This document discusses new temporal models for forecasting weekly, monthly, bimonthly, quarterly, and half-yearly stock index data. It presents models built for the China 300 and Shanghai Composite indices using high, low, open, and close data from 2001 to 2015. The models show very close fit to the observed temporal distribution of the stock indices, with a goodness of fit of 99.99%. Forecasts are provided for upcoming periods of the China 300 and Shanghai Composite, and the author concludes the temporal modelling and forecasting methods can provide useful quantitative tools for stock trading.