How to perform inverse transformation of exponential decay time series data

Question

I am implementing an ARIMA model for time series data. Since the data is not stationary I am performing data transformation log and performing exponential decay over the data.

Taking log of the data

passenger_log = np.log(indexdf['#Passengers'])

Then performing exponential decay of the log series

passenger_expdecay=passenger_log.ewm(halflife=12, min_periods=0, adjust=True).mean()
plt.plot(passenger_log)
plt.plot(passenger_expdecay, color='red')

The ADCF test shows better results for the exponential decay series (passenger_expdecay) compared to log series (passenger_log).

I want to use the exponential series as an input to ARIMA model but I dont know how to perform the inverse of this ewm function so that after prediction I can perform inverse transformation to get original values.

Can anybody help to perform inverse transformation of the exponential weighted (ewm) function

Answer 1

if you apply this as

import pandas as pd
passenger_log = np.log(indexdf['#Passengers'])
passen_log =  pd.DataFrame({'passenger_log_inf': passenger_log})
passenger_expdecay=df.ewm(halflife=12, min_periods=0, adjust=True).mean()
plt.plot(passenger_log)
plt.plot(passenger_expdecay, color='red')

I think this might Help...