For fast octaves, try the following practice strategies at a slow speed: Play each octave with wrist staccato ie with the hand only moving in a waving action from the wrist. Next do the same, but include a bounce involving the whole arm as well as the hand waving. The wrist will be seen to have an undulating movement creating a "hill" effect when the wrist goes up & a "valley" as the wrist goes down. Now add to these 2 movements a small grasping action with the thumb and 5th finger. Be patient, trying the passage quite a few times in the above fashion. At speed these movements will morph into a sense of general freedom especially at the wrist as well as an easeful command of the passage.
In general, the arm & hand will be at a normal playing height for white note octaves, but higher for black note octaves, so be sure to make this arm adjustment when playing octaves at a faster speed.
Also for speed in any type of passage, there will be an impulse at intervals with a downward arm movement, usually on the beat, or at the beginning of the technical pattern eg see RH of Chopin Etude Op 10, No 1. In addition, all passages at speed have a shape, eg the fast LH octaves in the Polonaise Op 53 go up & over for octaves from bar 83-94 & down & under from bars 95 onwards involving the c double sharp.
Another relaxing & effective exercise for octaves to involve the whole arm is to flip out the elbow and land with whole arm descent on each octave slowly. This is good for strong, more commanding, octaves.
Lastly, here is another example of a technical pattern (alluded to above): In Chopin Etude Op 25, No 10, the playing mechanism-hand & arm-goes down on the 1st octave & up on the 2nd & 3rd octaves in each group of 3 octaves. Look for similar groupings & impulse (controlled tension-energy) downwards on the 1st note or octave in each group in this way. NB Practice slowly several times, then once fast and repeat this process & you will eventually succeed.