The Federal Bureau of Investigation (FBI) operates the National Instant Background Check System (NICS)  to determine whether a prospective buyer is eligible to buy firearms. Before ringing up a sale, cashiers call in to the NICS to ensure that each customer does not have a criminal record or is not otherwise ineligible to make a purchase.

The number of FBI background checks is widely considered to be the most reliable gauge of how many firearms were sold in a given month because background checks are required on all sales made through federally licensed firearms dealers. The monthly number of checks (in thousands) is displayed below for the period January 1999 through May 2016. There are 209 data points. (Source: https://www.fbi.gov/about-us/cjis/nics)
 

591.355 696.323 753.083 646.712 576.272 569.493 589.476 703.394 808.627 945.701 1004.333 1253.354
639.972 707.07 736.543 617.689 538.648 550.561 542.52 682.501 782.087 845.886 898.598 1000.962
640.528 675.156 729.532 594.723 543.501 540.491 539.498 707.288 864.038 1029.691 983.186 1062.559
665.803 694.668 714.665 627.745 569.247 518.351 535.594 693.139 724.123 849.281 887.647 974.059
653.751 708.281 736.864 622.832 567.436 529.334 533.289 683.517 738.371 856.863 842.932 1008.118
695 723.654 738.298 642.589 542.456 546.847 561.773 666.598 740.26 865.741 890.754 1073.701
685.811 743.07 768.29 658.954 557.058 555.56 561.358 687.012 791.353 852.478 927.419 1164.582
775.518 820.679 845.219 700.373 626.27 616.097 631.156 833.07 919.487 970.03 1045.194 1253.84
894.608 914.954 975.806 840.271 803.051 792.943 757.884 917.358 944.889 1025.123 1079.923 1230.525
942.556 1021.13 1040.863 940.961 886.183 819.891 891.224 956.872 973.003 1183.279 1529.635 1523.426
1213.885 1259.078 1345.096 1225.98 1023.102 968.145 966.162 1074.757 1093.23 1233.982 1223.252 1407.155
1119.229 1243.211 1300.1 1233.761 1016.876 1005.876 1069.792 1089.374 1145.798 1368.184 1296.223 1521.192
1323.336 1473.513 1449.724 1351.255 1230.953 1168.322 1570.411 1310.041 1253.752 1340.273 1534.414 1862.327
1377.301 1749.903 1727.881 1427.343 1316.226 1302.66 1300.704 1526.206 1459.363 1614.032 2006.919 2783.765
2495.44 2309.393 2209.407 1714.433 1435.917 1281.351 1283.912 1419.088 1401.562 1687.599 1813.643 2041.528
1660.355 2086.863 2488.842 1742.946 1485.259 1382.975 1402.228 1546.497 1456.032 1603.469 1803.397 2309.684
1772.794 1859.584 2012.488 1711.34 1580.98 1529.057 1600.832 1745.41 1795.102 1976.759 2243.03 3314.594
2545.802 2613.074 2523.265 2145.865 1870