147 lines
3.5 KiB
Python
147 lines
3.5 KiB
Python
# -*- coding: utf8 -*-
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import numpy as np
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import pandas as pd
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# Autocorrelation function estimative
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def acf(data, k):
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mu = np.mean(data)
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sigma = np.var(data)
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n = len(data)
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s = 0
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for t in np.arange(0,n-k):
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s += (data[t]-mu) * (data[t+k] - mu)
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return 1/((n-k)*sigma)*s
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# Erro quadrático médio
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def rmse(targets, forecasts):
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return np.sqrt(np.nanmean((targets - forecasts) ** 2))
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def rmse_interval(targets, forecasts):
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fmean = [np.mean(i) for i in forecasts]
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return np.sqrt(np.nanmean((fmean - targets) ** 2))
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# Erro Percentual médio
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def mape(targets, forecasts):
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return np.mean(np.abs(targets - forecasts) / targets) * 100
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def smape(targets, forecasts, type=2):
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if type == 1:
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return np.mean(np.abs(forecasts - targets) / ((forecasts + targets)/2))
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elif type == 2:
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return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets)) )*100
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else:
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return sum(np.abs(forecasts - targets)) / sum(forecasts + targets)
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def mape_interval(targets, forecasts):
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fmean = [np.mean(i) for i in forecasts]
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return np.mean(abs(fmean - targets) / fmean) * 100
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# Theil's U Statistic
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def UStatistic(targets, forecasts):
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l = len(targets)
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naive = []
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y = []
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for k in np.arange(0,l-1):
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y.append((forecasts[k ] - targets[k ]) ** 2)
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naive.append((targets[k + 1] - targets[k]) ** 2)
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return np.sqrt(sum(y) / sum(naive))
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# Theil’s Inequality Coefficient
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def TheilsInequality(targets, forecasts):
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res = targets - forecasts
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t = len(res)
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us = np.sqrt(sum([u**2 for u in res]))
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ys = np.sqrt(sum([y**2 for y in targets]))
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fs = np.sqrt(sum([f**2 for f in forecasts]))
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return us / (ys + fs)
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# Q Statistic for Box-Pierce test
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def BoxPierceStatistic(data, h):
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n = len(data)
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s = 0
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for k in np.arange(1,h+1):
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r = acf(data, k)
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s += r**2
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return n*s
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# Q Statistic for Ljung–Box test
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def BoxLjungStatistic(data, h):
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n = len(data)
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s = 0
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for k in np.arange(1,h+1):
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r = acf(data, k)
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s += r**2 / (n -k)
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return n*(n-2)*s
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# Sharpness - Mean size of the intervals
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def sharpness(forecasts):
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tmp = [i[1] - i[0] for i in forecasts]
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return np.mean(tmp)
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# Resolution - Standard deviation of the intervals
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def resolution(forecasts):
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shp = sharpness(forecasts)
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tmp = [abs((i[1] - i[0]) - shp) for i in forecasts]
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return np.mean(tmp)
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# Percent of
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def coverage(targets, forecasts):
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preds = []
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for i in np.arange(0, len(forecasts)):
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if targets[i] >= forecasts[i][0] and targets[i] <= forecasts[i][1]:
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preds.append(1)
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else:
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preds.append(0)
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return np.mean(preds)
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def pmf_to_cdf(density):
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ret = []
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for row in density.index:
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tmp = []
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prev = 0
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for col in density.columns:
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prev += density[col][row]
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tmp.append( prev )
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ret.append(tmp)
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df = pd.DataFrame(ret, columns=density.columns)
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return df
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def heavyside_cdf(bins, targets):
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ret = []
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for t in targets:
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result = [1 if b >= t else 0 for b in bins]
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ret.append(result)
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df = pd.DataFrame(ret, columns=bins)
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return df
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# Continuous Ranked Probability Score
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def crps(targets, densities):
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l = len(densities.columns)
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n = len(densities.index)
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Ff = pmf_to_cdf(densities)
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Fa = heavyside_cdf(densities.columns, targets)
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_crps = float(0.0)
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for k in densities.index:
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_crps += sum([ (Ff[col][k]-Fa[col][k])**2 for col in densities.columns])
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return _crps / float(l * n)
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