| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.601766342255356 |
| beta | 0.133327045838075 |
| gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 1876.88 | 1882.5043883547 | -5.62438835470061 |
| 14 | 1876.68 | 1878.71675836282 | -2.03675836282105 |
| 15 | 1865.52 | 1866.00671403747 | -0.486714037465617 |
| 16 | 1858.99 | 1859.03496764084 | -0.0449676408384221 |
| 17 | 1856.87 | 1857.06710819262 | -0.197108192621272 |
| 18 | 1858.22 | 1858.58271468335 | -0.362714683347576 |
| 19 | 1858.22 | 1861.52081353583 | -3.30081353582705 |
| 20 | 1859.32 | 1858.21020007924 | 1.10979992075659 |
| 21 | 1859.52 | 1856.57611984902 | 2.9438801509848 |
| 22 | 1852.48 | 1855.13816996393 | -2.65816996392618 |
| 23 | 1850.07 | 1853.15290863401 | -3.08290863401112 |
| 24 | 1850.07 | 1850.56679011239 | -0.496790112394592 |
| 25 | 1850.07 | 1847.09098159758 | 2.97901840241661 |
| 26 | 1841.55 | 1849.45726188339 | -7.90726188339454 |
| 27 | 1845 | 1832.90877995106 | 12.0912200489379 |
| 28 | 1844.01 | 1833.7680326237 | 10.2419673762956 |
| 29 | 1842.67 | 1838.84135892241 | 3.82864107759497 |
| 30 | 1842.67 | 1843.94801054808 | -1.27801054807787 |
| 31 | 1842.67 | 1846.32626433394 | -3.65626433394118 |
| 32 | 1842.9 | 1845.69068787926 | -2.79068787926008 |
| 33 | 1840.37 | 1843.25935557115 | -2.88935557114814 |
| 34 | 1841.59 | 1836.43176298788 | 5.15823701211684 |
| 35 | 1844.33 | 1839.95965803721 | 4.37034196278501 |
| 36 | 1844.33 | 1844.46517246104 | -0.135172461035154 |
| 37 | 1844.33 | 1844.19680858301 | 0.133191416987302 |
| 38 | 1845.39 | 1841.89260850401 | 3.49739149599509 |
| 39 | 1861.84 | 1842.4634725339 | 19.3765274660961 |
| 40 | 1862.85 | 1849.8471969596 | 13.0028030403996 |
| 41 | 1869.46 | 1857.12625907754 | 12.3337409224578 |
| 42 | 1870.8 | 1869.09809206528 | 1.70190793471784 |
| 43 | 1870.8 | 1876.34228289745 | -5.54228289744674 |
| 44 | 1871.52 | 1878.78497020316 | -7.26497020315787 |
| 45 | 1875.52 | 1877.13139776058 | -1.61139776057985 |
| 46 | 1880.38 | 1877.889717339 | 2.49028266100049 |
| 47 | 1885.05 | 1882.89636427406 | 2.1536357259447 |
| 48 | 1886.42 | 1887.49384517578 | -1.0738451757752 |
| 49 | 1886.42 | 1889.91233301671 | -3.49233301671211 |
| 50 | 1891.65 | 1889.62011180691 | 2.02988819309144 |
| 51 | 1903.11 | 1898.36770755789 | 4.74229244211142 |
| 52 | 1905.29 | 1895.96889975257 | 9.32110024742838 |
| 53 | 1904.26 | 1902.03269405597 | 2.22730594402515 |
| 54 | 1905.37 | 1904.14470420792 | 1.22529579208094 |
| 55 | 1905.37 | 1908.63480917937 | -3.2648091793742 |
| 56 | 1905.12 | 1912.36230099809 | -7.24230099808642 |
| 57 | 1908.62 | 1913.57596129377 | -4.95596129376668 |
| 58 | 1915.08 | 1914.28887053207 | 0.791129467932933 |
| 59 | 1916.36 | 1918.33644235338 | -1.97644235338294 |
| 60 | 1916.68 | 1919.02940867582 | -2.34940867582259 |
| 61 | 1916.24 | 1919.48096033578 | -3.24096033578053 |
| 62 | 1922.05 | 1921.32308742058 | 0.726912579415966 |
| 63 | 1922.63 | 1930.04617330651 | -7.41617330651206 |
| 64 | 1922.47 | 1920.85815703398 | 1.61184296602482 |
| 65 | 1920.64 | 1917.54317670359 | 3.09682329640714 |
| 66 | 1920.66 | 1917.9345464193 | 2.7254535807017 |
| 67 | 1920.66 | 1919.81479263727 | 0.845207362725205 |
| 68 | 1921.19 | 1923.03684440137 | -1.84684440136607 |
| 69 | 1921.44 | 1927.44595455106 | -6.00595455106441 |
| 70 | 1921.73 | 1928.76960363851 | -7.03960363851024 |
| 71 | 1921.81 | 1925.32839581317 | -3.5183958131704 |
| 72 | 1921.81 | 1923.14685732919 | -1.33685732919503 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 73 | 1922.13583980549 | 1911.58406002497 | 1932.68761958602 |
| 74 | 1926.05159350656 | 1913.27948733595 | 1938.82369967718 |
| 75 | 1929.57926076302 | 1914.4857313341 | 1944.67279019194 |
| 76 | 1927.52918409403 | 1910.01241266771 | 1945.04595552036 |
| 77 | 1922.78617529576 | 1902.74551491054 | 1942.82683568098 |
| 78 | 1919.86818080639 | 1897.20498566663 | 1942.53137594615 |
| 79 | 1917.84298735388 | 1892.4609516218 | 1943.22502308597 |
| 80 | 1917.8999675968 | 1889.70522586252 | 1946.09470933107 |
| 81 | 1920.32793586049 | 1889.22904511635 | 1951.42682660464 |
| 82 | 1923.89978747083 | 1889.80765067996 | 1957.99192426169 |
| 83 | 1925.70749429705 | 1888.5352568245 | 1962.8797317696 |
| 84 | 1926.40471166761 | 1886.06764720249 | 1966.74177613273 |
