Process indicators

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>Model

ID:(67, 0)

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Interpolation

Description

>Top

To interpolate it fits around the points to calculate a polynomial with the points that exist.

The process can be done using the panta library:

import pandas as pd
import numpy as np

year = []
value = []

for i in range(dmin,dmax + 1):
    if i > dmin:
        nmin = int(df.date[i-1])
        nmax = int(df.date[i])
        for n in range(nmin + 1,nmax):
            year.append(n)
            value.append(np.nan)

    ndate = int(df.date[i])
    year.append(ndate)
    if df.value[i] == '':
        value.append(np.nan)
    else:
        val = float(df.value[i])
        if val > 99.9:
            val = 99.9
        elif val < 0.01:
            val = 0.01
        val = (val - 50)/50
        val = math.atanh(val)
        value.append(val)

        
servalue = pd.Series(value)
inpvalue = servalue.interpolate(method="polynomial", order=3)

ID:(318, 0)

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Extrapolation

Description

>Top

To extrapolate, the function is scaled and proceeds to calculate the Fourier transform to then use the representation of the oscillation to estimate the future development.

The process can be done using the panta library:

import pandas as pd
import numpy as np
from numpy import fft

def fourierExtrapolation(x, n_predict):

    n = x.size
    n_harm = 10                     # number of harmonics in model
    t = np.arange(0, n)
    p = np.polyfit(t, x, 1)         # find linear trend in x
    x_notrend = x - p[0] * t        # detrended x
    x_freqdom = fft.fft(x_notrend)  # detrended x in frequency domain
    f = fft.fftfreq(n)              # frequencies
    indexes = list(range(n))
 
    t = np.arange(0, n + n_predict)
    restored_sig = np.zeros(t.size)
    for i in indexes[:1 + n_harm * 2]:
        ampli = np.absolute(x_freqdom[i]) / n   # amplitude
        phase = np.angle(x_freqdom[i])          # phase
        restored_sig += ampli * np.cos(2 * np.pi * f[i] * t + phase)
        
    return restored_sig + p[0] * t

x = np.array(inpvalue)
z = (x - 50)/50
z = np.arctanh(z)
extrapolation = fourierExtrapolation(z, num)
extrapolation = 50*np.tanh(extrapolation) + 50

for i in range(len(extrapolation)):
    if i < len(value):
        print(year[i],value[i],inpvalue[i],extrapolation[i])
    else:
        print(year[0]+i,'-','-',extrapolation[i])

ID:(319, 0)

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