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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 24 Dec 2010 15:04:34 +0000

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/2010/Dec/24/t1293203274nbfgsbf3fyjwyn4.htm/, Retrieved Tue, 30 Apr 2024 06:16:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115076, Retrieved Tue, 30 Apr 2024 06:16:23 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

158

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

-     [Standard Deviation-Mean Plot] [SMP prof bach] [2008-12-15 22:25:20] [bc937651ef42bf891200cf0e0edc7238]
- RM    [Variance Reduction Matrix] [VRM prof bach] [2008-12-15 22:31:00] [bc937651ef42bf891200cf0e0edc7238]
- RMP     [(Partial) Autocorrelation Function] [ARIMA Prof bach A...] [2008-12-15 22:38:57] [bc937651ef42bf891200cf0e0edc7238]
- RMP       [ARIMA Backward Selection] [Arima backward se...] [2008-12-19 17:26:16] [bc937651ef42bf891200cf0e0edc7238]
- RMP         [ARIMA Forecasting] [ARIMA forecast pr...] [2008-12-20 11:34:44] [bc937651ef42bf891200cf0e0edc7238]
-  MPD          [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-22 13:25:50] [616fb52b46273b7e6805de1e68b3a688]
-    D              [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-24 15:04:34] [733bf75cb326fe693c93e834bfd34d22] [Current]

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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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115076&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115076&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

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[61])
49	501866	-	-	-	-	-	-	-
50	516141	-	-	-	-	-	-	-
51	528222	-	-	-	-	-	-	-
52	532638	-	-	-	-	-	-	-
53	536322	-	-	-	-	-	-	-
54	536535	-	-	-	-	-	-	-
55	523597	-	-	-	-	-	-	-
56	536214	-	-	-	-	-	-	-
57	586570	-	-	-	-	-	-	-
58	596594	-	-	-	-	-	-	-
59	580523	-	-	-	-	-	-	-
60	564478	-	-	-	-	-	-	-
61	557560	-	-	-	-	-	-	-
62	575093	571999.2044	556089.5661	587908.8427	0.3515	0.9624	1	0.9624
63	580112	584224.2574	559889.0446	608559.4702	0.3702	0.769	1	0.9841
64	574761	588766.632	556875.5815	620657.6826	0.1947	0.7026	0.9997	0.9724
65	563250	592561.4977	553509.5583	631613.4372	0.0706	0.8142	0.9976	0.9605
66	551531	592871.7579	546913.5286	638829.9871	0.0389	0.8968	0.9919	0.934
67	537034	580019.0821	527356.4077	632681.7564	0.0548	0.8555	0.9821	0.7984
68	544686	592710.9352	533523.2591	651898.6112	0.0559	0.9674	0.9693	0.8778
69	600991	643132.6022	577588.7407	708676.4637	0.1038	0.9984	0.9546	0.9948
70	604378	653214.2105	581477.0241	724951.3968	0.0911	0.9232	0.9391	0.9955
71	586111	637193.749	559421.8626	714965.6353	0.099	0.7959	0.9234	0.9776
72	563668	621193.0853	537541.3483	704844.8223	0.0889	0.7945	0.9081	0.932
73	548604	614313.9806	524933.408	703694.5533	0.0748	0.8666	0.8933	0.8933

\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[61]) \tabularnewline
49 & 501866 & - & - & - & - & - & - & - \tabularnewline
50 & 516141 & - & - & - & - & - & - & - \tabularnewline
51 & 528222 & - & - & - & - & - & - & - \tabularnewline
52 & 532638 & - & - & - & - & - & - & - \tabularnewline
53 & 536322 & - & - & - & - & - & - & - \tabularnewline
54 & 536535 & - & - & - & - & - & - & - \tabularnewline
55 & 523597 & - & - & - & - & - & - & - \tabularnewline
56 & 536214 & - & - & - & - & - & - & - \tabularnewline
57 & 586570 & - & - & - & - & - & - & - \tabularnewline
58 & 596594 & - & - & - & - & - & - & - \tabularnewline
59 & 580523 & - & - & - & - & - & - & - \tabularnewline
60 & 564478 & - & - & - & - & - & - & - \tabularnewline
61 & 557560 & - & - & - & - & - & - & - \tabularnewline
62 & 575093 & 571999.2044 & 556089.5661 & 587908.8427 & 0.3515 & 0.9624 & 1 & 0.9624 \tabularnewline
63 & 580112 & 584224.2574 & 559889.0446 & 608559.4702 & 0.3702 & 0.769 & 1 & 0.9841 \tabularnewline
64 & 574761 & 588766.632 & 556875.5815 & 620657.6826 & 0.1947 & 0.7026 & 0.9997 & 0.9724 \tabularnewline
65 & 563250 & 592561.4977 & 553509.5583 & 631613.4372 & 0.0706 & 0.8142 & 0.9976 & 0.9605 \tabularnewline
66 & 551531 & 592871.7579 & 546913.5286 & 638829.9871 & 0.0389 & 0.8968 & 0.9919 & 0.934 \tabularnewline
67 & 537034 & 580019.0821 & 527356.4077 & 632681.7564 & 0.0548 & 0.8555 & 0.9821 & 0.7984 \tabularnewline
68 & 544686 & 592710.9352 & 533523.2591 & 651898.6112 & 0.0559 & 0.9674 & 0.9693 & 0.8778 \tabularnewline
69 & 600991 & 643132.6022 & 577588.7407 & 708676.4637 & 0.1038 & 0.9984 & 0.9546 & 0.9948 \tabularnewline
70 & 604378 & 653214.2105 & 581477.0241 & 724951.3968 & 0.0911 & 0.9232 & 0.9391 & 0.9955 \tabularnewline
71 & 586111 & 637193.749 & 559421.8626 & 714965.6353 & 0.099 & 0.7959 & 0.9234 & 0.9776 \tabularnewline
72 & 563668 & 621193.0853 & 537541.3483 & 704844.8223 & 0.0889 & 0.7945 & 0.9081 & 0.932 \tabularnewline
73 & 548604 & 614313.9806 & 524933.408 & 703694.5533 & 0.0748 & 0.8666 & 0.8933 & 0.8933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115076&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[61])[/C][/ROW]
[ROW][C]49[/C][C]501866[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]516141[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]528222[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]532638[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]536322[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]536535[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]523597[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]536214[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]586570[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]596594[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]580523[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]564478[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]557560[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]575093[/C][C]571999.2044[/C][C]556089.5661[/C][C]587908.8427[/C][C]0.3515[/C][C]0.9624[/C][C]1[/C][C]0.9624[/C][/ROW]
[ROW][C]63[/C][C]580112[/C][C]584224.2574[/C][C]559889.0446[/C][C]608559.4702[/C][C]0.3702[/C][C]0.769[/C][C]1[/C][C]0.9841[/C][/ROW]
[ROW][C]64[/C][C]574761[/C][C]588766.632[/C][C]556875.5815[/C][C]620657.6826[/C][C]0.1947[/C][C]0.7026[/C][C]0.9997[/C][C]0.9724[/C][/ROW]
[ROW][C]65[/C][C]563250[/C][C]592561.4977[/C][C]553509.5583[/C][C]631613.4372[/C][C]0.0706[/C][C]0.8142[/C][C]0.9976[/C][C]0.9605[/C][/ROW]
[ROW][C]66[/C][C]551531[/C][C]592871.7579[/C][C]546913.5286[/C][C]638829.9871[/C][C]0.0389[/C][C]0.8968[/C][C]0.9919[/C][C]0.934[/C][/ROW]
[ROW][C]67[/C][C]537034[/C][C]580019.0821[/C][C]527356.4077[/C][C]632681.7564[/C][C]0.0548[/C][C]0.8555[/C][C]0.9821[/C][C]0.7984[/C][/ROW]
[ROW][C]68[/C][C]544686[/C][C]592710.9352[/C][C]533523.2591[/C][C]651898.6112[/C][C]0.0559[/C][C]0.9674[/C][C]0.9693[/C][C]0.8778[/C][/ROW]
[ROW][C]69[/C][C]600991[/C][C]643132.6022[/C][C]577588.7407[/C][C]708676.4637[/C][C]0.1038[/C][C]0.9984[/C][C]0.9546[/C][C]0.9948[/C][/ROW]
[ROW][C]70[/C][C]604378[/C][C]653214.2105[/C][C]581477.0241[/C][C]724951.3968[/C][C]0.0911[/C][C]0.9232[/C][C]0.9391[/C][C]0.9955[/C][/ROW]
[ROW][C]71[/C][C]586111[/C][C]637193.749[/C][C]559421.8626[/C][C]714965.6353[/C][C]0.099[/C][C]0.7959[/C][C]0.9234[/C][C]0.9776[/C][/ROW]
[ROW][C]72[/C][C]563668[/C][C]621193.0853[/C][C]537541.3483[/C][C]704844.8223[/C][C]0.0889[/C][C]0.7945[/C][C]0.9081[/C][C]0.932[/C][/ROW]
[ROW][C]73[/C][C]548604[/C][C]614313.9806[/C][C]524933.408[/C][C]703694.5533[/C][C]0.0748[/C][C]0.8666[/C][C]0.8933[/C][C]0.8933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115076&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[61])
49	501866	-	-	-	-	-	-	-
50	516141	-	-	-	-	-	-	-
51	528222	-	-	-	-	-	-	-
52	532638	-	-	-	-	-	-	-
53	536322	-	-	-	-	-	-	-
54	536535	-	-	-	-	-	-	-
55	523597	-	-	-	-	-	-	-
56	536214	-	-	-	-	-	-	-
57	586570	-	-	-	-	-	-	-
58	596594	-	-	-	-	-	-	-
59	580523	-	-	-	-	-	-	-
60	564478	-	-	-	-	-	-	-
61	557560	-	-	-	-	-	-	-
62	575093	571999.2044	556089.5661	587908.8427	0.3515	0.9624	1	0.9624
63	580112	584224.2574	559889.0446	608559.4702	0.3702	0.769	1	0.9841
64	574761	588766.632	556875.5815	620657.6826	0.1947	0.7026	0.9997	0.9724
65	563250	592561.4977	553509.5583	631613.4372	0.0706	0.8142	0.9976	0.9605
66	551531	592871.7579	546913.5286	638829.9871	0.0389	0.8968	0.9919	0.934
67	537034	580019.0821	527356.4077	632681.7564	0.0548	0.8555	0.9821	0.7984
68	544686	592710.9352	533523.2591	651898.6112	0.0559	0.9674	0.9693	0.8778
69	600991	643132.6022	577588.7407	708676.4637	0.1038	0.9984	0.9546	0.9948
70	604378	653214.2105	581477.0241	724951.3968	0.0911	0.9232	0.9391	0.9955
71	586111	637193.749	559421.8626	714965.6353	0.099	0.7959	0.9234	0.9776
72	563668	621193.0853	537541.3483	704844.8223	0.0889	0.7945	0.9081	0.932
73	548604	614313.9806	524933.408	703694.5533	0.0748	0.8666	0.8933	0.8933

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
62	0.0142	0.0054	5e-04	9571571.1811	797630.9318	893.1019
63	0.0213	-0.007	6e-04	16910660.9671	1409221.7473	1187.1065
64	0.0276	-0.0238	0.002	196157727.9887	16346477.3324	4043.0777
65	0.0336	-0.0495	0.0041	859163899.5923	71596991.6327	8461.5006
66	0.0395	-0.0697	0.0058	1709058260.4273	142421521.7023	11934.0488
67	0.0463	-0.0741	0.0062	1847717281.2219	153976440.1018	12408.7244
68	0.0509	-0.081	0.0068	2306394399.2583	192199533.2715	13863.6046
69	0.052	-0.0655	0.0055	1775914636.3214	147992886.3601	12165.2327
70	0.056	-0.0748	0.0062	2384975453.3172	198747954.4431	14097.7996
71	0.0623	-0.0802	0.0067	2609447242.3126	217453936.8594	14746.3194
72	0.0687	-0.0926	0.0077	3309135439.7564	275761286.6464	16606.0617
73	0.0742	-0.107	0.0089	4317801553.9688	359816796.1641	18968.8375

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
62 & 0.0142 & 0.0054 & 5e-04 & 9571571.1811 & 797630.9318 & 893.1019 \tabularnewline
63 & 0.0213 & -0.007 & 6e-04 & 16910660.9671 & 1409221.7473 & 1187.1065 \tabularnewline
64 & 0.0276 & -0.0238 & 0.002 & 196157727.9887 & 16346477.3324 & 4043.0777 \tabularnewline
65 & 0.0336 & -0.0495 & 0.0041 & 859163899.5923 & 71596991.6327 & 8461.5006 \tabularnewline
66 & 0.0395 & -0.0697 & 0.0058 & 1709058260.4273 & 142421521.7023 & 11934.0488 \tabularnewline
67 & 0.0463 & -0.0741 & 0.0062 & 1847717281.2219 & 153976440.1018 & 12408.7244 \tabularnewline
68 & 0.0509 & -0.081 & 0.0068 & 2306394399.2583 & 192199533.2715 & 13863.6046 \tabularnewline
69 & 0.052 & -0.0655 & 0.0055 & 1775914636.3214 & 147992886.3601 & 12165.2327 \tabularnewline
70 & 0.056 & -0.0748 & 0.0062 & 2384975453.3172 & 198747954.4431 & 14097.7996 \tabularnewline
71 & 0.0623 & -0.0802 & 0.0067 & 2609447242.3126 & 217453936.8594 & 14746.3194 \tabularnewline
72 & 0.0687 & -0.0926 & 0.0077 & 3309135439.7564 & 275761286.6464 & 16606.0617 \tabularnewline
73 & 0.0742 & -0.107 & 0.0089 & 4317801553.9688 & 359816796.1641 & 18968.8375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115076&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]62[/C][C]0.0142[/C][C]0.0054[/C][C]5e-04[/C][C]9571571.1811[/C][C]797630.9318[/C][C]893.1019[/C][/ROW]
[ROW][C]63[/C][C]0.0213[/C][C]-0.007[/C][C]6e-04[/C][C]16910660.9671[/C][C]1409221.7473[/C][C]1187.1065[/C][/ROW]
[ROW][C]64[/C][C]0.0276[/C][C]-0.0238[/C][C]0.002[/C][C]196157727.9887[/C][C]16346477.3324[/C][C]4043.0777[/C][/ROW]
[ROW][C]65[/C][C]0.0336[/C][C]-0.0495[/C][C]0.0041[/C][C]859163899.5923[/C][C]71596991.6327[/C][C]8461.5006[/C][/ROW]
[ROW][C]66[/C][C]0.0395[/C][C]-0.0697[/C][C]0.0058[/C][C]1709058260.4273[/C][C]142421521.7023[/C][C]11934.0488[/C][/ROW]
[ROW][C]67[/C][C]0.0463[/C][C]-0.0741[/C][C]0.0062[/C][C]1847717281.2219[/C][C]153976440.1018[/C][C]12408.7244[/C][/ROW]
[ROW][C]68[/C][C]0.0509[/C][C]-0.081[/C][C]0.0068[/C][C]2306394399.2583[/C][C]192199533.2715[/C][C]13863.6046[/C][/ROW]
[ROW][C]69[/C][C]0.052[/C][C]-0.0655[/C][C]0.0055[/C][C]1775914636.3214[/C][C]147992886.3601[/C][C]12165.2327[/C][/ROW]
[ROW][C]70[/C][C]0.056[/C][C]-0.0748[/C][C]0.0062[/C][C]2384975453.3172[/C][C]198747954.4431[/C][C]14097.7996[/C][/ROW]
[ROW][C]71[/C][C]0.0623[/C][C]-0.0802[/C][C]0.0067[/C][C]2609447242.3126[/C][C]217453936.8594[/C][C]14746.3194[/C][/ROW]
[ROW][C]72[/C][C]0.0687[/C][C]-0.0926[/C][C]0.0077[/C][C]3309135439.7564[/C][C]275761286.6464[/C][C]16606.0617[/C][/ROW]
[ROW][C]73[/C][C]0.0742[/C][C]-0.107[/C][C]0.0089[/C][C]4317801553.9688[/C][C]359816796.1641[/C][C]18968.8375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115076&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
62	0.0142	0.0054	5e-04	9571571.1811	797630.9318	893.1019
63	0.0213	-0.007	6e-04	16910660.9671	1409221.7473	1187.1065
64	0.0276	-0.0238	0.002	196157727.9887	16346477.3324	4043.0777
65	0.0336	-0.0495	0.0041	859163899.5923	71596991.6327	8461.5006
66	0.0395	-0.0697	0.0058	1709058260.4273	142421521.7023	11934.0488
67	0.0463	-0.0741	0.0062	1847717281.2219	153976440.1018	12408.7244
68	0.0509	-0.081	0.0068	2306394399.2583	192199533.2715	13863.6046
69	0.052	-0.0655	0.0055	1775914636.3214	147992886.3601	12165.2327
70	0.056	-0.0748	0.0062	2384975453.3172	198747954.4431	14097.7996
71	0.0623	-0.0802	0.0067	2609447242.3126	217453936.8594	14746.3194
72	0.0687	-0.0926	0.0077	3309135439.7564	275761286.6464	16606.0617
73	0.0742	-0.107	0.0089	4317801553.9688	359816796.1641	18968.8375

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,fx))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:12] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code