Here's a problem I can't quite figure out:
I'm auto-correlating some data with itself to find the periodicity. I slide the data over itself and compute the differencves.
So I end up with an array with values like these:
(0, 423179422, 828300948, 1212609754, 1580431328, 1927976212, 2261045098, 2576547366, 2880291562, 3170884920, 3448407680, 3712453192, 3963129656, 4202858738, 4428796224, 4642141464, 4838897098, 5022294960, 5189647866, 5336120170, 5468966802, 5573601410, 5661172944, 5722015070, 5764204226, 5784805298, 5795386094, 5794255268, 5783184466, 5761355708, 5725745692, 5678340672, 5612707394, 5527855798, 5421991904, 5296806718, 5153282668, 4992479880, 4816736914, 4627262472, 4424397458, 4211164230, 3987799654, 3757131960, 3516443192, 3266828654, 3006790876, 2731835909, 2460333151, 2202466559, 1938545198, 1667642709, 1389832004, 1109712475, 824855728, 588591149, 546361448, 811857393, 1161263940, 1500909693, 1830265354, 2141064765, 2442071178, 2727283919, 3004764138, 3268936897, 3523042222, 3765280899, 3994320860, 4213529495, 4419602464, 4616188975, 4796605032, 4965570485, 5121258994, 5255613245, 5377713032, 5469986089, 5551080124, 5603396265, 5641398544, 5658406913, 5668274054, 5665748491, 19636457355401828, 5047136332677536, 14, 0, 94816986516684800, 2105652297, 60130717272, 94816986516684801, 4785076709733484, 94818019412627324, 9034993454800879124, 4785074604081690, 205958216012529665, 201399947, 47953384, 31244160501548260, 13511005043490927)
In case you're not good at reading number without commans, here's the interesting part:
54: 824,855,728
55: 588,591,149
56: 546,361,448
57: 811,857,393
The values hit a minimum at element 56.
Now that's swell, but if you notice the value at 56 is a heck of a lot closer to #55 than to #57. If we assume a kinda normal and continuous function goes through these points, it sure would be nice to estimate the actual minimum.
I'd like to make an educated guess as to where the actual minimum is, but I can't figure out the math! Dang.
Any formulas appreciated.
Hi grg99,
Have you tried a very primitive straight-line approach? The numbers would appear to be from a curve, but that's more math than I can take on this morning.
Take the values to the left of #56 and plot their general slope. Take the values to the right and do the same. Where the lines intersect is the approximate minimum.
Disregard smoothing and start with points 54,55. They're defined as (54, 824,855,728) and (55, 588,591,149).
Define points at 57,58 as (57, 811,857,393) and (58, 1,161,263,940).
Where the lines intersect is your target. I'd then refine the process by varying the "outer" points (53, 55) & (57, 59), (52, 55) & (57, 60) to guage the curve.
Kent