Daily data, such as open and close prices, is often available for much longer periods than high-frequency data. However, whenever backtesting any strategy that examines instruments traded in different time zones and at different exchanges, one faces the problem of how to account for market movement while one exchange was open and the other closed. In other words, the open and close prices recorded by the exchanges and reported by most data providers do not line up. Thus if major market-moving news comes out during the US day time but after Asian or European markets have closed, then the impact of that news will be reflected in the same day's returns, but won't be reflected in Asian/European markets' returns until the following day. Consequently, any signals generated simultaneously from both markets' returns and/or open/close prices will be biased.
For example, suppose US markets rally strongly going into the close. Then US markets may appear overvalued relative to European and Asian markets judging by index prices as of the US close, although in reality the latter markets have moved as well (as ETFs traded on US exchanges would clearly indicate). Since no trading has occurred (yet) in non-US markets, index prices are not representative of true market prices.
What methods should one use to reconcile the open and close prices to be on a similar timescale? Would it be better to simply ignore the much longer history which has daily data but no high-frequency data? If you choose to interpolate, should you use the interpolated points to calculate other statistics, such as volatilities, as well? Suppose one is dealing with a relatively short-horizon signal (decaying over 5-10 days), so that smoothing out these differences by looking at longer return periods (e.g. weekly) is not feasible.