Yes, other altcoins can move faster but It depends on the BTC movement. we know Bitcoin is the mother coin in the crypto market. So altcoins movement speed depends on the Bitcoin movement. We can saw a great example for that at this moment. Now BTC price in low. So all altcoins prices and move very slowly. Maybe the market can recover again mid of this year. Let's see what happen... 
Altcoins still based on BTC movement. I have notice that when bitcoin price goes up, other market goes up. This is a thought that altcoins still rely with bitcoin.