Apply an Exponential Smoothing Model with the starting value of alpha = 0.50. Do

Question

Apply an Exponential Smoothing Model with the starting value of alpha = 0.50. Do not Optimize alpha with Solver.

Year

Year

Period U.S. Nat Gas Total Consumption (Bcf) Forecasted alpha() 0.5000 2008 Jan 2733.969 2733.97 2008 Feb 2503.42 2008 Mar 2278.15 2008 Apr 1823.866 2008 May 1576.387 2008 Jun 1604.248 2008 Jul 1708.64 2008 Aug 1682.923 2008 Sep 1460.924 2008 Oct 1635.826 2008 Nov 1868.947 2008 Dec 2399.701 2009 Jan 2729.714 2009 Feb 2332.539 2009 Mar 2170.708 2009 Apr 1741.293 2009 May 1504 2009 Jun 1527.833 2009 Jul 1657.997 2009 Aug 1736.462 2009 Sep 1574.974 2009 Oct 1666.519 2009 Nov 1776.171 2009 Dec 2491.864 2010 Jan 2809.788 2010 Feb 2480.949 2010 Mar 2142.925 2010 Apr 1691.813 2010 May 1617.273 2010 Jun 1649.514 2010 Jul 1825.827 2010 Aug 1878.926 2010 Sep 1637.491 2010 Oct 1664.937 2010 Nov 1973.294 2010 Dec 2714.054 2011 Jan 2888.639 2011 Feb 2452.403 2011 Mar 2230.493 2011 Apr 1825.023 2011 May 1667.395 2011 Jun 1657.334 2011 Jul 1890.515 2011 Aug 1891.782 2011 Sep 1655.633 2011 Oct 1744.453 2011 Nov 2031.871 2011 Dec 2541.878 2012 Jan 2756.179 2012 Feb 2500.654 2012 Mar 2127.76 2012 Apr 1953.07 2012 May 1873.834 2012 Jun 1868.356 2012 Jul 2069.773 2012 Aug 2008.815 2012 Sep 1807.208 2012 Oct 1901.084 2012 Nov 2167.841 2012 Dec 2503.907 2013 Jan 2878.784 2013 Feb 2567.154 2013 Mar 2521.108 2013 Apr 1967.458 2013 May 1752.469 2013 Jun 1742.917 2013 Jul 1926.329 2013 Aug 1927.379 2013 Sep 1766.972 2013 Oct 1866.762 2013 Nov 2316.908 2013 Dec 2920.825 2014 Jan 3204.128 2014 Feb 2741.239 2014 Mar 2557.89 2014 Apr 1961.677 2014 May 1810.221 2014 Jun 1745.35 2014 Jul 1881.017 2014 Aug 1933.06 2014 Sep 1809.291 2014 Oct 1912.81 2014 Nov 2357.52 2014 Dec 2679.165 2015 Jan 3115.624 2015 Feb 2926.686 2015 Mar 2592.374 2015 Apr 2012.767 2015 May 1863.453 2015 Jun 1908.353 2015 Jul 2076.833 2015 Aug 2061.224 2015 Sep 1909.306 2015 Oct 1994.017 2015 Nov 2254.757 2015 Dec 2590.887 2016 Jan 3097.348 2016 Feb 2655.581 2016 Mar 2359.435 2016 Apr 2089.816 2016 May 1971.878 2016 Jun 2004.084 2016 Jul 2190.001 2016 Aug 2214.282 2016 Sep 1950.141 2016 Oct 1925.741 2016 Nov 2168.122 2016 Dec 2870.782 2017 Jan 2882.404 2017 Feb 2317.955 2017 Mar 2219.546 2017 Apr 2198.452 2017 May MSE

Explanation / Answer

For exponential forecasting we use below formula

St = *y(t1) + (1)*S(t1)

Below table gives detailed computation

Sum of Squared Errors (SSE) = 15618924

MSE = SSE/n = 15618924/111 = 140711

Sr. No. Year Period U.S. Nat Gas Total Consumption (Bcf) (yt) Forecasted(St) using alpha(=0.5) Error Error Squared SSE MSE = SSE/n 1 2008 Jan 2733.969 15618924 140711 2 2008 Feb 2503.42 2733.969 230.549 53152.84 3 2008 Mar 2278.15 2618.6945 340.5445 115970.6 4 2008 Apr 1823.866 2448.42225 624.55625 390070.5 5 2008 May 1576.387 2136.144125 559.757125 313328 6 2008 Jun 1604.248 1856.265563 252.017563 63512.85 7 2008 Jul 1708.64 1730.256781 21.6167812 467.2852 8 2008 Aug 1682.923 1719.448391 36.5253906 1334.104 9 2008 Sep 1460.924 1701.185695 240.261695 57725.68 10 2008 Oct 1635.826 1581.054848 -54.7711523 2999.879 11 2008 Nov 1868.947 1608.440424 -260.506576 67863.68 12 2008 Dec 2399.701 1738.693712 -661.007288 436930.6 13 2009 Jan 2729.714 2069.197356 -660.516644 436282.2 14 2009 Feb 2332.539 2399.455678 66.916678 4477.842 15 2009 Mar 2170.708 2365.997339 195.289339 38137.93 16 2009 Apr 1741.293 2268.352669 527.059669 277791.9 17 2009 May 1504 2004.822835 500.822835 250823.5 18 2009 Jun 1527.833 1754.411417 226.578417 51337.78 19 2009 Jul 1657.997 1641.122209 -16.8747913 284.7586 20 2009 Aug 1736.462 1649.559604 -86.9023957 7552.026 21 2009 Sep 1574.974 1693.010802 118.036802 13932.69 22 2009 Oct 1666.519 1633.992401 -32.5265989 1057.98 23 2009 Nov 1776.171 1650.255701 -125.915299 15854.66 24 2009 Dec 2491.864 1713.21335 -778.65065 606296.8 25 2010 Jan 2809.788 2102.538675 -707.249325 500201.6 26 2010 Feb 2480.949 2456.163338 -24.7856624 614.3291 27 2010 Mar 2142.925 2468.556169 325.631169 106035.7 28 2010 Apr 1691.813 2305.740584 613.927584 376907.1 29 2010 May 1617.273 1998.776792 381.503792 145545.1 30 2010 Jun 1649.514 1808.024896 158.510896 25125.7 31 2010 Jul 1825.827 1728.769448 -97.057552 9420.168 32 2010 Aug 1878.926 1777.298224 -101.627776 10328.2 33 2010 Sep 1637.491 1828.112112 190.621112 36336.41 34 2010 Oct 1664.937 1732.801556 67.864556 4605.598 35 2010 Nov 1973.294 1698.869278 -274.424722 75308.93 36 2010 Dec 2714.054 1836.081639 -877.972361 770835.5 37 2011 Jan 2888.639 2275.06782 -613.57118 376469.6 38 2011 Feb 2452.403 2581.85341 129.45041 16757.41 39 2011 Mar 2230.493 2517.128205 286.635205 82159.74 40 2011 Apr 1825.023 2373.810602 548.787602 301167.8 41 2011 May 1667.395 2099.416801 432.021801 186642.8 42 2011 Jun 1657.334 1883.405901 226.071901 51108.5 43 2011 Jul 1890.515 1770.36995 -120.14505 14434.83 44 2011 Aug 1891.782 1830.442475 -61.3395248 3762.537 45 2011 Sep 1655.633 1861.112238 205.479238 42221.72 46 2011 Oct 1744.453 1758.372619 13.9196188 193.7558 47 2011 Nov 2031.871 1751.412809 -280.458191 78656.8 48 2011 Dec 2541.878 1891.641905 -650.236095 422807 49 2012 Jan 2756.179 2216.759952 -539.419048 290972.9 50 2012 Feb 2500.654 2486.469476 -14.1845238 201.2007 51 2012 Mar 2127.76 2493.561738 365.801738 133810.9 52 2012 Apr 1953.07 2310.660869 357.590869 127871.2 53 2012 May 1873.834 2131.865435 258.031435 66580.22 54 2012 Jun 1868.356 2002.849717 134.493717 18088.56 55 2012 Jul 2069.773 1935.602859 -134.170141 18001.63 56 2012 Aug 2008.815 2002.687929 -6.12707068 37.541 57 2012 Sep 1807.208 2005.751465 198.543465 39419.51 58 2012 Oct 1901.084 1906.479732 5.39573233 29.11393 59 2012 Nov 2167.841 1903.781866 -264.059134 69727.23 60 2012 Dec 2503.907 2035.811433 -468.095567 219113.5 61 2013 Jan 2878.784 2269.859217 -608.924783 370789.4 62 2013 Feb 2567.154 2574.321608 7.16760827 51.37461 63 2013 Mar 2521.108 2570.737804 49.6298041 2463.117 64 2013 Apr 1967.458 2545.922902 578.464902 334621.6 65 2013 May 1752.469 2256.690451 504.221451 254239.3 66 2013 Jun 1742.917 2004.579726 261.662726 68467.38 67 2013 Jul 1926.329 1873.748363 -52.5806372 2764.723 68 2013 Aug 1927.379 1900.038681 -27.3403186 747.493 69 2013 Sep 1766.972 1913.708841 146.736841 21531.7 70 2013 Oct 1866.762 1840.34042 -26.4215797 698.0999 71 2013 Nov 2316.908 1853.55121 -463.35679 214699.5 72 2013 Dec 2920.825 2085.229605 -835.595395 698219.7 73 2014 Jan 3204.128 2503.027303 -701.100697 491542.2 74 2014 Feb 2741.239 2853.577651 112.338651 12619.97 75 2014 Mar 2557.89 2797.408326 239.518326 57369.03 76 2014 Apr 1961.677 2677.649163 715.972163 512616.1 77 2014 May 1810.221 2319.663081 509.442081 259531.2 78 2014 Jun 1745.35 2064.942041 319.592041 102139.1 79 2014 Jul 1881.017 1905.14602 24.1290204 582.2096 80 2014 Aug 1933.06 1893.08151 -39.9784898 1598.28 81 2014 Sep 1809.291 1913.070755 103.779755 10770.24 82 2014 Oct 1912.81 1861.180878 -51.6291225 2665.566 83 2014 Nov 2357.52 1886.995439 -470.524561 221393.4 84 2014 Dec 2679.165 2122.257719 -556.907281 310145.7 85 2015 Jan 3115.624 2400.71136 -714.91264 511100.1 86 2015 Feb 2926.686 2758.16768 -168.51832 28398.42 87 2015 Mar 2592.374 2842.42684 250.05284 62526.42 88 2015 Apr 2012.767 2717.40042 704.63342 496508.3 89 2015 May 1863.453 2365.08371 501.63071 251633.4 90 2015 Jun 1908.353 2114.268355 205.915355 42401.13 91 2015 Jul 2076.833 2011.310677 -65.5223225 4293.175 92 2015 Aug 2061.224 2044.071839 -17.1521613 294.1966 93 2015 Sep 1909.306 2052.647919 143.341919 20546.91 94 2015 Oct 1994.017 1980.97696 -13.0400403 170.0427 95 2015 Nov 2254.757 1987.49698 -267.26002 71427.92 96 2015 Dec 2590.887 2121.12699 -469.76001 220674.5 97 2016 Jan 3097.348 2356.006995 -741.341005 549586.5 98 2016 Feb 2655.581 2726.677497 71.0964975 5054.712 99 2016 Mar 2359.435 2691.129249 331.694249 110021.1 100 2016 Apr 2089.816 2525.282124 435.466124 189630.7 101 2016 May 1971.878 2307.549062 335.671062 112675.1 102 2016 Jun 2004.084 2139.713531 135.629531 18395.37 103 2016 Jul 2190.001 2071.898766 -118.102234 13948.14 104 2016 Aug 2214.282 2130.949883 -83.3321172 6944.242 105 2016 Sep 1950.141 2172.615941 222.474941 49495.1 106 2016 Oct 1925.741 2061.378471 135.637471 18397.52 107 2016 Nov 2168.122 1993.559735 -174.562265 30471.98 108 2016 Dec 2870.782 2080.840868 -789.941132 624007 109 2017 Jan 2882.404 2475.811434 -406.592566 165317.5 110 2017 Feb 2317.955 2679.107717 361.152717 130431.3 111 2017 Mar 2219.546 2498.531358 278.985358 77832.83 112 2017 Apr 2198.452 2359.038679 160.586679 25788.08 113 2017 May 2278.74534

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