research/price_analysis/fit.py

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Python
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import spread
import math
import random
o = spread.declutter(spread.load('diff_txs_price.csv'))
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diffs = [float(q[2]) for q in o]
prices = [float(q[1]) for q in o]
txs = [float(q[3]) for q in o]
txfees = [float(q[4]) for q in o]
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def simple_estimator(fac):
o = [1]
for i in range(1, len(diffs)):
o.append(o[-1] * diffs[i] * 1.0 / diffs[i-1] / fac)
return o
def minimax_estimator(fac):
o = [1]
for i in range(1, len(diffs)):
if diffs[i] * 1.0 / diffs[i-1] > fac:
o.append(o[-1] * diffs[i] * 1.0 / diffs[i-1] / fac)
elif diffs[i] > diffs[i-1]:
o.append(o[-1])
else:
o.append(o[-1] * diffs[i] * 1.0 / diffs[i-1])
return o
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def diff_estimator(fac, dw, mf, exp=1):
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o = [1]
derivs = [0] * 14
for i in range(14, len(diffs)):
derivs.append(diffs[i] - diffs[i - 14])
for i in range(0, 14):
derivs[i] = derivs[14]
vals = [max(diffs[i] + derivs[i] * dw, diffs[i] * mf) for i in range(len(diffs))]
for i in range(1, len(diffs)):
if vals[i] * 1.0 / vals[i-1] > fac:
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o.append(o[-1] * 1.0 / fac * (vals[i] / vals[i-1])**exp)
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elif vals[i] > vals[i-1]:
o.append(o[-1])
else:
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o.append(o[-1] * 1.0 * (vals[i] / vals[i-1])**exp)
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return o
def tx_diff_estimator(fac, dw, mf, lin=1, exp=1):
fac = (fac - 1) or 0.000001
o = [1]
initavg = sum([txs[i] for i in range(5)]) / 5.0
txavgs = [initavg] * 5
for i in range(5, len(txs)):
txavgs.append(txavgs[-1] * 0.8 + txs[i] * 0.2)
derivs = [0] * 14
for i in range(14, len(txavgs)):
derivs.append(txavgs[i] - txavgs[i - 14])
for i in range(0, 14):
derivs[i] = derivs[14]
vals = [max(txavgs[i] + derivs[i] * dw, txavgs[i] * mf) for i in range(len(txavgs))]
for i in range(1, len(txavgs)):
growth = (vals[i] * 1.0 / vals[i-1] - 1)
if growth > fac:
surplus = (growth / fac) - 1
o.append(o[-1] * (1 + (surplus * lin * fac) ** exp))
elif vals[i] > vals[i-1]:
o.append(o[-1])
else:
surplus = 1 - growth
o.append(o[-1] * (1 - (surplus * lin * fac) ** exp))
if i and o[-1] < o[-2] * mf:
o[-1] = o[-2] * mf
return o
def minimax_fee_estimator(fac, days):
o = [1]
initavg = sum([txs[i] for i in range(int(days))]) * 1.0 / days
txavgs = [initavg] * int(days)
for i in range(int(days), len(txs)):
txavgs.append(txavgs[-1] * 1.0 * (days-1) / days + txs[i] * 1.0 / days)
initavg2 = sum([txfees[i] for i in range(int(days))]) * 1.0 / days
txfeeavgs = [initavg2] * int(days)
for i in range(int(days), len(txs)):
txfeeavgs.append(txfeeavgs[-1] * 1.0 * (days-1) / days + txfees[i] * 1.0 / days)
# Calculate inverse fee, invfee ~= price
txavgfees = [t / f for f, t in zip(txfeeavgs, txavgs)]
for i in range(1, len(txavgfees)):
if txavgfees[i] * 1.0 / txavgfees[i-1] > fac:
o.append(o[-1] * txavgfees[i] * 1.0 / txavgfees[i-1] / fac)
elif txavgfees[i] > txavgfees[i-1]:
o.append(o[-1])
else:
o.append(o[-1] * txavgfees[i] * 1.0 / txavgfees[i-1])
return o
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def ndiff_estimator(*args):
fac, dws, mf = args[0], args[1:-1], args[-1]
o = [1]
ds = [diffs]
for dw in dws:
derivs = [0] * 14
for i in range(14, len(diffs)):
derivs.append(ds[-1][i] - ds[-1][i - 14])
for i in range(0, 14):
derivs[i] = derivs[14]
ds.append(derivs)
vals = []
for i in range(len(diffs)):
q = ds[0][i] + sum([ds[j+1][i] * dws[j] for j in range(len(dws))])
vals.append(max(q, ds[0][i] * mf))
for i in range(1, len(diffs)):
if vals[i] * 1.0 / vals[i-1] > fac:
o.append(o[-1] * vals[i] * 1.0 / vals[i-1] / fac)
elif vals[i] > vals[i-1]:
o.append(o[-1])
else:
o.append(o[-1] * vals[i] * 1.0 / vals[i-1])
return o
def dual_threshold_estimator(fac1, fac2, dmul):
o = [1]
derivs = [0] * 14
for i in range(14, len(diffs)):
derivs.append(diffs[i] - diffs[i - 14])
for i in range(0, 14):
derivs[i] = derivs[14]
for i in range(1, len(diffs)):
if diffs[i] * 1.0 / diffs[i-1] > fac1 and derivs[i] * 1.0 / derivs[i-1] > fac2:
o.append(o[-1] * diffs[i] * 1.0 / diffs[i-1] / fac1 * (1 + (derivs[i] / derivs[i-1] - fac2) * dmul))
elif diffs[i] > diffs[i-1]:
o.append(o[-1])
else:
o.append(o[-1] * diffs[i] * 1.0 / diffs[i-1])
return o
infinity = 2.**1023
infinity *= 2
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def evaluate_estimates(estimates, crossvalidate=False):
sz = len(prices) if crossvalidate else 780
sqdiffsum = 0
# compute average
tot = 0
for i in range(sz):
if estimates[i] == infinity or estimates[i] <= 0:
return 10**20
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tot += math.log(prices[i] / estimates[i])
avg = 2.718281828459 ** (tot * 1.0 / sz)
if avg <= 0:
return 10**20
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for i in range(1, sz):
sqdiffsum += math.log(prices[i] / estimates[i] / avg) ** 2
return sqdiffsum
# Simulated annealing optimizer
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def optimize(producer, floors, ceilings, rate=0.7, rounds=5000, tries=1):
bestvals, besty = None, 10**21
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for t in range(tries):
print 'Starting test %d of %d' % (t + 1, tries)
vals = [f*0.5+c*0.5 for f, c in zip(floors, ceilings)]
y = evaluate_estimates(producer(*vals))
for i in range(1, rounds):
stepsizes = [(f*0.5-c*0.5) / i**rate for f, c in zip(floors, ceilings)]
steps = [(random.random() * 2 - 1) * s for s in stepsizes]
newvals = [max(mi, min(ma, v+s)) for v, s, mi, ma in zip(vals, steps, floors, ceilings)]
newy = evaluate_estimates(producer(*newvals))
if newy < y:
vals = newvals
y = newy
if not i % 1000:
print i, vals, y
if y < besty:
bestvals, besty = vals, y
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return bestvals
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def score(producer, *vals):
return evaluate_estimates(producer(*vals), True)