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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationWed, 09 Dec 2009 14:45:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/09/t1260395194l3h1c6pdvijw04n.htm/, Retrieved Mon, 29 Apr 2024 14:39:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65214, Retrieved Mon, 29 Apr 2024 14:39:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [] [2009-12-07 09:54:52] [b98453cac15ba1066b407e146608df68]
-   PD    [ARIMA Forecasting] [ws 11 f] [2009-12-09 21:45:45] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87,28
87,28
87,09
86,92
87,59
90,72
90,69
90,3
89,55
88,94
88,41
87,82
87,07
86,82
86,4
86,02
85,66
85,32
85
84,67
83,94
82,83
81,95
81,19
80,48
78,86
69,47
68,77
70,06
73,95
75,8
77,79
81,57
83,07
84,34
85,1
85,25
84,26
83,63
86,44
85,3
84,1
83,36
82,48
81,58
80,47
79,34
82,13
81,69
80,7
79,88
79,16
78,38
77,42
76,47
75,46
74,48
78,27
80,7
79,91
78,75
77,78
81,14
81,08
80,03
78,91
78,01
76,9
75,97
81,93
80,27
78,67
77,42
76,16
74,7
76,39
76,04
74,65
73,29
71,79
74,39
74,91
74,54
73,08
72,75
71,32
70,38
70,35
70,01
69,36
67,77
69,26
69,8
68,38
67,62
68,39
66,95
65,21
66,64
63,45
60,66
62,34
60,32
58,64
60,46
58,59
61,87
61,85
67,44
77,06
91,74
93,15
94,15
93,11
91,51
89,96
88,16
86,98
88,03
86,24
84,65
83,23
81,7
80,25
78,8
77,51
76,2
75,04
74
75,49
77,14
76,15
76,27
78,19
76,49
77,31
76,65
74,99
73,51
72,07
70,59
71,96
76,29
74,86
74,93
71,9
71,01
77,47
75,78
76,6
76,07
74,57
73,02
72,65
73,16
71,53
69,78
67,98
69,96
72,16
70,47
68,86
67,37
65,87
72,16
71,34
69,93
68,44
67,16
66,01
67,25
70,91
69,75
68,59
67,48
66,31
64,81
66,58
65,97
64,7
64,7
60,94
59,08
58,42
57,77
57,11
53,31
49,96
49,4
48,84
48,3
47,74
47,24
46,76
46,29
48,9
49,23
48,53
48,03
54,34
53,79
53,24
52,96
52,17
51,7
58,55
78,2
77,03
76,19
77,15
75,87
95,47
109,67
112,28
112,01
107,93
105,96
105,06
102,98
102,2
105,23
101,85
99,89
96,23
94,76
91,51
91,63
91,54
85,23
87,83
87,38
84,44
85,19
84,03
86,73
102,52
104,45
106,98
107,02
99,26
94,45
113,44
157,33
147,38
171,89
171,95
132,71
126,02
121,18
115,45
110,48
117,85
117,63
124,65
109,59
111,27
99,78
98,21
99,2
97,97
89,55
87,91
93,34
94,42
93,2
90,29
91,46
89,98
88,35
88,41
82,44
79,89
75,69
75,66
84,5
96,73
87,48
82,39
83,48
79,31
78,16
72,77
72,45
68,46
67,62
68,76
70,07
68,55
65,3
58,96
59,17
62,37
66,28
55,62
55,23
55,85
56,75
50,89
53,88
52,95
55,08
53,61
58,78
61,85
55,91
53,32
46,41
44,57
50
50
53,36
46,23
50,45
49,07
45,85
48,45
49,96
46,53
50,51
47,58
48,05
46,84
47,67
49,16
55,54
55,82
58,22
56,19
57,77
63,19
54,76
55,74
62,54
61,39
69,6
79,23
80
93,68
107,63
100,18
97,3
90,45
80,64
80,58
75,82
85,59
89,35
89,42
104,73
95,32
89,27
90,44
86,97
79,98
81,22
87,35
83,64
82,22

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65214&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65214&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65214&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[330])
31846.53-------
31950.51-------
32047.58-------
32148.05-------
32246.84-------
32347.67-------
32449.16-------
32555.54-------
32655.82-------
32758.22-------
32856.19-------
32957.77-------
33063.19-------
33154.7663.827654.124473.53080.03350.55120.99640.5512
33255.7465.27350.581679.96440.10170.91960.99090.6095
33362.5465.19546.370884.01920.39110.83760.96290.5827
33461.3964.216341.483286.94940.40370.55750.9330.5353
33569.663.42737.951788.90230.31740.56230.88730.5073
33679.2363.952636.295791.60950.13950.34450.85280.5215
3378064.83935.177394.50080.15820.17080.73050.5434
33893.6865.039233.110896.96760.03940.17920.71430.5452
339107.6364.326830.15298.50150.00650.04610.63690.526
340100.1863.755227.62199.88930.02410.00870.65920.5122
34197.363.973226.2205101.72590.04180.03010.62630.5162
34290.4564.634725.3223103.94710.0990.05170.52870.5287
34380.6464.842823.8635105.8220.2250.11030.68520.5315
34480.5864.416321.7145107.1180.22910.22820.65480.5224
34575.8263.955119.6797108.23050.29970.23090.5250.5135
34685.5964.041818.3791109.70440.17750.30660.54530.5146
34789.3564.490117.505111.47520.14990.18940.41560.5216
34889.4264.702816.3337113.07190.15830.1590.2780.5244
349104.7364.445214.6522114.23820.05640.16280.27020.5197
35095.3264.100612.9552115.24590.11580.05970.12850.5139
35189.2764.104311.7262116.48230.17320.12140.05170.5136
35290.4464.406710.849117.96440.17040.18140.09520.5178
35386.9764.59359.8286119.35850.21160.17750.12090.52
35479.9864.45028.4488120.45160.29340.21530.18140.5176
35581.2264.19716.9974121.39690.27980.29430.28660.5138
35687.3564.16195.8408122.4830.21790.28320.29060.513
35783.6464.35874.9603123.75710.26230.2240.35260.5154
35882.2264.51384.0283124.99930.28310.26770.24730.5171

\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[330]) \tabularnewline
318 & 46.53 & - & - & - & - & - & - & - \tabularnewline
319 & 50.51 & - & - & - & - & - & - & - \tabularnewline
320 & 47.58 & - & - & - & - & - & - & - \tabularnewline
321 & 48.05 & - & - & - & - & - & - & - \tabularnewline
322 & 46.84 & - & - & - & - & - & - & - \tabularnewline
323 & 47.67 & - & - & - & - & - & - & - \tabularnewline
324 & 49.16 & - & - & - & - & - & - & - \tabularnewline
325 & 55.54 & - & - & - & - & - & - & - \tabularnewline
326 & 55.82 & - & - & - & - & - & - & - \tabularnewline
327 & 58.22 & - & - & - & - & - & - & - \tabularnewline
328 & 56.19 & - & - & - & - & - & - & - \tabularnewline
329 & 57.77 & - & - & - & - & - & - & - \tabularnewline
330 & 63.19 & - & - & - & - & - & - & - \tabularnewline
331 & 54.76 & 63.8276 & 54.1244 & 73.5308 & 0.0335 & 0.5512 & 0.9964 & 0.5512 \tabularnewline
332 & 55.74 & 65.273 & 50.5816 & 79.9644 & 0.1017 & 0.9196 & 0.9909 & 0.6095 \tabularnewline
333 & 62.54 & 65.195 & 46.3708 & 84.0192 & 0.3911 & 0.8376 & 0.9629 & 0.5827 \tabularnewline
334 & 61.39 & 64.2163 & 41.4832 & 86.9494 & 0.4037 & 0.5575 & 0.933 & 0.5353 \tabularnewline
335 & 69.6 & 63.427 & 37.9517 & 88.9023 & 0.3174 & 0.5623 & 0.8873 & 0.5073 \tabularnewline
336 & 79.23 & 63.9526 & 36.2957 & 91.6095 & 0.1395 & 0.3445 & 0.8528 & 0.5215 \tabularnewline
337 & 80 & 64.839 & 35.1773 & 94.5008 & 0.1582 & 0.1708 & 0.7305 & 0.5434 \tabularnewline
338 & 93.68 & 65.0392 & 33.1108 & 96.9676 & 0.0394 & 0.1792 & 0.7143 & 0.5452 \tabularnewline
339 & 107.63 & 64.3268 & 30.152 & 98.5015 & 0.0065 & 0.0461 & 0.6369 & 0.526 \tabularnewline
340 & 100.18 & 63.7552 & 27.621 & 99.8893 & 0.0241 & 0.0087 & 0.6592 & 0.5122 \tabularnewline
341 & 97.3 & 63.9732 & 26.2205 & 101.7259 & 0.0418 & 0.0301 & 0.6263 & 0.5162 \tabularnewline
342 & 90.45 & 64.6347 & 25.3223 & 103.9471 & 0.099 & 0.0517 & 0.5287 & 0.5287 \tabularnewline
343 & 80.64 & 64.8428 & 23.8635 & 105.822 & 0.225 & 0.1103 & 0.6852 & 0.5315 \tabularnewline
344 & 80.58 & 64.4163 & 21.7145 & 107.118 & 0.2291 & 0.2282 & 0.6548 & 0.5224 \tabularnewline
345 & 75.82 & 63.9551 & 19.6797 & 108.2305 & 0.2997 & 0.2309 & 0.525 & 0.5135 \tabularnewline
346 & 85.59 & 64.0418 & 18.3791 & 109.7044 & 0.1775 & 0.3066 & 0.5453 & 0.5146 \tabularnewline
347 & 89.35 & 64.4901 & 17.505 & 111.4752 & 0.1499 & 0.1894 & 0.4156 & 0.5216 \tabularnewline
348 & 89.42 & 64.7028 & 16.3337 & 113.0719 & 0.1583 & 0.159 & 0.278 & 0.5244 \tabularnewline
349 & 104.73 & 64.4452 & 14.6522 & 114.2382 & 0.0564 & 0.1628 & 0.2702 & 0.5197 \tabularnewline
350 & 95.32 & 64.1006 & 12.9552 & 115.2459 & 0.1158 & 0.0597 & 0.1285 & 0.5139 \tabularnewline
351 & 89.27 & 64.1043 & 11.7262 & 116.4823 & 0.1732 & 0.1214 & 0.0517 & 0.5136 \tabularnewline
352 & 90.44 & 64.4067 & 10.849 & 117.9644 & 0.1704 & 0.1814 & 0.0952 & 0.5178 \tabularnewline
353 & 86.97 & 64.5935 & 9.8286 & 119.3585 & 0.2116 & 0.1775 & 0.1209 & 0.52 \tabularnewline
354 & 79.98 & 64.4502 & 8.4488 & 120.4516 & 0.2934 & 0.2153 & 0.1814 & 0.5176 \tabularnewline
355 & 81.22 & 64.1971 & 6.9974 & 121.3969 & 0.2798 & 0.2943 & 0.2866 & 0.5138 \tabularnewline
356 & 87.35 & 64.1619 & 5.8408 & 122.483 & 0.2179 & 0.2832 & 0.2906 & 0.513 \tabularnewline
357 & 83.64 & 64.3587 & 4.9603 & 123.7571 & 0.2623 & 0.224 & 0.3526 & 0.5154 \tabularnewline
358 & 82.22 & 64.5138 & 4.0283 & 124.9993 & 0.2831 & 0.2677 & 0.2473 & 0.5171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65214&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[330])[/C][/ROW]
[ROW][C]318[/C][C]46.53[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]319[/C][C]50.51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]320[/C][C]47.58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]321[/C][C]48.05[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]322[/C][C]46.84[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]323[/C][C]47.67[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]324[/C][C]49.16[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]325[/C][C]55.54[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]326[/C][C]55.82[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]327[/C][C]58.22[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]328[/C][C]56.19[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]329[/C][C]57.77[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]330[/C][C]63.19[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]331[/C][C]54.76[/C][C]63.8276[/C][C]54.1244[/C][C]73.5308[/C][C]0.0335[/C][C]0.5512[/C][C]0.9964[/C][C]0.5512[/C][/ROW]
[ROW][C]332[/C][C]55.74[/C][C]65.273[/C][C]50.5816[/C][C]79.9644[/C][C]0.1017[/C][C]0.9196[/C][C]0.9909[/C][C]0.6095[/C][/ROW]
[ROW][C]333[/C][C]62.54[/C][C]65.195[/C][C]46.3708[/C][C]84.0192[/C][C]0.3911[/C][C]0.8376[/C][C]0.9629[/C][C]0.5827[/C][/ROW]
[ROW][C]334[/C][C]61.39[/C][C]64.2163[/C][C]41.4832[/C][C]86.9494[/C][C]0.4037[/C][C]0.5575[/C][C]0.933[/C][C]0.5353[/C][/ROW]
[ROW][C]335[/C][C]69.6[/C][C]63.427[/C][C]37.9517[/C][C]88.9023[/C][C]0.3174[/C][C]0.5623[/C][C]0.8873[/C][C]0.5073[/C][/ROW]
[ROW][C]336[/C][C]79.23[/C][C]63.9526[/C][C]36.2957[/C][C]91.6095[/C][C]0.1395[/C][C]0.3445[/C][C]0.8528[/C][C]0.5215[/C][/ROW]
[ROW][C]337[/C][C]80[/C][C]64.839[/C][C]35.1773[/C][C]94.5008[/C][C]0.1582[/C][C]0.1708[/C][C]0.7305[/C][C]0.5434[/C][/ROW]
[ROW][C]338[/C][C]93.68[/C][C]65.0392[/C][C]33.1108[/C][C]96.9676[/C][C]0.0394[/C][C]0.1792[/C][C]0.7143[/C][C]0.5452[/C][/ROW]
[ROW][C]339[/C][C]107.63[/C][C]64.3268[/C][C]30.152[/C][C]98.5015[/C][C]0.0065[/C][C]0.0461[/C][C]0.6369[/C][C]0.526[/C][/ROW]
[ROW][C]340[/C][C]100.18[/C][C]63.7552[/C][C]27.621[/C][C]99.8893[/C][C]0.0241[/C][C]0.0087[/C][C]0.6592[/C][C]0.5122[/C][/ROW]
[ROW][C]341[/C][C]97.3[/C][C]63.9732[/C][C]26.2205[/C][C]101.7259[/C][C]0.0418[/C][C]0.0301[/C][C]0.6263[/C][C]0.5162[/C][/ROW]
[ROW][C]342[/C][C]90.45[/C][C]64.6347[/C][C]25.3223[/C][C]103.9471[/C][C]0.099[/C][C]0.0517[/C][C]0.5287[/C][C]0.5287[/C][/ROW]
[ROW][C]343[/C][C]80.64[/C][C]64.8428[/C][C]23.8635[/C][C]105.822[/C][C]0.225[/C][C]0.1103[/C][C]0.6852[/C][C]0.5315[/C][/ROW]
[ROW][C]344[/C][C]80.58[/C][C]64.4163[/C][C]21.7145[/C][C]107.118[/C][C]0.2291[/C][C]0.2282[/C][C]0.6548[/C][C]0.5224[/C][/ROW]
[ROW][C]345[/C][C]75.82[/C][C]63.9551[/C][C]19.6797[/C][C]108.2305[/C][C]0.2997[/C][C]0.2309[/C][C]0.525[/C][C]0.5135[/C][/ROW]
[ROW][C]346[/C][C]85.59[/C][C]64.0418[/C][C]18.3791[/C][C]109.7044[/C][C]0.1775[/C][C]0.3066[/C][C]0.5453[/C][C]0.5146[/C][/ROW]
[ROW][C]347[/C][C]89.35[/C][C]64.4901[/C][C]17.505[/C][C]111.4752[/C][C]0.1499[/C][C]0.1894[/C][C]0.4156[/C][C]0.5216[/C][/ROW]
[ROW][C]348[/C][C]89.42[/C][C]64.7028[/C][C]16.3337[/C][C]113.0719[/C][C]0.1583[/C][C]0.159[/C][C]0.278[/C][C]0.5244[/C][/ROW]
[ROW][C]349[/C][C]104.73[/C][C]64.4452[/C][C]14.6522[/C][C]114.2382[/C][C]0.0564[/C][C]0.1628[/C][C]0.2702[/C][C]0.5197[/C][/ROW]
[ROW][C]350[/C][C]95.32[/C][C]64.1006[/C][C]12.9552[/C][C]115.2459[/C][C]0.1158[/C][C]0.0597[/C][C]0.1285[/C][C]0.5139[/C][/ROW]
[ROW][C]351[/C][C]89.27[/C][C]64.1043[/C][C]11.7262[/C][C]116.4823[/C][C]0.1732[/C][C]0.1214[/C][C]0.0517[/C][C]0.5136[/C][/ROW]
[ROW][C]352[/C][C]90.44[/C][C]64.4067[/C][C]10.849[/C][C]117.9644[/C][C]0.1704[/C][C]0.1814[/C][C]0.0952[/C][C]0.5178[/C][/ROW]
[ROW][C]353[/C][C]86.97[/C][C]64.5935[/C][C]9.8286[/C][C]119.3585[/C][C]0.2116[/C][C]0.1775[/C][C]0.1209[/C][C]0.52[/C][/ROW]
[ROW][C]354[/C][C]79.98[/C][C]64.4502[/C][C]8.4488[/C][C]120.4516[/C][C]0.2934[/C][C]0.2153[/C][C]0.1814[/C][C]0.5176[/C][/ROW]
[ROW][C]355[/C][C]81.22[/C][C]64.1971[/C][C]6.9974[/C][C]121.3969[/C][C]0.2798[/C][C]0.2943[/C][C]0.2866[/C][C]0.5138[/C][/ROW]
[ROW][C]356[/C][C]87.35[/C][C]64.1619[/C][C]5.8408[/C][C]122.483[/C][C]0.2179[/C][C]0.2832[/C][C]0.2906[/C][C]0.513[/C][/ROW]
[ROW][C]357[/C][C]83.64[/C][C]64.3587[/C][C]4.9603[/C][C]123.7571[/C][C]0.2623[/C][C]0.224[/C][C]0.3526[/C][C]0.5154[/C][/ROW]
[ROW][C]358[/C][C]82.22[/C][C]64.5138[/C][C]4.0283[/C][C]124.9993[/C][C]0.2831[/C][C]0.2677[/C][C]0.2473[/C][C]0.5171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65214&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65214&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[330])
31846.53-------
31950.51-------
32047.58-------
32148.05-------
32246.84-------
32347.67-------
32449.16-------
32555.54-------
32655.82-------
32758.22-------
32856.19-------
32957.77-------
33063.19-------
33154.7663.827654.124473.53080.03350.55120.99640.5512
33255.7465.27350.581679.96440.10170.91960.99090.6095
33362.5465.19546.370884.01920.39110.83760.96290.5827
33461.3964.216341.483286.94940.40370.55750.9330.5353
33569.663.42737.951788.90230.31740.56230.88730.5073
33679.2363.952636.295791.60950.13950.34450.85280.5215
3378064.83935.177394.50080.15820.17080.73050.5434
33893.6865.039233.110896.96760.03940.17920.71430.5452
339107.6364.326830.15298.50150.00650.04610.63690.526
340100.1863.755227.62199.88930.02410.00870.65920.5122
34197.363.973226.2205101.72590.04180.03010.62630.5162
34290.4564.634725.3223103.94710.0990.05170.52870.5287
34380.6464.842823.8635105.8220.2250.11030.68520.5315
34480.5864.416321.7145107.1180.22910.22820.65480.5224
34575.8263.955119.6797108.23050.29970.23090.5250.5135
34685.5964.041818.3791109.70440.17750.30660.54530.5146
34789.3564.490117.505111.47520.14990.18940.41560.5216
34889.4264.702816.3337113.07190.15830.1590.2780.5244
349104.7364.445214.6522114.23820.05640.16280.27020.5197
35095.3264.100612.9552115.24590.11580.05970.12850.5139
35189.2764.104311.7262116.48230.17320.12140.05170.5136
35290.4464.406710.849117.96440.17040.18140.09520.5178
35386.9764.59359.8286119.35850.21160.17750.12090.52
35479.9864.45028.4488120.45160.29340.21530.18140.5176
35581.2264.19716.9974121.39690.27980.29430.28660.5138
35687.3564.16195.8408122.4830.21790.28320.29060.513
35783.6464.35874.9603123.75710.26230.2240.35260.5154
35882.2264.51384.0283124.99930.28310.26770.24730.5171






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
3310.0776-0.1421082.22100
3320.1148-0.1460.144190.877986.54949.3032
3330.1473-0.04070.10967.04960.04937.7491
3340.1806-0.0440.09327.987847.03396.8581
3350.20490.09730.09438.105645.24836.7267
3360.22060.23890.1182233.399476.60688.7525
3370.23340.23380.1347229.854498.49939.9247
3380.25050.44040.1729820.2947188.723713.7377
3390.27110.67320.22851875.1691376.106519.3935
3400.28920.57130.26281326.7683471.172721.7065
3410.30110.52090.28621110.6756529.309323.0067
3420.31030.39940.2957666.43540.736123.2537
3430.32240.24360.2917249.5519518.337322.767
3440.33820.25090.2888261.2662499.975122.3601
3450.35320.18550.2819140.7763476.028521.8181
3460.36380.33650.2853464.3265475.297121.8013
3470.37170.38550.2912618.0141483.692221.993
3480.38140.3820.2962610.9404490.761622.1531
3490.39420.62510.31351622.8659550.34623.4595
3500.40710.4870.3222974.6533571.561423.9073
3510.41690.39260.3256633.3132574.501923.9688
3520.42430.40420.3291677.7327579.194224.0665
3530.43260.34640.3299500.7056575.781723.9955
3540.44330.2410.3262241.1746561.839723.7032
3550.45460.26520.3237289.7777550.957223.4725
3560.46380.36140.3252537.6879550.446923.4616
3570.47090.29960.3242371.7687543.829223.3201
3580.47830.27450.3225313.5099535.603523.1431

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
331 & 0.0776 & -0.1421 & 0 & 82.221 & 0 & 0 \tabularnewline
332 & 0.1148 & -0.146 & 0.1441 & 90.8779 & 86.5494 & 9.3032 \tabularnewline
333 & 0.1473 & -0.0407 & 0.1096 & 7.049 & 60.0493 & 7.7491 \tabularnewline
334 & 0.1806 & -0.044 & 0.0932 & 7.9878 & 47.0339 & 6.8581 \tabularnewline
335 & 0.2049 & 0.0973 & 0.094 & 38.1056 & 45.2483 & 6.7267 \tabularnewline
336 & 0.2206 & 0.2389 & 0.1182 & 233.3994 & 76.6068 & 8.7525 \tabularnewline
337 & 0.2334 & 0.2338 & 0.1347 & 229.8544 & 98.4993 & 9.9247 \tabularnewline
338 & 0.2505 & 0.4404 & 0.1729 & 820.2947 & 188.7237 & 13.7377 \tabularnewline
339 & 0.2711 & 0.6732 & 0.2285 & 1875.1691 & 376.1065 & 19.3935 \tabularnewline
340 & 0.2892 & 0.5713 & 0.2628 & 1326.7683 & 471.1727 & 21.7065 \tabularnewline
341 & 0.3011 & 0.5209 & 0.2862 & 1110.6756 & 529.3093 & 23.0067 \tabularnewline
342 & 0.3103 & 0.3994 & 0.2957 & 666.43 & 540.7361 & 23.2537 \tabularnewline
343 & 0.3224 & 0.2436 & 0.2917 & 249.5519 & 518.3373 & 22.767 \tabularnewline
344 & 0.3382 & 0.2509 & 0.2888 & 261.2662 & 499.9751 & 22.3601 \tabularnewline
345 & 0.3532 & 0.1855 & 0.2819 & 140.7763 & 476.0285 & 21.8181 \tabularnewline
346 & 0.3638 & 0.3365 & 0.2853 & 464.3265 & 475.2971 & 21.8013 \tabularnewline
347 & 0.3717 & 0.3855 & 0.2912 & 618.0141 & 483.6922 & 21.993 \tabularnewline
348 & 0.3814 & 0.382 & 0.2962 & 610.9404 & 490.7616 & 22.1531 \tabularnewline
349 & 0.3942 & 0.6251 & 0.3135 & 1622.8659 & 550.346 & 23.4595 \tabularnewline
350 & 0.4071 & 0.487 & 0.3222 & 974.6533 & 571.5614 & 23.9073 \tabularnewline
351 & 0.4169 & 0.3926 & 0.3256 & 633.3132 & 574.5019 & 23.9688 \tabularnewline
352 & 0.4243 & 0.4042 & 0.3291 & 677.7327 & 579.1942 & 24.0665 \tabularnewline
353 & 0.4326 & 0.3464 & 0.3299 & 500.7056 & 575.7817 & 23.9955 \tabularnewline
354 & 0.4433 & 0.241 & 0.3262 & 241.1746 & 561.8397 & 23.7032 \tabularnewline
355 & 0.4546 & 0.2652 & 0.3237 & 289.7777 & 550.9572 & 23.4725 \tabularnewline
356 & 0.4638 & 0.3614 & 0.3252 & 537.6879 & 550.4469 & 23.4616 \tabularnewline
357 & 0.4709 & 0.2996 & 0.3242 & 371.7687 & 543.8292 & 23.3201 \tabularnewline
358 & 0.4783 & 0.2745 & 0.3225 & 313.5099 & 535.6035 & 23.1431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65214&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]331[/C][C]0.0776[/C][C]-0.1421[/C][C]0[/C][C]82.221[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]332[/C][C]0.1148[/C][C]-0.146[/C][C]0.1441[/C][C]90.8779[/C][C]86.5494[/C][C]9.3032[/C][/ROW]
[ROW][C]333[/C][C]0.1473[/C][C]-0.0407[/C][C]0.1096[/C][C]7.049[/C][C]60.0493[/C][C]7.7491[/C][/ROW]
[ROW][C]334[/C][C]0.1806[/C][C]-0.044[/C][C]0.0932[/C][C]7.9878[/C][C]47.0339[/C][C]6.8581[/C][/ROW]
[ROW][C]335[/C][C]0.2049[/C][C]0.0973[/C][C]0.094[/C][C]38.1056[/C][C]45.2483[/C][C]6.7267[/C][/ROW]
[ROW][C]336[/C][C]0.2206[/C][C]0.2389[/C][C]0.1182[/C][C]233.3994[/C][C]76.6068[/C][C]8.7525[/C][/ROW]
[ROW][C]337[/C][C]0.2334[/C][C]0.2338[/C][C]0.1347[/C][C]229.8544[/C][C]98.4993[/C][C]9.9247[/C][/ROW]
[ROW][C]338[/C][C]0.2505[/C][C]0.4404[/C][C]0.1729[/C][C]820.2947[/C][C]188.7237[/C][C]13.7377[/C][/ROW]
[ROW][C]339[/C][C]0.2711[/C][C]0.6732[/C][C]0.2285[/C][C]1875.1691[/C][C]376.1065[/C][C]19.3935[/C][/ROW]
[ROW][C]340[/C][C]0.2892[/C][C]0.5713[/C][C]0.2628[/C][C]1326.7683[/C][C]471.1727[/C][C]21.7065[/C][/ROW]
[ROW][C]341[/C][C]0.3011[/C][C]0.5209[/C][C]0.2862[/C][C]1110.6756[/C][C]529.3093[/C][C]23.0067[/C][/ROW]
[ROW][C]342[/C][C]0.3103[/C][C]0.3994[/C][C]0.2957[/C][C]666.43[/C][C]540.7361[/C][C]23.2537[/C][/ROW]
[ROW][C]343[/C][C]0.3224[/C][C]0.2436[/C][C]0.2917[/C][C]249.5519[/C][C]518.3373[/C][C]22.767[/C][/ROW]
[ROW][C]344[/C][C]0.3382[/C][C]0.2509[/C][C]0.2888[/C][C]261.2662[/C][C]499.9751[/C][C]22.3601[/C][/ROW]
[ROW][C]345[/C][C]0.3532[/C][C]0.1855[/C][C]0.2819[/C][C]140.7763[/C][C]476.0285[/C][C]21.8181[/C][/ROW]
[ROW][C]346[/C][C]0.3638[/C][C]0.3365[/C][C]0.2853[/C][C]464.3265[/C][C]475.2971[/C][C]21.8013[/C][/ROW]
[ROW][C]347[/C][C]0.3717[/C][C]0.3855[/C][C]0.2912[/C][C]618.0141[/C][C]483.6922[/C][C]21.993[/C][/ROW]
[ROW][C]348[/C][C]0.3814[/C][C]0.382[/C][C]0.2962[/C][C]610.9404[/C][C]490.7616[/C][C]22.1531[/C][/ROW]
[ROW][C]349[/C][C]0.3942[/C][C]0.6251[/C][C]0.3135[/C][C]1622.8659[/C][C]550.346[/C][C]23.4595[/C][/ROW]
[ROW][C]350[/C][C]0.4071[/C][C]0.487[/C][C]0.3222[/C][C]974.6533[/C][C]571.5614[/C][C]23.9073[/C][/ROW]
[ROW][C]351[/C][C]0.4169[/C][C]0.3926[/C][C]0.3256[/C][C]633.3132[/C][C]574.5019[/C][C]23.9688[/C][/ROW]
[ROW][C]352[/C][C]0.4243[/C][C]0.4042[/C][C]0.3291[/C][C]677.7327[/C][C]579.1942[/C][C]24.0665[/C][/ROW]
[ROW][C]353[/C][C]0.4326[/C][C]0.3464[/C][C]0.3299[/C][C]500.7056[/C][C]575.7817[/C][C]23.9955[/C][/ROW]
[ROW][C]354[/C][C]0.4433[/C][C]0.241[/C][C]0.3262[/C][C]241.1746[/C][C]561.8397[/C][C]23.7032[/C][/ROW]
[ROW][C]355[/C][C]0.4546[/C][C]0.2652[/C][C]0.3237[/C][C]289.7777[/C][C]550.9572[/C][C]23.4725[/C][/ROW]
[ROW][C]356[/C][C]0.4638[/C][C]0.3614[/C][C]0.3252[/C][C]537.6879[/C][C]550.4469[/C][C]23.4616[/C][/ROW]
[ROW][C]357[/C][C]0.4709[/C][C]0.2996[/C][C]0.3242[/C][C]371.7687[/C][C]543.8292[/C][C]23.3201[/C][/ROW]
[ROW][C]358[/C][C]0.4783[/C][C]0.2745[/C][C]0.3225[/C][C]313.5099[/C][C]535.6035[/C][C]23.1431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65214&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65214&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
3310.0776-0.1421082.22100
3320.1148-0.1460.144190.877986.54949.3032
3330.1473-0.04070.10967.04960.04937.7491
3340.1806-0.0440.09327.987847.03396.8581
3350.20490.09730.09438.105645.24836.7267
3360.22060.23890.1182233.399476.60688.7525
3370.23340.23380.1347229.854498.49939.9247
3380.25050.44040.1729820.2947188.723713.7377
3390.27110.67320.22851875.1691376.106519.3935
3400.28920.57130.26281326.7683471.172721.7065
3410.30110.52090.28621110.6756529.309323.0067
3420.31030.39940.2957666.43540.736123.2537
3430.32240.24360.2917249.5519518.337322.767
3440.33820.25090.2888261.2662499.975122.3601
3450.35320.18550.2819140.7763476.028521.8181
3460.36380.33650.2853464.3265475.297121.8013
3470.37170.38550.2912618.0141483.692221.993
3480.38140.3820.2962610.9404490.761622.1531
3490.39420.62510.31351622.8659550.34623.4595
3500.40710.4870.3222974.6533571.561423.9073
3510.41690.39260.3256633.3132574.501923.9688
3520.42430.40420.3291677.7327579.194224.0665
3530.43260.34640.3299500.7056575.781723.9955
3540.44330.2410.3262241.1746561.839723.7032
3550.45460.26520.3237289.7777550.957223.4725
3560.46380.36140.3252537.6879550.446923.4616
3570.47090.29960.3242371.7687543.829223.3201
3580.47830.27450.3225313.5099535.603523.1431


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
par1 <- 28
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
par6 <- 3
par7 <- as.numeric(par7) #q
par7 <- 3
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')