data_q = [ 18.02 1474.5 150.2 17.94 1538.2 150.9 18.01 1584.5 151.4 18.42 1644.1 152 18.73 1678.6 152.7 19.46 1693.1 153.3 19.55 1724 153.9 19.56 1758.2 154.7 19.79 1760.6 155.4 19.77 1779.2 156 19.82 1778.8 156.6 20.03 1790.9 157.3 20.12 1846 158 20.1 1882.6 158.6 20.14 1897.3 159.2 20.22 1887.4 160 20.27 1858.2 160.7 20.34 1849.9 161.4 20.39 1848.5 162 20.42 1868.9 162.8 20.47 1905.6 163.6 20.56 1959.6 164.3 20.62 1994.4 164.9 20.78 2020.1 165.7 21 2030.5 166.5 21.2 2023.6 167.2 21.33 2037.7 167.9 21.62 2033.4 168.7 21.71 2066.2 169.5 22.01 2077.5 170.2 22.15 2071.9 170.9 22.27 2094 171.7 22.29 2070.8 172.5 22.56 2012.6 173.1 22.64 2024.7 173.8 22.77 2072.3 174.5 22.88 2120.6 175.3 22.92 2165 176.045 22.91 2223.3 176.727 22.94 2221.4 177.481 23.03 2230.95 178.268 23.13 2279.22 179.694 23.22 2265.48 180.335 23.32 2268.29 181.094 23.4 2238.57 181.915 23.45 2251.68 182.634 23.51 2292.02 183.337 23.56 2332.61 184.103 23.63 2381.01 184.894 23.75 2422.59 185.553 23.81 2448.01 186.203 23.87 2471.86 186.926 23.94 2476.67 187.68 24 2508.7 188.299 24.07 2538.05 188.906 24.12 2586.26 189.631 24.29 2604.62 190.362 24.35 2666.69 190.954 24.41 2697.54 191.56 24.52 2729.63 192.256 24.64 2739.75 192.938 24.77 2808.88 193.467 24.88 2846.34 193.994 25.01 2898.79 194.647 25.17 2970.48 195.279 25.32 3042.35 195.763 25.53 3055.53 196.277 25.79 3076.51 196.877 26.02 3102.36 197.481 26.14 3127.15 197.967 26.31 3129.53 198.455 26.6 3154.19 199.012 26.9 3177.98 199.572 27.21 3236.18 199.995 27.49 3292.07 200.452 27.75 3316.11 200.997 28.12 3331.22 201.538 28.39 3381.86 201.955 28.73 3390.23 202.419 29.14 3409.65 202.986 29.51 3392.6 203.584 29.94 3386.49 204.086 30.36 3391.61 204.721 30.61 3422.95 205.419 31.02 3389.36 206.13 31.5 3481.4 206.763 31.93 3500.95 207.362 32.27 3523.8 208 32.54 3533.79 208.642 33.02 3604.73 209.142 33.2 3687.9 209.637 33.49 3726.18 210.181 33.95 3790.44 210.737 34.36 3892.22 211.192 34.94 3919.01 211.663 35.61 3907.08 212.191 36.29 3947.11 212.708 37.01 3908.15 213.144 37.79 3922.57 213.602 38.96 3879.98 214.147 40.13 3854.13 214.7 41.05 3800.93 215.135 41.66 3835.21 215.652 42.41 3907.02 216.289 43.19 3952.48 216.848 43.69 4044.59 217.314 44.15 4072.19 217.776 44.77 4088.49 218.338 45.57 4126.39 218.917 46.32 4176.28 219.427 47.07 4260.08 219.956 47.66 4329.46 220.573 48.63 4328.33 221.201 49.42 4345.51 221.719 50.41 4510.73 222.281 51.27 4552.14 222.933 52.35 4603.65 223.583 53.51 4605.65 224.152 54.65 4615.64 224.737 55.82 4644.93 225.418 56.92 4656.23 226.117 58.18 4678.96 226.754 59.55 4566.62 227.389 61.01 4562.25 228.07 62.59 4651.86 228.689 64.15 4739.16 229.155 65.37 4696.82 229.674 66.65 4753.02 230.301 67.87 4693.76 230.903 68.86 4615.89 231.395 69.72 4634.88 231.906 70.66 4612.08 232.498 71.44 4618.26 233.074 72.08 4662.97 233.546 72.83 4763.57 234.028 73.48 4849 234.603 74.19 4939.23 235.153 75.02 5053.56 235.605 75.58 5132.87 236.082 76.25 5170.34 236.657 76.81 5203.68 237.232 77.63 5257.26 237.673 78.25 5283.73 238.176 78.76 5359.6 238.789 79.45 5393.57 239.387 79.81 5460.83 239.861 80.22 5466.95 240.368 80.84 5496.29 240.962 81.45 5526.77 241.539 82.09 5561.8 242.009 82.68 5618 242.52 83.33 5667.39 243.12 84.09 5750.57 243.721 84.67 5785.29 244.208 85.56 5844.05 244.716 86.66 5878.7 245.354 87.44 5952.83 245.966 88.45 6010.96 246.46 89.39 6055.61 247.017 90.13 6087.96 247.698 90.88 6093.51 248.374 92 6152.59 248.928 93.18 6171.57 249.564 94.14 6142.1 250.299 95.11 6078.96 251.031 96.27 6047.49 251.65 97 6074.66 252.295 97.7 6090.14 253.033 98.31 6105.25 253.743 99.13 6175.69 254.338 99.79 6214.22 255.032 100.17 6260.74 255.815 100.88 6327.12 256.543 101.84 6327.93 257.151 102.35 6359.9 257.785 102.83 6393.5 258.516 103.51 6476.86 259.191 104.13 6524.5 259.738 104.71 6600.31 260.351 105.39 6629.47 261.04 106.09 6688.61 261.692 106.75 6717.46 262.236 107.24 6724.2 262.847 107.75 6779.53 263.527 108.29 6825.8 264.169 108.91 6882 264.681 109.24 6983.91 265.258 109.74 7020 265.887 110.23 7093.12 266.491 111 7166.68 266.987 111.43 7236.5 267.545 111.76 7311.24 268.171 112.08 7364.63 268.815 ]; %GDPD GDPQ GPOP series = zeros(193,2); series(:,2) = data_q(:,1); series(:,1) = 1000*data_q(:,2)./data_q(:,3); Y_obs = series(:,1); P_obs = series(:,2); series = series(2:193,:)./series(1:192,:); gy_obs = series(:,1); gp_obs = series(:,2); ti = [1950:0.25:1997.75];