Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.105758688735590 |
beta | 0.252901562163533 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 20016 | 18330 | 1686 |
4 | 17708 | 20150.403811591 | -2442.40381159101 |
5 | 18019 | 21468.8672041317 | -3449.86720413167 |
6 | 19227 | 22588.5105864599 | -3361.5105864599 |
7 | 22893 | 23627.5896795422 | -734.589679542187 |
8 | 23739 | 24924.8407526724 | -1185.84075267245 |
9 | 21133 | 26142.6509697466 | -5009.65096974655 |
10 | 22591 | 26822.069214296 | -4231.06921429602 |
11 | 26786 | 27470.6627925741 | -684.662792574109 |
12 | 29740 | 28476.0073046165 | 1263.99269538354 |
13 | 15028 | 29721.2464940077 | -14693.2464940077 |
14 | 17977 | 28885.8755211648 | -10908.8755211648 |
15 | 20008 | 28158.9600108681 | -8150.96001086813 |
16 | 21354 | 27505.7080702293 | -6151.70807022935 |
17 | 19498 | 26899.3575021194 | -7401.35750211938 |
18 | 22125 | 25962.8849620395 | -3837.88496203946 |
19 | 25817 | 25300.6304707266 | 516.369529273419 |
20 | 28779 | 25112.6873218629 | 3666.31267813710 |
21 | 20960 | 25355.9391998904 | -4395.93919989038 |
22 | 22254 | 24628.9617379726 | -2374.96173797259 |
23 | 27392 | 24052.1981989834 | 3339.80180101664 |
24 | 29945 | 24169.1486927377 | 5775.85130726235 |
25 | 16933 | 24698.2166120922 | -7765.2166120922 |
26 | 17892 | 23587.5062861785 | -5695.50628617848 |
27 | 20533 | 22543.3507373981 | -2010.35073739807 |
28 | 23569 | 21835.1624856692 | 1733.83751433078 |
29 | 22417 | 21569.3288240807 | 847.671175919346 |
30 | 22084 | 21232.4476415138 | 851.552358486184 |
31 | 26580 | 20918.7530048952 | 5661.24699510484 |
32 | 27454 | 21265.1441218451 | 6188.8558781549 |
33 | 24081 | 21832.8649288381 | 2248.13507116191 |
34 | 23451 | 22043.9500998068 | 1407.04990019323 |
35 | 28991 | 22203.7169190304 | 6787.28308096957 |
36 | 31386 | 23114.0264666283 | 8271.97353337174 |
37 | 16896 | 24402.6015807340 | -7506.60158073395 |
38 | 20045 | 23821.6796792766 | -3776.67967927656 |
39 | 23471 | 23534.2163221827 | -63.216322182714 |
40 | 21747 | 23637.793162665 | -1890.79316266499 |
41 | 25621 | 23497.5157025274 | 2123.48429747262 |
42 | 23859 | 23838.5788153865 | 20.421184613464 |
43 | 25500 | 23957.7709270835 | 1542.22907291651 |
44 | 30998 | 24279.1567334315 | 6718.84326656846 |
45 | 24475 | 25327.7202630050 | -852.720263005034 |
46 | 23145 | 25552.7178474413 | -2407.71784744133 |
47 | 29701 | 25548.8628104393 | 4152.13718956073 |
48 | 34365 | 26349.8247338805 | 8015.17526611954 |
49 | 17556 | 27773.7146854087 | -10217.7146854087 |
50 | 22077 | 26996.0296138491 | -4919.02961384907 |
51 | 25702 | 26647.1595169896 | -945.159516989592 |
52 | 22214 | 26693.2809662264 | -4479.28096622644 |
53 | 26886 | 26245.8331084042 | 640.166891595793 |
54 | 23191 | 26356.9335909077 | -3165.93359090773 |
55 | 27831 | 25980.8281153777 | 1850.17188462227 |
56 | 35406 | 26184.7050693659 | 9221.29493063413 |
57 | 23195 | 27414.7800427328 | -4219.78004273276 |
58 | 25110 | 27110.4800461699 | -2000.48004616995 |
59 | 30009 | 26987.3843923944 | 3021.61560760560 |
60 | 36242 | 27476.2367451091 | 8765.76325489092 |
61 | 18450 | 28807.0364373378 | -10357.0364373378 |
62 | 21845 | 27838.4190447335 | -5993.41904473353 |
63 | 26488 | 27170.9888979208 | -682.988897920768 |
64 | 22394 | 27046.9152918226 | -4652.91529182262 |
65 | 28057 | 26378.5381021560 | 1678.46189784395 |
66 | 25451 | 26424.6521062091 | -973.652106209138 |
67 | 24872 | 26164.2401881545 | -1292.24018815447 |
68 | 33424 | 25835.5718615340 | 7588.42813846596 |
69 | 24052 | 26649.0755507145 | -2597.07555071447 |
70 | 28449 | 26315.9109467651 | 2133.08905323493 |
71 | 33533 | 26540.0550953857 | 6992.9449046143 |
72 | 37351 | 27465.2082900734 | 9885.79170992658 |
73 | 19969 | 28960.7158692159 | -8991.71586921592 |
74 | 21701 | 28219.2657336652 | -6518.26573366523 |
75 | 26249 | 27565.0634016127 | -1316.06340161271 |
76 | 24493 | 27425.8390274885 | -2932.83902748850 |
77 | 24603 | 27037.1832938873 | -2434.18329388730 |
78 | 26485 | 26636.1587618226 | -151.158761822597 |
79 | 30723 | 26472.5409371145 | 4250.45906288545 |
80 | 34569 | 26888.1175049783 | 7680.88249502166 |
81 | 26689 | 27871.9281692378 | -1182.92816923780 |
82 | 26157 | 27886.6746076956 | -1729.67460769559 |
83 | 32064 | 27797.3350528318 | 4266.66494716819 |
84 | 38870 | 28456.2790209125 | 10413.7209790875 |
85 | 21337 | 30043.8585541696 | -8706.85855416957 |
86 | 19419 | 29376.3923484836 | -9957.39234848358 |
87 | 23166 | 28310.3455597085 | -5144.34555970848 |
88 | 28286 | 27615.7268562301 | 670.273143769922 |
89 | 24570 | 27553.9820881668 | -2983.98208816681 |
90 | 24001 | 27025.9568893690 | -3024.95688936896 |
91 | 33151 | 26412.6911261643 | 6738.30887383574 |
92 | 24878 | 27012.2019794645 | -2134.20197946448 |
93 | 26804 | 26616.2852056513 | 187.714794348689 |
94 | 28967 | 26470.9520259937 | 2496.04797400629 |
95 | 33311 | 26636.5057775537 | 6674.49422244627 |
96 | 40226 | 27422.4861359398 | 12803.5138640602 |
97 | 20504 | 29199.1132397529 | -8695.1132397529 |
98 | 23060 | 28469.5095583037 | -5409.50955830367 |
99 | 23562 | 27942.7013631452 | -4380.70136314523 |
100 | 27562 | 27407.5299799715 | 154.470020028504 |
101 | 23940 | 27356.1239136712 | -3416.12391367116 |
102 | 24584 | 26835.7270282541 | -2251.72702825411 |
103 | 34303 | 26378.2493289948 | 7924.75067100516 |
104 | 25517 | 27208.9822088981 | -1691.98220889814 |
105 | 23494 | 26977.4073637444 | -3483.40736374444 |
106 | 29095 | 26463.2046572380 | 2631.79534276196 |
107 | 32903 | 26666.1291833979 | 6236.87081660208 |
108 | 34379 | 27417.1364642266 | 6961.86353577337 |
109 | 16991 | 28431.0237691588 | -11440.0237691588 |
110 | 21109 | 27192.7705766478 | -6083.77057664779 |
111 | 23740 | 26358.2678998734 | -2618.26789987343 |
112 | 25552 | 25820.2426411903 | -268.242641190329 |
113 | 21752 | 25523.5784104743 | -3771.57841047426 |
114 | 20294 | 24755.5293188553 | -4461.52931885529 |
115 | 29009 | 23795.1814622223 | 5213.81853777769 |
116 | 25500 | 23997.5373014944 | 1502.46269850560 |
117 | 24166 | 23847.5706888225 | 318.429311177541 |
118 | 26960 | 23580.8991392299 | 3379.10086077014 |
119 | 31222 | 23728.2994475776 | 7493.70055242236 |
120 | 38641 | 24511.2849675269 | 14129.7150324731 |
121 | 14672 | 26374.0076316197 | -11702.0076316197 |
122 | 17543 | 25191.8129919368 | -7648.81299193684 |
123 | 25453 | 24233.6996383018 | 1219.30036169824 |
124 | 32683 | 24246.0783874677 | 8436.92161253226 |
125 | 22449 | 25247.4417369959 | -2798.44173699589 |
126 | 22316 | 24985.719164088 | -2669.71916408799 |
127 | 27595 | 24666.2043777149 | 2928.79562228514 |
128 | 25451 | 25017.1163162308 | 433.883683769211 |
129 | 25421 | 25115.7745258777 | 305.225474122319 |
130 | 25288 | 25208.9897365954 | 79.0102634046125 |
131 | 32568 | 25280.393974236 | 7287.60602576403 |
132 | 35110 | 26309.0880758640 | 8800.91192413595 |
133 | 16052 | 27733.2213465966 | -11681.2213465966 |
134 | 22146 | 26678.7588342230 | -4532.75883422303 |
135 | 21198 | 26259.0727390713 | -5061.07273907133 |
136 | 19543 | 25648.1466858226 | -6105.1466858226 |
137 | 22084 | 24763.5092056757 | -2679.50920567567 |
138 | 23816 | 24169.4950598106 | -353.495059810586 |
139 | 29961 | 23812.0223510862 | 6148.97764891375 |
140 | 26773 | 24306.7064914244 | 2466.29350857559 |
141 | 26635 | 24477.879598097 | 2157.12040190298 |
142 | 26972 | 24674.0504643390 | 2297.94953566095 |
143 | 30207 | 24946.5774287468 | 5260.42257125317 |
144 | 38687 | 25673.1097468736 | 13013.8902531264 |
145 | 16974 | 27567.7151450833 | -10593.7151450833 |
146 | 21697 | 26682.2659518072 | -4985.26595180724 |
147 | 24179 | 26256.6203878581 | -2077.62038785814 |
148 | 23757 | 26082.9144542511 | -2325.91445425109 |
149 | 25013 | 25820.7391073714 | -807.739107371366 |
150 | 24019 | 25697.5197700472 | -1678.51977004722 |
151 | 30345 | 25437.313219531 | 4907.686780469 |
152 | 24488 | 26004.9188665105 | -1516.91886651054 |
153 | 25156 | 25852.4943171327 | -696.494317132703 |
154 | 25650 | 25768.2079808666 | -118.207980866635 |
155 | 30923 | 25741.9187950337 | 5181.08120496634 |
156 | 37240 | 26414.6514679492 | 10825.3485320508 |
157 | 17466 | 27973.8550437266 | -10507.8550437266 |
158 | 19463 | 26995.8382428453 | -7532.83824284528 |
159 | 24352 | 26130.9779765428 | -1778.97797654277 |
160 | 26805 | 25827.0569258444 | 977.943074155562 |
161 | 25236 | 25840.8608216128 | -604.860821612812 |
162 | 24735 | 25671.0915201350 | -936.091520134974 |
163 | 29356 | 25441.2544872781 | 3914.74551272188 |
164 | 31234 | 25829.1415063116 | 5404.85849368837 |
165 | 22724 | 26519.1821711696 | -3795.18217116956 |
166 | 28496 | 26134.7306163823 | 2361.26938361774 |
167 | 32857 | 26464.533085631 | 6392.46691436901 |
168 | 37198 | 27391.6460764071 | 9806.35392359288 |
169 | 13652 | 28942.0932946437 | -15290.0932946437 |
170 | 22784 | 27429.4161080429 | -4645.4161080429 |
171 | 23565 | 26918.2572261389 | -3353.25722613894 |
172 | 26323 | 26454.0673527633 | -131.067352763261 |
173 | 23779 | 26327.1464573749 | -2548.14645737492 |
174 | 27549 | 25876.4443502965 | 1672.55564970352 |
175 | 29660 | 25916.8532361684 | 3743.14676383162 |
176 | 23356 | 26276.3613388152 | -2920.36133881520 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
177 | 25853.0360078116 | 14859.9192893100 | 36846.1527263133 |
178 | 25738.5642626352 | 14649.3609069901 | 36827.7676182804 |
179 | 25624.0925174589 | 14397.5486229384 | 36850.6364119793 |
180 | 25509.6207722825 | 14098.3942759568 | 36920.8472686081 |
181 | 25395.1490271061 | 13746.7266973218 | 37043.5713568904 |
182 | 25280.6772819297 | 13338.4350138744 | 37222.9195499851 |
183 | 25166.2055367533 | 12870.5470467093 | 37461.8640267973 |
184 | 25051.7337915769 | 12341.2322505982 | 37762.2353325557 |
185 | 24937.2620464006 | 11749.7319420619 | 38124.7921507393 |
186 | 24822.7903012242 | 11096.2311949421 | 38549.3494075062 |
187 | 24708.3185560478 | 10381.6937593594 | 39034.9433527362 |
188 | 24593.8468108714 | 9607.68270997665 | 39580.0109117662 |