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];