Building Price Prediction Intervals from ARIMA Return Forecasts

Summary

The document asks how to turn forecasts from an ARIMA model of daily power futures returns into prediction intervals for prices. It describes a simple approach: reverse the data transformations, compound the forecasted returns from the latest observed price, and use the resulting range as a price forecast. The author reports that this produces intervals that widen too quickly in a 20-day example using an ARIMA model on a power futures contract.

The returns were standardized and transformed with Yeo-Johnson before fitting; the model parameters were selected with an automated procedure. The document asks whether another method, including a nonparametric one, could provide more realistic intervals over a horizon of roughly six months. It offers no proposed solution, comparison, or evidence beyond the reported example, so readers cannot infer which alternative would work or how uncertainty should be propagated through the transformations.

Key ideas

• Compounding forecasted returns from the latest price can produce rapidly widening price forecasts.
• The returns were standardized and Yeo-Johnson transformed before ARIMA fitting.
• The author seeks price prediction intervals over a horizon of about six months.
• The document poses the modeling problem but provides no recommended solution or comparative evidence.

Tags

# Price Prediction Intervals from Forecasted Returns (ARIMA)


# Price Prediction Intervals from Forecasted Returns (ARIMA)












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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.