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Python Prediction / Extrapolation of Future Data Based on a Dataset

I am very new to Python. I have a dataset and am trying to use numPy / sciPy to predict / extrapolate future data points. Is there an easy way to come up with a math function (say, a Sine function) that matches my current data, and then I can pass new values ​​to this function to get my prediction?

Here is what I have, but I don’t think he is doing what I want:

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def main():

    y = [8.3, 8.3, 8.3, 8.3, 7.2, 7.8, 7.8, 8.3, 9.4, 10.6, 10.0, 10.6, 11.1, 12.8,
         12.8, 12.8, 11.7, 10.6, 10.6, 10.0, 10.0, 8.9, 8.9, 8.3, 7.2, 6.7, 6.7, 6.7,
         7.2, 8.3, 7.2, 10.6, 11.1, 11.7, 12.8, 13.3, 15.0, 15.6, 13.3, 15.0, 13.3,
         11.7, 11.1, 10.0, 10.6, 9.4, 8.9, 8.3, 8.9, 6.7, 6.7, 6.0, 6.1, 8.3, 8.3,
         10.6, 11.1, 11.1, 11.7, 12.2, 13.3, 14.4, 16.7, 14.4, 13.3, 12.2, 11.7,
         11.1, 10.0, 8.3, 7.8, 7.2, 8.0, 6.7, 7.2, 7.2, 7.8, 10.0, 12.2, 12.8,
         12.8, 13.9, 15.0, 16.7, 16.7, 16.7, 15.6, 13.9, 12.8, 12.2, 10.6, 9.0,
         8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 10.0, 10.6, 11.1, 12.0, 11.7,
         11.1, 13.0, 13.3, 13.0, 11.1, 10.6, 10.6, 10.0, 10.0, 10.0, 9.4, 9.4,
         8.9, 8.3, 9.0, 8.9, 9.4, 9.0, 9.4, 10.6, 11.7, 11.1, 11.7, 12.8, 12.8,
         12.8, 13.0, 11.7, 10.6, 10.0, 10.0, 8.9, 9.4, 7.8, 7.8, 8.3, 7.8, 8.9,
         8.9, 8.9, 9.4, 10.0, 10.0, 10.6, 11.0, 11.1, 11.1, 12.2, 10.6, 10.0, 8.9,
         8.9, 9.0, 8.9, 8.3, 8.9, 8.9, 9.4, 9.4, 9.4, 8.9, 8.9, 8.9, 9.4, 10.0,
         11.1, 11.7, 11.7, 11.7, 11.7, 12.0, 11.7, 11.7, 12.0, 11.7, 11.0, 10.6,
         9.4, 10.0, 8.3, 8.0, 7.2, 5.6, 6.1, 5.6, 6.1, 6.7, 8.0, 10.0, 10.6, 11.1,
         13.3, 12.8, 12.8, 12.2, 11.1, 10.0, 10.0, 10.0, 10.0, 9.4, 8.3]    
    x = np.array(np.arange(len(y)))        

    fitting_parameters, covariance = curve_fit(fit, x, y)
    a = fitting_parameters[0]
    b = fitting_parameters[1]
    c = fitting_parameters[2]
    d = fitting_parameters[3]

    for x_predict in range(len(y) + 1, len(y) + 24):
        next_x = x_predict
        next_y = fit(next_x, a, b, c, d)

        print("next_x: " + str(next_x))
        print("next_y: " + str(next_y))
        y.append(next_y)

    plt.plot(y)
    plt.show()

def fit(x, a, b, c, d):
    return a*np.sin(b*x + c) + d

I tried curve_fit and univariatespline my data, but it only matches my current data and smooths my points, respectively. I want to say that these tools only “fit” my data, but they really do not give me a function that I can use to get future points.

, Discrete Fourier Transforms, , Sines Cosines. , , "", :

import numpy as np
import matplotlib.pyplot as plt

mydata = [8.3, 8.3, 8.3, 8.3, 7.2, 7.8, 7.8, 8.3, 9.4, 10.6, 10.0, 10.6, 11.1, 12.8,
         12.8, 12.8, 11.7, 10.6, 10.6, 10.0, 10.0, 8.9, 8.9, 8.3, 7.2, 6.7, 6.7, 6.7,
         7.2, 8.3, 7.2, 10.6, 11.1, 11.7, 12.8, 13.3, 15.0, 15.6, 13.3, 15.0, 13.3,
         11.7, 11.1, 10.0, 10.6, 9.4, 8.9, 8.3, 8.9, 6.7, 6.7, 6.0, 6.1, 8.3, 8.3,
         10.6, 11.1, 11.1, 11.7, 12.2, 13.3, 14.4, 16.7, 14.4, 13.3, 12.2, 11.7,
         11.1, 10.0, 8.3, 7.8, 7.2, 8.0, 6.7, 7.2, 7.2, 7.8, 10.0, 12.2, 12.8,
         12.8, 13.9, 15.0, 16.7, 16.7, 16.7, 15.6, 13.9, 12.8, 12.2, 10.6, 9.0,
         8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 10.0, 10.6, 11.1, 12.0, 11.7,
         11.1, 13.0, 13.3, 13.0, 11.1, 10.6, 10.6, 10.0, 10.0, 10.0, 9.4, 9.4,
         8.9, 8.3, 9.0, 8.9, 9.4, 9.0, 9.4, 10.6, 11.7, 11.1, 11.7, 12.8, 12.8,
         12.8, 13.0, 11.7, 10.6, 10.0, 10.0, 8.9, 9.4, 7.8, 7.8, 8.3, 7.8, 8.9,
         8.9, 8.9, 9.4, 10.0, 10.0, 10.6, 11.0, 11.1, 11.1, 12.2, 10.6, 10.0, 8.9,
         8.9, 9.0, 8.9, 8.3, 8.9, 8.9, 9.4, 9.4, 9.4, 8.9, 8.9, 8.9, 9.4, 10.0,
         11.1, 11.7, 11.7, 11.7, 11.7, 12.0, 11.7, 11.7, 12.0, 11.7, 11.0, 10.6,
         9.4, 10.0, 8.3, 8.0, 7.2, 5.6, 6.1, 5.6, 6.1, 6.7, 8.0, 10.0, 10.6, 11.1,
         13.3, 12.8, 12.8, 12.2, 11.1, 10.0, 10.0, 10.0, 10.0, 9.4, 8.3] 

sp = np.fft.rfft(mydata)
freq = np.fft.rfftfreq(len(mydata), d= 1.0)

plt.subplot(211)
plt.plot(mydata)
plt.subplot(212)
plt.plot(freq, sp, 'r')
plt.show()

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import numpy as np
import matplotlib.pyplot as plt
import scipy.fftpack as fftpack

def fft_inverse(Yhat, x):
    """Based on http://stackoverflow.com/a/4452499/190597 (mtrw)"""
    Yhat = np.asarray(Yhat)
    x = np.asarray(x).reshape(-1, 1)
    N = len(Yhat)
    k = np.arange(N)
    total = Yhat * np.exp(1j * x * k * 2 * np.pi / N)
    return np.real(total.sum(axis=1))/N

mydata = [8.3, 8.3, 8.3, 8.3, 7.2, 7.8, 7.8, 8.3, 9.4, 10.6, 10.0, 10.6, 11.1, 12.8,
         12.8, 12.8, 11.7, 10.6, 10.6, 10.0, 10.0, 8.9, 8.9, 8.3, 7.2, 6.7, 6.7, 6.7,
         7.2, 8.3, 7.2, 10.6, 11.1, 11.7, 12.8, 13.3, 15.0, 15.6, 13.3, 15.0, 13.3,
         11.7, 11.1, 10.0, 10.6, 9.4, 8.9, 8.3, 8.9, 6.7, 6.7, 6.0, 6.1, 8.3, 8.3,
         10.6, 11.1, 11.1, 11.7, 12.2, 13.3, 14.4, 16.7, 14.4, 13.3, 12.2, 11.7,
         11.1, 10.0, 8.3, 7.8, 7.2, 8.0, 6.7, 7.2, 7.2, 7.8, 10.0, 12.2, 12.8,
         12.8, 13.9, 15.0, 16.7, 16.7, 16.7, 15.6, 13.9, 12.8, 12.2, 10.6, 9.0,
         8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 10.0, 10.6, 11.1, 12.0, 11.7,
         11.1, 13.0, 13.3, 13.0, 11.1, 10.6, 10.6, 10.0, 10.0, 10.0, 9.4, 9.4,
         8.9, 8.3, 9.0, 8.9, 9.4, 9.0, 9.4, 10.6, 11.7, 11.1, 11.7, 12.8, 12.8,
         12.8, 13.0, 11.7, 10.6, 10.0, 10.0, 8.9, 9.4, 7.8, 7.8, 8.3, 7.8, 8.9,
         8.9, 8.9, 9.4, 10.0, 10.0, 10.6, 11.0, 11.1, 11.1, 12.2, 10.6, 10.0, 8.9,
         8.9, 9.0, 8.9, 8.3, 8.9, 8.9, 9.4, 9.4, 9.4, 8.9, 8.9, 8.9, 9.4, 10.0,
         11.1, 11.7, 11.7, 11.7, 11.7, 12.0, 11.7, 11.7, 12.0, 11.7, 11.0, 10.6,
         9.4, 10.0, 8.3, 8.0, 7.2, 5.6, 6.1, 5.6, 6.1, 6.7, 8.0, 10.0, 10.6, 11.1,
         13.3, 12.8, 12.8, 12.2, 11.1, 10.0, 10.0, 10.0, 10.0, 9.4, 8.3] 

Yhat = fftpack.fft(mydata)

fig, ax = plt.subplots(nrows=2, sharex=True)
xs = np.arange(len(mydata))
ax[0].plot(xs, mydata)

new_xs = np.linspace(xs.min(), xs.max(), len(mydata)*1.5)
new_ys = fft_inverse(Yhat, new_xs)
ax[1].plot(new_xs, new_ys)

plt.xlim(xs.min(), xs.max())
plt.show()

enter image description here

scipy.optimize, , x. sin , , , scipy.optimize :

import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as optimize

mydata = np.array(
    [8.3, 8.3, 8.3, 8.3, 7.2, 7.8, 7.8, 8.3, 9.4, 10.6, 10.0, 10.6, 11.1, 12.8,
     12.8, 12.8, 11.7, 10.6, 10.6, 10.0, 10.0, 8.9, 8.9, 8.3, 7.2, 6.7, 6.7, 6.7,
     7.2, 8.3, 7.2, 10.6, 11.1, 11.7, 12.8, 13.3, 15.0, 15.6, 13.3, 15.0, 13.3,
     11.7, 11.1, 10.0, 10.6, 9.4, 8.9, 8.3, 8.9, 6.7, 6.7, 6.0, 6.1, 8.3, 8.3,
     10.6, 11.1, 11.1, 11.7, 12.2, 13.3, 14.4, 16.7, 14.4, 13.3, 12.2, 11.7,
     11.1, 10.0, 8.3, 7.8, 7.2, 8.0, 6.7, 7.2, 7.2, 7.8, 10.0, 12.2, 12.8,
     12.8, 13.9, 15.0, 16.7, 16.7, 16.7, 15.6, 13.9, 12.8, 12.2, 10.6, 9.0,
     8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 10.0, 10.6, 11.1, 12.0, 11.7,
     11.1, 13.0, 13.3, 13.0, 11.1, 10.6, 10.6, 10.0, 10.0, 10.0, 9.4, 9.4,
     8.9, 8.3, 9.0, 8.9, 9.4, 9.0, 9.4, 10.6, 11.7, 11.1, 11.7, 12.8, 12.8,
     12.8, 13.0, 11.7, 10.6, 10.0, 10.0, 8.9, 9.4, 7.8, 7.8, 8.3, 7.8, 8.9,
     8.9, 8.9, 9.4, 10.0, 10.0, 10.6, 11.0, 11.1, 11.1, 12.2, 10.6, 10.0, 8.9,
     8.9, 9.0, 8.9, 8.3, 8.9, 8.9, 9.4, 9.4, 9.4, 8.9, 8.9, 8.9, 9.4, 10.0,
     11.1, 11.7, 11.7, 11.7, 11.7, 12.0, 11.7, 11.7, 12.0, 11.7, 11.0, 10.6,
     9.4, 10.0, 8.3, 8.0, 7.2, 5.6, 6.1, 5.6, 6.1, 6.7, 8.0, 10.0, 10.6, 11.1,
     13.3, 12.8, 12.8, 12.2, 11.1, 10.0, 10.0, 10.0, 10.0, 9.4, 8.3]) 


def fit(x, a, b, c, d):
    return a*np.sin(b*x + c) + d

xs = np.linspace(0, 2*np.pi, len(mydata))

guess = (mydata.ptp()/2, 10, 0, mydata.mean())
fitting_parameters, covariance = optimize.curve_fit(fit, xs, mydata, p0=guess)
a, b, c, d = fitting_parameters
print(a, b, c, d)

fig, ax = plt.subplots(nrows=2, sharex=True)
ax[0].plot(xs, mydata)

new_xs = np.linspace(xs.min(), xs.max(), len(mydata)*1.5)
new_ys = fit(new_xs, a, b, c, d)
ax[1].plot(new_xs, new_ys)

plt.xlim(xs.min(), xs.max())
plt.show()

enter image description here

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