Geometric interpolation of Return variable

[Anita Mendi]

Hi ,

Thanks to the post replied on the various issues at Statalist, I am able to understand things better.

I have a few queries and looking forward here for the solution. I have a panel data - 470 firms from 2007 to 2016 for 13 financial variables. My variables are missing at some point and I want to interpolate those. I can interpolate the variables like LTD (Long term Debt)and NI (Net Income) by command -

by name, sort:ipolate LTD year, gen(LTD_1)

However, I still get many missing values, so I use extrapolate option with ipolate -

by name, sort:ipolate LTD year, gen(LTD_11)epolate

Now, I need to interpolate the return variables, such as ROA (Return on Assets), ROE (Return on Equity), ROCE (Return on Capital Employed), R &D to NS (Research and Development Expense to Net Sales) and I think that geometric interpolation would be useful in this situation. Grateful for the posts here, I know that this needs to be interpolated on the logarithms and then exponentiate.

Kindly advice how to go about it. I appreciate all the help.
Thanks.


Example generated by -dataex-. To install: ssc install dataex

clear
input float firmid int year double(LTD ROA TA ROCE TobQ MCap ROE) byte UNGC double Sales long Employees double(RDexp RDtoNS NI)
116 2007 1310.194 3.5793 4511.406 9.4704 .8332 760.721 9.8752 0 5294.516 1625 9.938 .1877 143.173
269 2007 0 14.2312 4895.3 27.3399 1.6697 7507.46 16.8691 . 3148.3 922 14.8 .4701 630.1
259 2007 47.5 6.6728 540.058 21.9592 1.1314 256.5836 19.6371 . 700.258 . . . 28.609
91 2007 3768.785 12.5025 16550.012 21.0105 2.7374 37060.9883 28.7292 . 5875.93 745 . . 679.573
469 2007 750.116 11.3578 3241.8069 . .4433 433.324 15.774 . 457.071 . . . 402.999
240 2007 131302.716 2.3101 286308.094 . 1.4322 156359.0464 19.5001 0 43513.052 10800 . . 7298.029000000001
308 2007 . . . . . . . . . . . . .
236 2007 7181.9751 . 75183.3616 . 1.3982 8894.6521 . . 52389.812 8614 . . -4195.761
98 2007 21626.798 13.7515 77180.658 37.137 2.0665 122282.0451 31.8452 0 64346.284 9000 . . 1467.298
127 2007 . . . . . . . . . . . . .
20 2007 2447.8 16.2146 71499.8 24.8309 3.3948 223865.3058 24.1216 0 57920.8 2702 6.6 .0114 13897.1
139 2007 895.831 6.8464 4600.6699 22.6451 . . 22.6609 . 15634.5605 . . . 123.884
167 2007 14203.7 .9483 39221.5 2.6755 1.3613 22934.3392 3.1026 0 23007.4 . . . 793.734
201 2007 134575.3 3.1602 183839.73 . 1.3523 94240.1778 17.6367 0 15686.37 175 . . 3323.77
361 2007 . . . . . . . . . . . . .
65 2007 2722.534 14.1498 13763.555 31.5191 2.7943 31618.6307 28.0706 0 27762.501 2358 34.72 .1251 1105.036
88 2007 73.424 25.8258 11215.87 73.2546 7.8812 81973.9618 57.6924 0 22337.178 2306 65.1 .2914 2138.577
6 2007 186.625 17.0897 807.961 37.7254 . . 53.6068 . 1330.014 . . . 33.224
129 2007 10164.9004 1.1526 34901.8984 3.4079 1.3993 26084.1214 3.1528 . 23564.6992 . . . 1445.871
144 2007 44749.7 14.1947 159873.8 32.9812 1.7848 191864.1672 34.9255 0 140951.5 15022 36.6 .026 11566.2
321 2007 364.3854 3.2362 1723.3049 10.816 .9828 427.28 11.0323 . 1734.5918 . . . 13.4104
241 2007 . . . . . . . 0 . . . . .
153 2007 . . . . . . . 0 . . . . .
420 2007 23002.5 .1301 121108.4 .0498 1.513 114655.5 .2891 0 86112.1 2926 . . 698.065
171 2007 91293.6016 5.7104 327836.4063 12.8539 .9646 84085.9707 18.3425 1 884994.1875 10897 4.689 .0005 4520.7002
105 2007 249.904 17.8603 3323.852 30.6244 3.9048 11948.71 23.4703 . 5182.564 . 7.092 .1368 492.729
118 2007 215913.7656 . 262439.4063 . . . . . 19012.9297 . . . 2380.4851
60 2007 1280.392 13.9959 15743.512 19.4449 3.4095 48620 20.4693 0 8227.531 2543 . . 1739.523
412 2007 33877.1 9.906 125412.9 27.1762 3.018 288196.4272 27.6682 0 79857.3 10000 . . 7595
261 2007 . . . . . . . 0 . . . . .
184 2007 24380.7188 . 32386.2852 . . . . 0 2999.8716 . . . 225.4411
59 2007 . . . . . . . 0 . . . . .
213 2007 4 2.9146 16930.6992 . 2.4316 30115.5 18.6829 0 4423.2002 . . . 668.09
208 2007 . . . . . . . . . . . . .
463 2007 0 -1.9472 115.0519 . 1.4515 143.998 -2.4399 . 3.2945 10 . . .7324
204 2007 3596.6831 2.5385 10410.2373 8.7506 .8359 2142.5801 6.4435 0 4870.2681 . 31.168 .64 350.315
16 2007 . . . . . . . . . . . . .
417 2007 . . . . . . . . . . . . .
335 2007 3910.3433 11.1309 12220.9863 15.6005 .7553 3653.54 22.3336 0 9329.4248 . 0 0 703.1412
475 2007 6.7176 . 2834.8354 . 3.6421 9302.8415 . . 2405.1244 . . . 74.7056
54 2007 37554.278 17.2166 276653.171 39.2096 5.8198 1448304.1025 43.0977 0 184202.022 20314 . . 20279.486
377 2007 110.094 6.6414 892.616 11.5038 1.3543 659.4466 17.0609 . 833.206 . 19.164 2.3 65.612
345 2007 16477.8336 7.1617 108973.1154 31.283 .7865 9675.648 23.3225 . 95414.8494 . 2 .0021 3889.3006
45 2007 . . . . . . . . . . . . .
407 2007 866.9 . 14535.3 . 7.3564 104325.7363 . 0 6779.6 . . . 2469.4
89 2007 . . . . . . . . . . . . .
383 2007 . . . . . . . 0 . . . . .
193 2007 19364.5 1.5604 561993.7 . .9516 7752.69 25.9659 0 50494.4 20809 . . 5003.9
351 2007 . . . . . . . 0 . . . . .
284 2007 104717.9 3.3437 329418.1 5.6619 . . 6.5458 0 22459.4 . 0 0 8646.6
353 2007 10139.8721 4.5888 33822.4219 9.0494 1.2063 21326.7769 10.3358 0 20406.7656 . . . 1360.911
401 2007 19115.9551 .9342 379931.3125 . .9975 15041.75 22.2636 . 29521.9883 11607 . . 2586.788
323 2007 9102.3828 . 36283.1758 . 1.9073 47836.3152 . 0 15102.9531 875 . . 3098.6079
57 2007 527.1749 . 1624.5922 . .936 161.0641 . 0 4741.9116 . . . 72.5198
119 2007 . . . . . . . . . . . . .
107 2007 0 8.7274 17254.6367 18.0592 1.8557 25340.4407 14.2843 0 5828.1182 2591 . . 1428.234
207 2007 395.331 19.0782 4462.775 40.0214 4.3305 18295.1517 24.15 0 2664.351 1716 . . 72.902
134 2007 218 14.3236 6436.533 44.7359 2.2038 11994.4774 22.5052 0 7614.838 1386 . . 645.048
291 2007 0 43.2133 62474.5 48.0232 4.2634 261676.8 47.2381 0 41858.4 . . . 17789.9
41 2007 657.1958 -.9837 821.2193 -.5721 1.0265 118.8575 -7.6451 . 1306.1027 . . . 4.3879
294 2007 4345.52 16.0951 10533.1465 21.2063 1.1788 6316.3613 35.8011 0 5507.168 1047 5.477 .1311 592.946
336 2007 . . . . . . . 0 . . . . .
329 2007 1959 10.4614 23018.4 25.9945 2.7667 51145.5136 20.8934 0 24201.8 7542 1074 4.4377 1206.5
302 2007 44.5314 5.4828 1106.8554 12.5895 .8204 488.46 8.988199999999999 0 1311.9549 326 2.4 .1829 -41.164
437 2007 97414.791 .4625 748638.955 . .9874 17186.24 12.3365 0 57154.166 24904 . . 1966.521
355 2007 . . . . . . . . . . . . -35.76
170 2007 . . . . . . . 0 . . . . .
94 2007 33706.0156 1.5435 38862.9805 . .9952 3062.486 16.8704 0 3572.0339 416 . . 435.975
157 2007 43206.8 1.3959 913082.5 . 1.2629 304745.5945 19.5116 0 82244.9 21477 . . 8815.6
449 2007 2769.5779 -4.7181 6187.7485 9.3545 1.0549 2245.7683 -13.2627 . 2788.656 . . . 227.5347
160 2007 . . . . . . . . . . . . .
309 2007 3143.38 9.029 15135.4 11.4252 . . 17.488 . 2351.76 . . . 349.23
151 2007 . . . . . . . 0 . . . . .
232 2007 2312.25 1.5357 6075.2202 6.8533 1.1486 2328.9203 5.8064 0 4330.8999 . . . 299.03
221 2007 371.477 1.7396 3381.9561 14.3967 .9327 1271.6165 3.849 . 2359.6741 . . . 116.142
421 2007 4462.6 38.6523 131861.5 67.1773 9.4859 1207458.563 56.7399 1 186852.1 89419 280.2 .15 29667.4
228 2007 2846.9 . 18408.9 . 1.8361 22321.2066 . . 20439.1 . . . 1203.8
137 2007 . . . . . . . . . . . . .
101 2007 . . . . . . . . . . . . .
472 2007 26854.6191 8.7019 51530.8906 22.3731 1.6408 45755.1521 32.9777 0 24908.1504 . 1515.6801 6.0851 -1388.58
131 2007 0 19.2693 9131.0596 27.4711 3.7011 31127.4066 27.3618 0 12784.668 2632 109.45 .9843 1883.323
195 2007 148475 7.9301 1041519.2 18.7925 1.0973 466796.0757 23.4287 1 1844607 29862 809.8 .0439 51159
304 2007 2701.73 8.6055 9913.8086 15.3549 1.2786 6441.6006 26.1011 0 8090.4888 . . . 378.509
224 2007 12917.032 5.1779 39066.02 12.5733 1.1768 15537.0339 20.3791 0 38731.418 . . . 1671.896
9 2007 40664.4 2.8132 79101.5 12.2554 1.5091 51774.5891 17.2816 0 152370.1 610 . . 1345.8
196 2007 31293.036 1.4242 822568.284 . 1.0195 55978.2 28.1379 0 62191.217 23861 . . 7833.442
459 2007 834.2995 4.0568 2431.7422 7.7771 .8543 388.0771 10.8027 0 1694.8212 . 0 0 41.6543
133 2007 4601.239 18.8194 19438.551 43.3234 4.4222 73385.5185 58.3815 0 12515.336 . . . 879.76
378 2007 9784.2002 8.9723 16601.3008 14.0386 1.4049 11658.8872 34.3796 0 8179.7002 . . . 765.621
136 2007 4279.187 3.0148 22817.789 20.7382 2.8566 47090.2641 13.1326 . 23789.71 1528 13.938 .0586 489.977
115 2007 3321.5271 -1.7619 12985.6514 . .9056 4855.5092 -3.628 0 8397.0264 . . . 801.908
381 2007 0 .0126 894.96 .707 1.4323 625.2504 .0441 . 1303.285 320 3.1528 .2419 -76.271
124 2007 6848.4434 2.7925 9682.8936 . .9312 913.9033 14.4611 . 1294.1835 . . . 811.5045
73 2007 6451.442 . 16566.836 . .7773 1195.0714 . 0 23664.892 5384 41.413 .175 -161.117
62 2007 0 -.5377 1194.4969 . .885 547.5 -.9168 . 521.363 160 . . 22.126
418 2007 207.658 7.4661 895.116 13.7503 .9102 334.1625 17.2086 0 1231.3409 . 1.334 .1205 10.266
282 2007 258.894 . 382.0352 . 1.3629 232.05 . . 80.2481 . . . 20.4598
344 2007 104709.9 1.9377 217046.9 . . . 40.5827 0 19146.6 9325 . . 2856.8
320 2007 1268.2966 12.6017 4332.3188 23.7037 1.1686 2412.6739 33.2564 . 3147.353 . . . 221.2927
138 2007 1004.573 9.5852 8231.8916 19.2705 1.4692 7946.0123 18.702 . 10050.75 52000 . . 609.676
end

[Clyde Schechter]

No, geometric interpolation of those variables is impossible because they contain negative values.

Added: However, you might want to interpolate geometrically on the growth ratio from year to year. Here's how it would go with ROA:

gen log_rf = log(1+ROA/100)
sort firmid year
by firmid: ipolate log_rf year, gen(log_rf1) epolate
gen ROA1 = (exp(log_rf1)-1)*100

Now, this code does not actually do an interpolation/extrapolation in your example data because you provided only a single observation for each firmid, so there is nothing to interpolate/extrapolate. But presumably in your real data you won't encounter this limitation. In the future, when posting example data, use the -if- and -in- options of -dataex- so choose a subset of your data for which the questions you are asking can actually be answered.

Finally, before analyzing anything with these results, please do consult with an expert in finance (it's not my field) as to whether any kind of interpolation/extrapolation is appropriate for this kind of data. I have the vague impression that financial variables are subject to idiosyncratic shocks that make simple models such as linear or geometric interpolation inappropriate, except possibly over time periods much shorter than a year.

[Anita Mendi]

Thanks a Lot, Clyde for the guidance. Really grateful for all the suggestions you put up over here. I have been reading those for quite a long time. It really helped me.

Yes, I want to interpolate geometrically. Kindly explain the difference between geometric interpolation and interpolate geometrically. May I ask you to advise what interpolation would suit this kind of data.

My apologies for the incomplete example dataset shared above. Below is a subset of my data. I have incorporated ROA1, as suggested in the code above.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float firmid int year double(LTD ROA TA ROCE TobQ MCap ROE) byte UNGC double Sales long Employees double(RDexp RDtoNS NI) float ROA1
 1 2007      2940.7           21.9093     70643.5 36.8216 3.1326       192277.4892   38.9604 0           70509.4 10032    4690 6.6516   10996.5    21.9093
 1 2008      2760.2           14.1371     84925.7 25.0877 1.4931        90115.4254    24.473 0           77196.9  9557    50.9  .0659   10775.3    14.1371
 1 2009      5669.2             16.86    100591.5  28.128 2.0448       163794.0178   29.2478 1           84795.5  9557    36.2  .0427   10592.8      16.86
 1 2010      5239.6           10.2133    110413.4 16.4017 2.2601       201938.9049   17.7361 1           82587.7  9557    52.1  .0631   11618.2    10.2133
 1 2011      5107.3           11.3815    118167.1 18.6017 2.2157       213447.6952   19.6202 1          100123.3  9031      63  .0629    6582.9    11.3815
 1 2012       850.3            8.9222    119281.8  14.732 2.6362       268888.8989    14.762 1          113581.9  9769    82.4  .0725         .     8.9222
 1 2013           0            9.1111    121010.6 15.0517 2.0745       208162.6635    14.417 1          111694.2  9658    84.9   .076         .   9.111099
 1 2014           0            9.3761    126816.3 15.0517 2.4249       262871.6602   14.4946 1          117387.9  9071    94.1  .0802         .     9.3761
 1 2015           0             4.612    127999.6  8.6114 2.3379       255455.7186     7.063 1          117971.6  9071       0      0         .      4.612
 1 2016           0            5.0263    133939.4  9.4065 2.2082       249954.2364    7.6392 1          107677.9  9071       0      0         .     5.0263
 1 2017           0            6.5469    148457.4 12.2084  2.606       331974.0385   10.1755 1          129309.5  9071    76.4  .0591         .     6.5469
 2 2007           0                 .     98.1509       . 1.5258           102.912         . .             .4616     .       .      .   -2.0761  -44.94476
 2 2008           0          -25.5354     70.0807       . 1.7215           102.912  -41.4454 .            1.2044     .       .      .  -21.4793   -25.5354
 2 2009           0             .7166      53.116       . 1.9437           102.912     .8398 .            1.1511     .       .      .     .4414      .7166
 2 2010           0             .3636     180.156       .  .9235          165.5808     .3654 .             .3011     .       0      0     .4241      .3636
 2 2011           0             .5027    258.8283       . 1.2365           310.282     .5151 .                 0     .       0      0    1.1034  .50270003
 2 2012           0             .0176    275.2711       .  .3206           62.0564     .0188 .                 0     .       0      0     .0469      .0176
 2 2013           0            -.1053    260.4517       .  .1118           17.7304    -.1132 . 8.725999999999999     .       0      0     -.282     -.1053
 2 2014           0            -.1053    260.4517       .  .1118           17.7304    -.1132 .             5.288     .       0      0      .013     -.1053
 2 2015           0            -.1053    260.4517       .  .1118           17.7304    -.1132 .             41.47     .       0      0   -142.96     -.1053
 2 2016           0            -.1053    260.4517       .  .1118           31.0282    -.1132 .             52.79     .       0      0      -.08     -.1053
 2 2017           0            -.1053    260.4517       .  .1118           31.0282    -.1132 .             43.01     .       0      0      .014     -.1053
 3 2007      10.004           33.8518    465.4562       .  1.524               591   43.1313 .          469.1483     .       .      .  100.3555    33.8518
 3 2008   1010.2687           19.0516   2346.9248       . 1.2697           1467.69   44.3413 .          884.4656     .       .      .  129.3175    19.0516
 3 2009    175.8447           16.8488   2209.9873       .  .8335             823.6   37.8948 .         1343.4045     .       .      .  267.9025    16.8488
 3 2010    147.7703           21.6457   2988.0784       .  .9446           1722.93   36.5302 .         1642.8535     .       .      .  383.8914    21.6457
 3 2011     10.3209           19.1121   2948.4382       . 1.1242           2796.42   26.2712 .         1663.9978     .       .      .  562.5781    19.1121
 3 2012      7.6891            8.8615   5651.2766       .  .7056           1098.57   14.6763 .         1984.8565     .       .      .  567.2958     8.8615
 3 2013    297.7762             6.875   7720.4493       .  .7215           1025.31   15.4831 .         1936.4872     .       .      .  381.0303      6.875
 3 2014    388.8875            3.9905   9917.7022       .  .7306            807.84    10.576 .         2421.5968     .       .      .  459.6502     3.9905
 3 2015      532.88            3.6949   12352.521       .  .8138           1537.14   11.2452 .          2511.219     .       .      .  351.9239     3.6949
 3 2016   1625.5281            2.6911  18549.0359       . 1.6001           15338.4   10.3453 .         2450.0983     .       .      .    411.43     2.6911
 3 2017   3774.5995            2.6337  25059.6112       .  .9122           2577.96   12.7818 .         3389.4402     .       .      .  415.8017     2.6337
 4 2007    369.6177                 .   1889.1039       . 1.1492         1367.5475         . .          636.4473     .       .      .   25.4994 -2.1943245
 4 2008    431.3788           -1.0986   1871.4758       .  .7688          540.5023   -2.0067 .          696.4957     .       .      .  -20.6565    -1.0986
 4 2009    469.9482             .0094   1962.0696   -.206  .7122            386.21     .0188 .          803.0685     .       .      .     .1807      .0094
 4 2010    769.4461            1.4272   2463.7815  3.3286    .79          442.7519    3.3056 .         1017.3149     .       .      .   31.5833     1.4272
 4 2011    593.0573            1.4744    2801.694  6.1117  .7695          330.6264     4.009 .         1381.1403     .       .      .    38.816     1.4744
 4 2012    449.5191            2.2689    2604.807  8.1284  .7176          279.8345    6.1584 .         1820.0775     .       .      .   61.3347     2.2689
 4 2013    449.5191            2.2689    2604.807  8.1284  .7176             191.7    6.1584 .          1537.415     .       .      .     10.73     2.2689
 4 2014    449.5191            2.2689    2604.807  8.1284  .7176          245.3376    6.1584 .          1860.251     .       .      .    61.775     2.2689
 4 2015    449.5191            2.2689    2604.807  8.1284  .7176           399.632    6.1584 .           1675.99     .       .      .     53.66     2.2689
 4 2016    449.5191            2.2689    2604.807  8.1284  .7176          617.1774    6.1584 .           1670.97     .       .      .     26.89     2.2689
 4 2017           .                 .           .       .      .                 .         . .                 .     .       .      .         .     2.2689
 5 2007           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2008           .                 .           .       .      .                 .         . .                 .     .       .      .     7.871          .
 5 2009   1350.5845                 .   3110.1622       .      .                 .         . .         3188.0747     .       .      . -162.9895          .
 5 2010   1576.4669           -4.9066   3533.5715       .   .926            344.25    -23.63 .         3130.2221     .       .      .         .    -4.9066
 5 2011           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2012           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2013           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2014           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2015           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2016           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 5 2017           .                 .           .       .      .                 .         . .                 .     .       .      .         .          .
 6 2007     186.625           17.0897     807.961 37.7254      .                 .   53.6068 .          1330.014     .       .      .    33.224    17.0897
 6 2008     552.519           14.5174    2884.386 31.9318      .                 .    42.037 .          3136.709     .       .      .   105.563    14.5174
 6 2009   2223.2553           12.5609   5090.6198  25.439      .                 .   40.5352 .         6243.7523     .       0      0   268.016    12.5609
 6 2010   4469.8908           12.1997    9675.804 21.4819 2.0745        13776.0018   37.0429 .        10065.5043     .       0      0  500.8651    12.1997
 6 2011     2709.61            8.3066   17330.418 23.8861 1.1939 7843.904900000001   28.5272 .         12490.111     .       0      0  900.7323     8.3066
 6 2012    2888.968           -1.6337   18919.874 23.8861  .8637          1608.264   -6.8289 .         11827.399     .       0      0  1121.652    -1.6337
 6 2013   6590.2125           -3.2685  20601.2891 23.8861   .849          431.1958  -16.7105 .         7709.8335     .       0      0  -296.104    -3.2685
 6 2014   7335.6309             .0773  22546.7167 23.8861  .8562           316.903     .4698 .         9014.1867     .       0      0 -645.8654      .0773
 6 2015   7020.1995             .2734  22954.3563 23.8861  .8646          513.5758    1.7328 .         6555.2699     .       0      0   16.6817      .2734
 6 2016   7323.6049             .2135  24041.6188 55.2724  .8677          490.5688    1.3761 .          6233.003     .       0      0   62.2039      .2135
 6 2017   6583.5219          -15.5506  18480.8192 55.2724  1.035         1011.5661 -163.8359 .         8503.6138     .       0      0   50.1725   -15.5506
 7 2007   1433.4976            3.5301   7175.4658 12.0067  .8568         1711.0215    9.4908 0         7638.8525     .   13.78  .1719  553.2128     3.5301
 7 2008   1690.6519            5.0768   9435.3135 15.7953  .9183         2271.6541   14.5885 0         8988.7715     .   13.78  .1719  249.9735     5.0768
 7 2009   4435.8189            9.3108  10887.7399 26.0305  .8454         2064.1472   27.8686 0        14612.5938     .   15.57  .1066  421.6511     9.3108
 7 2010    4384.886            7.1368     12189.4 13.7067  .9274         3659.5475   19.8623 0         13012.224     .  50.065  .3848  946.1162     7.1368
 7 2011    1362.356 6.227700000000001   13977.883 16.6953  .9051         3763.1196   16.9155 0         14257.145     .  46.409  .3255   823.482     6.2277
 7 2012    1036.958            6.7545    16598.25 26.8119  .9329         4786.7644    18.791 0         16322.597     .  36.092  .2211   814.813     6.7545
 7 2013    1174.714            7.0084   21759.858 30.3066  .9453         6373.1219   19.9668 0         20576.431     . 100.859  .4902  1032.631   7.008399
 7 2014    2625.706            6.7038   26701.309 28.7835 1.0815        10883.4887   19.9675 0         25983.969     . 232.428  .8945  1344.136     6.7038
 7 2015    4192.476            7.3423   29378.235 26.7135 1.7119        31077.9638   21.8186 0         28614.419     . 135.884  .4749  1624.373     7.3423
 7 2016      5269.4            8.7014     29664.8 23.6931 2.0644        42947.4914   23.8547 0           29562.1  3254   160.1  .5416   2058.77     8.7014
 7 2017      5968.9            9.7681     34990.5 22.8577 2.4073        62867.2592   25.2647 0           31146.3  3862   216.3  .6945    2568.8     9.7681
 8 2007 108351.3347            -.1857 121520.1325 -1.7557 1.5963        74708.2652   -8.7766 0         7186.7506   830       .      .  822.6213     -.1857
 8 2008  130433.993              .917 146727.5216 -1.7557 1.7422       113962.8201   25.3233 0        40939.1998   700       .      . -128.7409       .917
 8 2009 166354.6769            3.1332 198407.8058 10.2483 1.0044         15047.974   52.8925 0        30500.9125   541       0      0 1229.8754     3.1332
 8 2010 140353.8878            1.6737  173224.729   6.249 1.1849        50574.1511    17.012 0        33586.5716   541       0      0 5406.9342     1.6737
 8 2011     97128.6             .8679   160773.39  4.1316 1.0543        26813.0375    6.1452 0          33472.23  1604       0      0 3110.0324      .8679
 8 2012   111443.71            1.9226   173684.71 14.6512  .9599        18837.6545    13.317 0          31629.21  1491       0      0   1449.45     1.9226
 8 2013   113613.63            1.0905   181885.16 10.3447   .898         11477.938    5.7919 0          36727.01  1494       0      0   3215.19     1.0905
 8 2014   110508.32             2.056   200473.93 14.1295  .9217         23146.112   10.4585 0          39362.55  1415       0      0   1938.73      2.056
 8 2015   130877.51             2.657   209725.74 13.4244   .859         24628.864   11.0301 0          40408.38  1792       0      0   3930.65      2.657
 8 2016   132141.89             -1.17    202290.8 13.4244  .8683         10297.622   -5.2894 0          33345.53  1106       0      0   5449.42      -1.17
 8 2017    118272.1           -5.3435   187277.05 13.4244  .9294         13139.754   -32.892 0           17579.2   633       0      0  -2410.22    -5.3435
 9 2007     40664.4            2.8132     79101.5 12.2554 1.5091        51774.5891   17.2816 0          152370.1   610       .      .    1345.8     2.8132
 9 2008     61041.2            3.6381    124161.2 10.8354 2.0194       147818.2389   22.5767 0          196097.1   610       .      .    1730.8     3.6381
 9 2009    120842.4            3.0985    201577.4   7.949 1.1777        66004.9457   19.6214 0          262582.8   505       0      0    3697.5     3.0985
 9 2010    174388.5            3.6293    305026.2  6.7691  1.569       233923.0705   20.3012 0          258898.7   391       0      0    5046.5     3.6293
 9 2011    242524.8            5.2643    635677.7  9.6102 1.8744       733078.4108   20.8388 0          196312.9   478       0      0      9193     5.2643
 9 2012      488943            2.1569   1069740.2  5.2693 1.1314       335277.1038    9.8886 0          311646.6   597       0      0   24760.9     2.1569
 9 2013    488501.3            1.4715     1122585  4.2545 1.0069       222381.5988    7.8816 0          367296.5   597       0      0   18392.1     1.4715
 9 2014    495842.3            1.9268   1182537.4  4.2545 1.1414       404730.1105     9.823 0          550668.8   597       0      0   16129.8     1.9268
 9 2015    554867.6             1.564   1308585.7 10.3397 1.3206       676768.1346    7.8733 0          643979.2   597       0      0   22207.7      1.564
 9 2016     70090.4            1.1711    417560.9   4.511   .874        81165.9841    5.1692 0          337862.8   597       0      0   19480.5     1.1711
 9 2017     91733.2            2.2086    476894.1 10.2142  .9539       119384.3845      7.18 0          365227.1  1518       0      0   10107.2     2.2086
10 2007   20680.187            4.7196   58969.946  7.2475 4.4886       231892.8671   12.5066 0           8170.23   665       .      .    1918.8     4.7196
end

.
Thanks!!

[Clyde Schechter]

There is no difference between "geometric interpolation" and "interpolate geometrically." Just different syntaxes (of English) for saying the same thing.

You need somebody with expertise in finance to advise you on whether any kind of interpolation is appropriate for this kind of data, and if so, what kind. This is not in my area of expertise. There are numerous people in finance and econometrics who are part of this Forum and perhaps one will join the thread.

[Anita Mendi]

Thanks Clyde !! Looking forward to it ))