# Recurrent Neural Net (LSTM) batch size and input

I am working in Keras to build LSTM models. I understand that setting STATEFUL=FALSE means that the different batches are treated as independent when training the model.

Suppose I want to build a model that uses 6 weeks of hourly temperature observations in order to predict tomorrow's 24 hourly temperatures. I have been using a batch size of 24, meaning each day of training data gets used independently by the LSTM when training. But this means that I am not allowing the RNN to pick up longer correlations across days, and only within days, correct? So should I instead be using a batch size of 6*7*24=168? Would this larger batch size allow for the LSTM to pick up longer range correlations across the 6 week training period?

Secondly, I have been using the previous day's observations $y_{(t-24)}$ as predictors for the current day's temperature (at the same time period) $y_t$. Is this a valid approach, or is this redundant with the long term correlations that the LSTM will be looking for?