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To use a moving average to buy troughs in a trend, should an investor use a weekly chart?

It doesn't matter whether you use a daily, weekly or monthly chart. It is all the same trend, you are just choosing whether to display daily, weekly or monthly bars.

As to whether you use daily, weekly or monthly closing prices (data compression is another term in some software), again it does not matter much. Supposing you decided to use a 130 day/26 week/six month moving average. If the data was daily, you use 130 periods. If the data is weekly, you use 26 periods. If the data is monthly, you use 6 periods. There are slight differences in these three lines, but they are essentially the same. I would use daily data or weekly data unless you were a very long term investor.