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# r example
# y <- rpois(20,lambda=.3)
# fcast <- croston(y)
#> y
# [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
# r result :
# > fcast
# Point Forecast
# 21 0.180018
# > fcast$fitted
# Time Series:
# Start = 1
# End = 20
# Frequency = 1
# [1] NA 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.1666667
# [8] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
# [15] 0.1666667 0.1666667 0.1666667 0.1538462 0.1680672 0.1680672
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import pandas as pd
%matplotlib inline
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lCounts = "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0".split()
lCounts = [float(c) for c in lCounts]
N = len(lCounts)
lDates = pd.date_range(start="2000-01-01", periods=N, freq='m')
df = pd.DataFrame({"Date" : lDates, "Count" : lCounts})
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df.transpose()
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# q is often called the “demand” and a the “inter-arrival time”.
q = df[abs(df['Count']) > 0.0]['Count']
demand_times = pd.Series(list(q.index)) + 1
a = demand_times - demand_times.shift(1).fillna(0.0)
df2 = pd.DataFrame({'demand_time' : list(demand_times), 'q' : list(q) , 'a' : list(a) })
df2
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def get_coeff(alpha , croston_type):
if(croston_type == "sba"):
return 1.0-(alpha/2.0)
elif(croston_type == "sbj"):
return (1.0 - alpha/(2.0-alpha))
# default
return 1.0
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# q and a forecast
alpha = 0.3
df2['q_est'] = None
df2['a_est'] = None
df2.loc[0 , 'q_est'] = df2['q'][0]
df2.loc[0, 'a_est'] = df2['a'][0]
for i in range(df2.shape[0] - 1):
q1 = (1.0 - alpha) * df2['q_est'][ i ] + alpha * df2['q'][ i ]
a1 = (1.0 - alpha) * df2['a_est'][ i ] + alpha * df2['a'][ i ]
df2.loc[i + 1, 'q_est'] = q1
df2.loc[i + 1, 'a_est'] = a1
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df2['forecast'] = get_coeff(alpha , "default") * df2['q_est'] / df2['a_est']
df2
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forecast_11 = df2['q_est'][df2.shape[0] - 1] / df2['a_est'][df2.shape[0] - 1]
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forecast_11
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df2['index'] = df2['demand_time'] - 1
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df1 = df.reset_index()
df3 = df1.merge(df2 , how='left', on=('index' , 'index'))
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df3
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df4 = df3.fillna(method='ffill')
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df4
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df4.plot('Date', ['Count' , 'forecast'])
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