Time series with 2 Values

Question

I have a problem to solve with the time series. My data set looks like:

Date;hours;result
2021-01-01;180;2.78
2021-01-01;196;2.68
2021-01-01;170;2.53
2021-01-01;181;2.71
2021-01-01;169;2.43
2021-01-01;201;2.89

What would be the best approach to estimate the number of hours for the next day, to achieve the highest result?

I was thinking about Random Walk for Times Series but i have no clue how can I force the algorith to combine all 3 factors. In all examples i found there is always prediction f(x).

Answer 1

The question is unclear, especially regarding the part on the next day.

Assuming you want to find the hours needed to obtain the maximum result for the current day, using a polynomial regression:

import numpy as np

def hour_max(g, deg=2):
    p = np.polynomial.Polynomial.fit(df['hours'], df['result'], deg=deg)
    x, y = p.linspace()
    idx = y.argmax()
    return x[idx]

df.groupby('Date').apply(hour_max)

Output:

Date
2021-01-01    195.828283
dtype: float64

If you also want to have a visual:

def hour_max(g, deg=2, plot=False):
    p = np.polynomial.Polynomial.fit(df['hours'], df['result'], deg=deg)
    x, y = p.linspace()
    idx = y.argmax()
    
    if plot:
        ax = g.plot.scatter(x='hours', y='result')
        ax.plot(x, y)
        ax.plot(x[idx], y[idx], marker='o')
        ax.set_title(g.name)
    
    return x[idx]

df.groupby('Date').apply(hour_max, plot=True)

Output:

Date
2021-01-01    195.828283
dtype: float64

Image: