Training ARIMA Models with Powell Optimization and Flexible Lags

Summary

The document outlines an ARIMA training method implemented as an MQL5 class. It reviews autoregressive, moving-average, and differencing components, then describes fitting coefficients by generating predictions over known observations and minimizing their squared errors with Powell’s method. The implementation supports a constant term, ordinary contiguous AR and MA lags, and a separately described option for noncontiguous lags. It builds innovation estimates sequentially so that moving-average terms can be incorporated as residuals become available.

The article also discusses model selection, including inspection of autocorrelation and partial autocorrelation patterns and time-series cross-validation. It illustrates the class with synthetic and financial time-series examples, but the supplied excerpt does not establish forecasting performance in live trading. Model suitability depends on adequate sample size, stationarity after differencing, initialization choices, and the specified order and lags. The fitting procedure optimizes in-sample squared error; order selection and out-of-sample evaluation remain separate tasks, and no single ARIMA order is presented as universally appropriate.

Key ideas

• ARIMA combines autoregressive terms, moving-average innovations, and differencing to model series that are not stationary in their original form.
• The training method estimates coefficients by minimizing prediction errors with Powell’s optimization procedure.
• The class supports optional constants and allows lag specifications to be adjusted beyond the usual contiguous pattern.
• Moving-average components are incorporated sequentially as prediction residuals become available.
• Autocorrelation diagnostics and time-series cross-validation can help select model order, but fitting error alone does not establish predictive value.

Tags

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