I have successfully fit an ARIMA model to a time series of the daily returns of power futures prices. The question I have is: How can I create a prediction interval for the prices? Or, alternatively, is there a nonparametric alternative to ARIMA that you would recommend? I understand econometric models are a bit iffy for long-term forecasts, and I would like this model to be extendable to at least six months (~120 periods).

Simply taking the cumulative product of the forecasted returns and the most recent historical price creates a band that diverges far too quickly to be realistic (sample image below for a 20-day futures price forecast using an ARIMA(2, 0, 2) model on the March 2021 contract as of December 2020). If it makes a difference, to make the data stationary and reduce the required "d" order, please note that the data were a) first standardized and b) then transformed via Yeo-Johnson before they were fed into the ARIMA model. Needless to say, I then reversed the transformations to scale the data. The ARIMA parameters were calculated using auto_arima in Python. March 2021 Futures

  • $\begingroup$ Hi: if you extend an ARIMA prediction out 120 days where the data is estimated using daily data, unfortunately you'll probably be predicting the long term mean of the model + error because any of the AR effects will die out. Also, I wasn't clear if you are using ARIMA on the log prices $\endgroup$
    – mark leeds
    Mar 16, 2021 at 1:51
  • $\begingroup$ Thank you for your response, Mark. The underlying data are standardized daily geometric returns. They have been transformed through a Yeo-Johnson to “increase their normality” and make the residual terms in the ARIMA model approximately Gaussian. So, to summarize, given this mean reversion, I might as well stick to the traditional Brownian motion / Wiener process with log returns? Essentially, as long as the residuals aren’t auto correlated and the underlying data are stationary, I should be fine? (Going back to all models are wrong but some are useful.) $\endgroup$
    – CasusBelli
    Mar 16, 2021 at 4:15
  • 1
    $\begingroup$ It sounds like you've definitely dealt with th various pitfalls ( I gotta check oput yeo-jonhson because I haven't heard of it ). But, if it's "pure arima", like I said, I don't think there's much you can do with it because you would need to know the future epsilon's. $\endgroup$
    – mark leeds
    Mar 16, 2021 at 17:30


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.