Simulation that is not synced to NY 9:30 am

Is there a low cost paper money stock day trading simulation software that allows me to experience morning trading hours (9:30-11 am NY time) any time I want, with the past data?

I don't want to get up 3 in the morning here at LA to practice paper money trading.

Thanks in advance...

I posted in newby forum but didn't specify what I am trading (Stocks), so here I am posting again to clarify.

the one that springs instantly to mind is sierra charts.

but you can readily google for others using "chart packages with replay function" to help find a suitable low cost candidate.

do you need an analysis software that allows you to create trading systems or a platform that simulates the orders to be inserted?

Both please...

I am looking at Ameritrade - anyone know if that one qualifies for what I am looking for?

that could work. they have thinkorswim which has a paper trading element to it, but it would possibly depend on account funding requirements to get it i'm thinking. not sure if it has a market replay function, they're not shouting that feature from the rooftops, you would have to research further.

for market replay and trade simulation and further research into market replay and trade simulation look at

sierra chart
ninjatrader

there seems to be a lot out there if you google, maybe look at tradingsimulator.net or tradingsim.com

ninjatrader I think it's just for futures and forex
multicharts is free for 30 days
overcharts should be free for a period of time (beta phase)
zorro-project excellent and free (see the conditions) but also very complex

good trading
tallytrading

ThinkOrSwim - their real trading platform is free and have OnDemand feature, you can replay any day from the last few years...