title: How to perform inverse transformation of exponential decay time series data
body: <p>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.</p>
  <p>Taking log of the data</p>
  <pre><code>passenger_log = np.log(indexdf['#Passengers'])
  </code></pre>
  <p>Then performing exponential decay of the log series</p>
  <pre><code>passenger_expdecay=passenger_log.ewm(halflife=12, min_periods=0, adjust=True).mean()
  plt.plot(passenger_log)
  plt.plot(passenger_expdecay, color='red')
  </code></pre>
  <p>The ADCF test shows better results for the exponential decay series (passenger_expdecay) compared to log series (passenger_log).</p>
  <p>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.</p>
  <p>Can anybody help to perform inverse transformation of the exponential weighted (ewm) function</p>