how do you construct a carry-adjusted time series for backtest FX? Suppose you want to have the flexibility of not only doing tick data intraday, but also the position will be last for a few days or even a few months so you need to adjust the data for carry effects. How to do that? The goal is to construct a carry-adjusted time series to have the flexibility of trading time horizon... Please shed some lights... thank you!

yep, the first day's tick data is fine. how do you adjust for the carry to the second day's tick data?

You work on a macro trading desk, right? What do the FX accounts look like each day? How does the pnl change? What are the components of the pnl? Have you ever looked at this?

Okay, lets say I successfully constructed a carry-adjusted time series. I generate signal based on it. What do I then trade actually? Spot or forwards?

As mentioned in your other trade, you can trade either, as they're the same series. You just have to make sure you trade the one, where the actual carry you get is close to what you used when constructing the time series. That's assuming you don't have any other constraints, such as funding, lines, etc.