It is generally not recommended to set the moving average order (q) to a very high value like 70. This is because large values of q can make the model very complex and may lead to overfitting. Additionally, it may cause the model to take a very long time to fit or fail to converge.
When working with seasonal time series data, using a seasonal ARIMA (SARIMA) model is often more appropriate instead of a standard ARIMA model. SARIMA models are designed specifically for time series data with seasonal patterns.
To determine the appropriate parameters for a SARIMA model, you can use a combination of visual inspection of the time series data, the autocorrelation and partial autocorrelation plots, and model selection criteria such as AIC or BIC.
In terms of setting the moving average order (q) for yearly data, it would depend on the seasonality of the data. If the data exhibits a yearly seasonality (i.e., a repeating pattern that occurs once per year), then you would typically set the seasonal moving average order (Q) to 1 and the seasonal period (m) to 12. However, if there is no clear seasonality in the data, then you may not need to use a SARIMA model at all.