Calculating Historical Data for Exotic Pairs

 

Let's say that I have 15 years of historical data (1M OHLC) for AUD/USD and NZD/USD; however, I don't have any data for the AUDNZD. Is it possible to calculate the AUDNZD with AUD/USD and NZD/USD?

Example, for open price 

AUD/USD * USD/NZD, the USD will cancel itself out; hence, we can obtain the AUDNZD. 

 

Does anyone have any opinion against this simple method?