-	-	-	-	-
61	10112	-	-	-	-	-	-	-
62	9266	-	-	-	-	-	-	-
63	9820	-	-	-	-	-	-	-
64	10097	9969.4531	9429.2032	10540.6568	0.3308	0.696	0.8215	0.696
65	9115	9075.2585	8577.621	9601.7667	0.4412	1e-04	0.5389	0.0028
66	10411	10176.4416	9615.845	10769.7206	0.2192	0.9998	0.4821	0.8805
67	9678	9765.5906	9210.2494	10354.4166	0.3853	0.0158	0.5786	0.4281
68	10408	9868.8604	9303.8997	10468.1271	0.0389	0.7338	0.633	0.5635
69	10153	9846.6868	9272.8254	10456.0624	0.1623	0.0355	0.4408	0.5342
70	10368	10247.3366	9644.8088	10887.5054	0.3559	0.6136	0.781	0.9046
71	10581	10352.0233	9736.0553	11006.9615	0.2466	0.4809	0.4043	0.9443
72	10597	9990.1888	9390.4498	10628.2313	0.0312	0.0348	0.3996	0.6994
73	10680	10083.5437	9476.6928	10729.2551	0.0351	0.0596	0.4656	0.7881
74	9738	9287.4555	8723.9078	9887.4073	0.0705	0	0.5279	0.0409
75	9556	9754.0222	9157.4411	10389.4688	0.2707	0.5197	0.4194	0.4194

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
64	0.0292	0.0128	0	16268.2185	0	0
65	0.0296	0.0044	0.0086	1579.3903	8923.8044	94.4659
66	0.0297	0.023	0.0134	55017.6221	24288.4103	155.8474
67	0.0308	-0.009	0.0123	7672.1047	20134.3339	141.8955
68	0.031	0.0546	0.0208	290671.5553	74241.7782	272.4734
69	0.0316	0.0311	0.0225	93827.7694	77506.11	278.3992
70	0.0319	0.0118	0.021	14559.6479	68513.7583	261.7513
71	0.0323	0.0221	0.0211	52430.3374	66503.3307	257.8824
72	0.0326	0.0607	0.0255	368219.8409	100027.3874	316.2711
73	0.0327	0.0592	0.0289	355760.0715	125600.6558	354.4018
74	0.033	0.0485	0.0307	202990.3621	132636.0837	364.1924
75	0.0332	-0.0203	0.0298	39212.797	124850.8098	353.3423

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
64 & 0.0292 & 0.0128 & 0 & 16268.2185 & 0 & 0 \tabularnewline
65 & 0.0296 & 0.0044 & 0.0086 & 1579.3903 & 8923.8044 & 94.4659 \tabularnewline
66 & 0.0297 & 0.023 & 0.0134 & 55017.6221 & 24288.4103 & 155.8474 \tabularnewline
67 & 0.0308 & -0.009 & 0.0123 & 7672.1047 & 20134.3339 & 141.8955 \tabularnewline
68 & 0.031 & 0.0546 & 0.0208 & 290671.5553 & 74241.7782 & 272.4734 \tabularnewline
69 & 0.0316 & 0.0311 & 0.0225 & 93827.7694 & 77506.11 & 278.3992 \tabularnewline
70 & 0.0319 & 0.0118 & 0.021 & 14559.6479 & 68513.7583 & 261.7513 \tabularnewline
71 & 0.0323 & 0.0221 & 0.0211 & 52430.3374 & 66503.3307 & 257.8824 \tabularnewline
72 & 0.0326 & 0.0607 & 0.0255 & 368219.8409 & 100027.3874 & 316.2711 \tabularnewline
73 & 0.0327 & 0.0592 & 0.0289 & 355760.0715 & 125600.6558 & 354.4018 \tabularnewline
74 & 0.033 & 0.0485 & 0.0307 & 202990.3621 & 132636.0837 & 364.1924 \tabularnewline
75 & 0.0332 & -0.0203 & 0.0298 & 39212.797 & 124850.8098 & 353.3423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201976&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]0.0292[/C][C]0.0128[/C][C]0[/C][C]16268.2185[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]0.0296[/C][C]0.0044[/C][C]0.0086[/C][C]1579.3903[/C][C]8923.8044[/C][C]94.4659[/C][/ROW]
[ROW][C]66[/C][C]0.0297[/C][C]0.023[/C][C]0.0134[/C][C]55017.6221[/C][C]24288.4103[/C][C]155.8474[/C][/ROW]
[ROW][C]67[/C][C]0.0308[/C][C]-0.009[/C][C]0.0123[/C][C]7672.1047[/C][C]20134.3339[/C][C]141.8955[/C][/ROW]
[ROW][C]68[/C][C]0.031[/C][C]0.0546[/C][C]0.0208[/C][C]290671.5553[/C][C]74241.7782[/C][C]272.4734[/C][/ROW]
[ROW][C]69[/C][C]0.0316[/C][C]0.0311[/C][C]0.0225[/C][C]93827.7694[/C][C]77506.11[/C][C]278.3992[/C][/ROW]
[ROW][C]70[/C][C]0.0319[/C][C]0.0118[/C][C]0.021[/C][C]14559.6479[/C][C]68513.7583[/C][C]261.7513[/C][/ROW]
[ROW][C]71[/C][C]0.0323[/C][C]0.0221[/C][C]0.0211[/C][C]52430.3374[/C][C]66503.3307[/C][C]257.8824[/C][/ROW]
[ROW][C]72[/C][C]0.0326[/C][C]0.0607[/C][C]0.0255[/C][C]368219.8409[/C][C]100027.3874[/C][C]316.2711[/C][/ROW]
[ROW][C]73[/C][C]0.0327[/C][C]0.0592[/C][C]0.0289[/C][C]355760.0715[/C][C]125600.6558[/C][C]354.4018[/C][/ROW]
[ROW][C]74[/C][C]0.033[/C][C]0.0485[/C][C]0.0307[/C][C]202990.3621[/C][C]132636.0837[/C][C]364.1924[/C][/ROW]
[ROW][C]75[/C][C]0.0332[/C][C]-0.0203[/C][C]0.0298[/C][C]39212.797[/C][C]124850.8098[/C][C]353.3423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201976&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	0.0292	0.0128	0	16268.2185	0	0
65	0.0296	0.0044	0.0086	1579.3903	8923.8044	94.4659
66	0.0297	0.023	0.0134	55017.6221	24288.4103	155.8474
67	0.0308	-0.009	0.0123	7672.1047	20134.3339	141.8955
68	0.031	0.0546	0.0208	290671.5553	74241.7782	272.4734
69	0.0316	0.0311	0.0225	93827.7694	77506.11	278.3992
70	0.0319	0.0118	0.021	14559.6479	68513.7583	261.7513
71	0.0323	0.0221	0.0211	52430.3374	66503.3307	257.8824
72	0.0326	0.0607	0.0255	368219.8409	100027.3874	316.2711
73	0.0327	0.0592	0.0289	355760.0715	125600.6558	354.4018
74	0.033	0.0485	0.0307	202990.3621	132636.0837	364.1924
75	0.0332	-0.0203	0.0298	39212.797	124850.8098	353.3423

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 12 ; par2 = 0.0 ; par3 = 0 ; 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