US_raw_data = [2334.4 1.03 26.840 16.326 2381.2 0.99 26.757 16.368 2449.7 1.34 26.793 16.447 2490.3 1.50 26.757 16.513 2523.5 1.94 26.777 16.635 2537.6 2.36 26.857 16.801 2526.1 2.48 26.860 16.969 2545.9 2.69 27.037 17.068 2542.7 2.81 27.317 17.287 2584.3 2.93 27.550 17.354 2600.2 2.93 27.777 17.597 2593.9 3.00 28.013 17.717 2618.9 3.23 28.263 17.824 2591.3 3.25 28.400 17.825 2521.2 1.86 28.737 18.020 2536.6 0.94 28.930 18.072 2596.1 1.32 28.913 18.186 2656.6 2.16 28.943 18.271 2710.3 2.57 28.993 18.297 2778.8 3.08 29.043 18.314 2775.5 3.58 29.193 18.366 2785.2 3.99 29.370 18.443 2847.7 3.93 29.397 18.521 2834.4 3.70 29.573 18.579 2839.0 2.94 29.590 18.648 2802.6 2.30 29.780 18.700 2819.3 2.00 29.840 18.743 2872.0 1.73 29.830 18.785 2918.4 1.68 29.947 18.843 2977.8 2.40 29.990 18.908 3031.2 2.46 30.107 19.020 3064.7 2.61 30.220 19.047 3093.0 2.85 30.307 19.092 3100.6 2.92 30.380 19.152 3141.1 2.97 30.477 19.196 3180.4 2.96 30.533 19.233 3240.3 3.33 30.720 19.272 3265.0 3.45 30.803 19.418 3338.2 3.46 30.930 19.477 3376.6 3.49 30.980 19.529 3422.5 3.46 31.050 19.607 3432.0 3.58 31.193 19.703 3516.3 3.97 31.290 19.801 3564.0 4.08 31.490 19.887 3636.3 4.07 31.583 19.960 3724.0 4.17 31.750 20.088 3815.4 4.56 32.047 20.218 3828.1 4.91 32.337 20.391 3853.3 5.41 32.617 20.601 3884.5 5.56 32.883 20.791 3918.7 4.82 32.967 20.886 3919.6 3.99 33.167 20.997 3950.8 3.89 33.500 21.203 3981.0 4.17 33.867 21.438 4063.0 4.79 34.200 21.672 4132.0 5.98 34.533 21.899 4160.3 5.94 35.000 22.115 4178.3 5.92 35.433 22.426 4244.1 6.57 35.867 22.660 4256.5 8.33 36.433 22.952 4283.4 8.98 36.933 23.280 4263.3 8.94 37.500 23.581 4256.6 8.57 38.100 23.915 4264.3 7.88 38.633 24.247 4302.3 6.70 39.033 24.438 4256.6 5.57 39.600 24.752 4374.0 3.86 39.933 25.126 4398.8 4.56 40.300 25.455 4433.9 5.47 40.700 25.711 4446.3 4.75 41.000 25.918 4525.8 3.54 41.333 26.319 4633.1 4.30 41.600 26.475 4677.5 4.74 41.933 26.731 4754.5 5.14 42.367 27.083 4876.2 6.54 43.033 27.403 4932.6 7.82 43.933 27.828 4906.3 10.56 44.800 28.370 4953.1 10.00 45.933 28.932 4909.6 9.32 47.300 29.488 4922.2 11.25 48.567 30.192 4873.5 12.09 49.933 31.085 4854.3 9.35 51.467 32.015 4795.3 6.30 52.567 32.757 4831.9 5.42 53.200 33.245 4913.3 6.16 54.267 33.864 4977.5 5.41 55.267 34.463 5090.7 4.83 55.900 34.837 5128.9 5.20 56.400 35.208 5154.1 5.28 57.300 35.686 5191.5 4.87 58.133 36.331 5251.8 4.66 59.200 36.943 5356.1 5.16 60.233 37.470 5451.9 5.82 61.067 37.927 5450.8 6.51 61.967 38.758 5469.4 6.76 63.033 39.326 5684.6 7.28 64.467 40.050 5740.3 8.10 65.967 40.716 5816.2 9.58 67.500 41.575 5825.9 10.07 69.200 42.318 5831.4 10.18 71.400 43.362 5873.3 10.95 73.700 44.301 5889.5 13.58 76.033 45.194 5908.5 15.05 79.033 46.144 5787.4 12.69 81.700 47.178 5776.6 9.84 83.233 48.256 5883.5 15.85 85.567 49.593 6005.7 16.57 87.933 50.851 5957.8 17.78 89.767 51.813 6030.2 17.58 92.267 52.730 5955.1 13.59 93.767 53.692 5857.3 14.23 94.600 54.421 5889.1 14.51 95.967 55.080 5866.4 11.01 97.633 55.864 5871.0 9.29 97.933 56.470 5944.0 8.65 98.000 56.929 6077.6 8.80 99.133 57.345 6197.5 9.46 100.100 57.929 6325.6 9.43 101.100 58.355 6448.3 9.69 102.533 59.096 6559.6 10.56 103.500 59.602 6623.3 11.39 104.400 60.081 6677.3 9.27 105.300 60.465 6740.3 8.48 106.267 61.136 6797.3 7.92 107.233 61.483 6903.5 7.90 107.900 61.736 6955.9 8.10 109.000 62.140 7022.8 7.83 109.567 62.456 7051.0 6.92 109.033 62.786 7119.0 6.21 109.700 63.143 7153.4 6.27 110.467 63.567 7193.0 6.22 111.800 64.160 7269.5 6.65 113.067 64.526 7332.6 6.84 114.267 65.033 7458.0 6.92 115.333 65.530 7496.6 6.66 116.233 66.068 7592.9 7.16 117.567 66.689 7632.1 7.98 119.000 67.442 7734.0 8.47 120.300 67.953 7806.6 9.44 121.667 68.723 7865.0 9.73 123.633 69.399 7927.4 9.08 124.600 69.855 7944.7 8.61 125.867 70.317 8027.7 8.25 128.033 71.166 8059.6 8.24 129.300 71.993 8059.5 8.16 131.533 72.655 7988.9 7.74 133.767 73.239 7950.2 6.43 134.767 74.026 8003.8 5.86 135.567 74.553 8037.5 5.64 136.600 75.133 8069.0 4.82 137.733 75.569 8157.6 4.02 138.667 75.954 8244.3 3.77 139.733 76.423 8329.4 3.26 140.800 76.778 8417.0 3.04 142.033 77.214 8432.5 3.04 143.067 77.677 8486.4 3.00 144.100 78.106 8531.1 3.06 144.767 78.466 8643.8 2.99 145.967 78.897 8727.9 3.21 146.700 79.311 8847.3 3.94 147.533 79.689 8904.3 4.49 148.900 80.163 9003.2 5.17 149.767 80.576 9025.3 5.81 150.867 81.038 9044.7 6.02 152.100 81.397 9120.7 5.80 152.867 81.780 9184.3 5.72 153.700 82.195 9247.2 5.36 155.067 82.670 9407.1 5.24 156.400 82.987 9488.9 5.31 157.300 83.250 9592.5 5.28 158.667 83.710 9666.2 5.28 159.633 84.251 9809.6 5.52 160.000 84.447 9932.7 5.53 160.800 84.742 10008.9 5.51 161.667 85.055 10103.4 5.52 162.000 85.198 10194.3 5.50 162.533 85.402 10328.8 5.53 163.367 85.729 10507.6 4.86 164.133 85.988 10592.1 4.73 164.733 86.371 10674.9 4.75 165.967 86.675 10810.7 5.09 167.200 86.998 11004.8 5.31 168.433 87.305 11033.6 5.68 170.100 88.000 11248.8 6.27 171.433 88.446 11258.3 6.52 173.000 88.979 11325.0 6.47 174.233 89.447 11287.8 5.59 175.900 90.054 11361.7 4.33 177.133 90.666 11330.4 3.50 177.633 90.952 11370.0 2.13 177.500 91.232 11467.1 1.73 178.067 91.555 11528.1 1.75 179.467 91.965 11586.6 1.74 180.433 92.363 11590.6 1.44 181.500 92.894 11638.9 1.25 183.367 93.543 11737.5 1.25 183.067 93.815 11930.7 1.02 184.433 94.337 12038.6 1.00 185.133 94.818 12117.9 1.00 186.700 95.643 12195.9 1.01 188.167 96.450 12286.7 1.43 189.367 97.149 12387.2 1.95 191.400 97.874 12515.0 2.47 192.367 98.776 12570.7 2.94 193.667 99.437 12670.5 3.46 196.600 100.458 12735.6 3.98 198.433 101.302 12896.4 4.46 199.467 102.055 12948.7 4.91 201.267 102.948 12950.4 5.25 203.167 103.724 13038.4 5.25 202.333 104.186 13056.1 5.26 204.317 105.380 13173.6 5.25 206.631 106.098 13269.8 5.07 207.939 106.453 13326.0 4.50 210.490 106.958 13266.8 3.18 212.754 107.591 13310.5 2.09 215.549 108.302 13186.9 1.94 218.904 109.162 12883.5 0.51 213.814 109.300 12663.2 0.18 212.449 109.717 12641.3 0.18 213.475 109.594 12694.5 0.16 215.363 109.658 12813.5 0.12 216.973 109.943 12937.7 0.13 217.435 110.358 13058.5 0.19 217.254 110.793 13139.6 0.19 218.025 111.156 13216.1 0.19 219.625 111.644 13227.9 0.16 222.079 112.398 13271.8 0.09 224.500 113.118 13331.6 0.08 226.217 113.836 13429.9 0.07 226.950 114.077]; % start date 1954-07-01 = 1954:Q2 size_smpl = size(US_raw_data,1); % Y = log(Y_t/Y_t-1)*400; Y_raw_SA = US_raw_data(:,1); Y_long = log(Y_raw_SA(2:size_smpl)./Y_raw_SA(1:size_smpl-1))*400; R_long = US_raw_data(2:size_smpl,2); CPI_long = US_raw_data(:,3); PPI_long = US_raw_data(:,4); PiPPI_long = log(PPI_long(2:size_smpl)./PPI_long(1:size_smpl-1))*400; PiCPI_long = log(CPI_long(2:size_smpl)./CPI_long(1:size_smpl-1))*400; % starting data 1980:Q1 corresponds to n_start = 103 % end date 2008:Q2 corresponds to nobservations = 114 observations n_start = 103; nobservations = 114; Y = Y_long(n_start:n_start+nobservations-1,1); Pi = PiPPI_long(n_start:n_start+nobservations-1,1); R = R_long(n_start:n_start+nobservations-1,1); num_obs = size(R,1);