Fitting an OLS Residual Spread to an AR(1) Model

Summary

The document describes an intended workflow for forecasting a crypto spread. The author first runs an OLS regression on first differences of time series, then treats the resulting residual spread as a tradable series. They inspect its autocorrelation and partial autocorrelation plots and conclude that an AR(1) model may be appropriate. Their question is how to fit and forecast that spread with an ARMA model.

The document does not include a response, estimated AR coefficient, fitted model, or forecast evaluation. It therefore records a modeling question rather than demonstrating that the residual spread is stationary, that AR(1) is the right specification, or that the resulting forecast is tradable. The proposed sequence gives context for the problem, but the evidence and validation needed to assess the approach are absent.

Key ideas

• The proposed workflow regresses first differences of time series using OLS to form a spread.
• The author examines ACF and PACF plots of the regression residuals to select a time-series model.
• An AR(1) specification is proposed for forecasting the spread.
• The document does not show model fitting, stationarity checks, forecast results, or strategy validation.

Tags

# Fitting a Spread into ARIMA AR(1) process


# Fitting a Spread into ARIMA AR(1) process












I'm a newbie to econometrics. I've simply ran a regression and have coefficient values of the variables. I'm running a regression for a crypto data, and I've gotten the Spread of the variables. To forecast, I'll need to fit this spread into ARIMA AR(1) process after finding the best fit is AR(1).

This is the scenario. Configuring a tradable mean for a time series data is what I'm trying to achieve. The steps I've taken are creating a regression using OLS from the first difference of the time series data.

From this I got the tradable formula, which is a spread between the variables used. It's now time to forecast using ARMA model.

I created the ACF and PACF charts using the residuals from the OLS model, and got to know it's an AR(1) process.

If the spread of the difference between the variables I'll like to know how to fit the spread into this AR(1) process of ARMA.

Please, kindly help out.

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