Fill time series pandas dataframe with synthetic data that has a similar shape as the original data

I have a time series in pandas with a large gap in between, I would like to fill that gap with "synthetic" data that resembles the same shape and trend of the data that is existing.

Some of the methods that I've tried have been linear, cubic, spline interpolation, but the noise and general shape of the data is gone. It will pretty much just plot a line through all the nulls.

Below is a graph of the data. Is there any library that can create this data?

You can try and use Prophet to create some future predictions to fill the missing data. This assuming that your missing data is NaN not 0 and that all the missing data is continuous.

This is just a quick example and you will probably need to adjust the seasonality to get a better fit.

import pandas as pd
import numpy as np
from prophet import Prophet


# sample data
np.random.seed(0)
arr = np.random.randint(1, 200, 100)
df = pd.DataFrame(arr, columns=['y'])
df['ds'] = pd.date_range('2023-01-1', periods=100)
df.iloc[50:90, 0] = np.nan
og_df = df.copy()

# find first nan and create a train dataset
train = df.iloc[:df['y'].isna().idxmax()]
# find the number of periods to predict
periods = sum(df['y'].isna())

# fit your model, create a future DataFrame, and forecast
# add seasonality based on your actual data to get a better fit
m = Prophet()
m.fit(train)
future = m.make_future_dataframe(periods=periods)  # add freq param if not using daily: freq='1h'
forecast = m.predict(future)

# assign your forecasted data to the original frame
missing_data = forecast.iloc[df['y'].isna().idxmax():][['ds', 'yhat']].rename(columns={'yhat': 'y'})
df.loc[df['y'].isna()] = missing_data

# sample plot
og_df.plot(x='ds', y='y', ylim=(0,500))
df.plot(x='ds', y='y', ylim=(0,500))

If you expect the next frames of data to have the same behavior as the existing data, then you can experiment with TimeGAN to generate data to replace the missing gap. You can give ydata-synthetic a try for this.