There is no scientific evidence that animals can predict earthquakes. Some people believe that animals such as dogs and cats may be able to sense an earthquake before it happens, but there is no proof of this.
In some areas, scientists have found evidence that animals might actually behave differently during earthquakes than they do at other times. For example: in the days or weeks before a major earthquake happened in Italy and Japan (in 1703), many birds left the area where the quake would happen; fish jumped out of rivers onto land for several minutes; butterflies were seen flying around outside their regular season; rats stayed away from buildings because they could feel vibrations through their feet on different surfaces (instead of running toward them). However, these behaviors may not mean anything special about earthquakes -- instead, it's possible that these are normal behaviors for certain types of weather events like storms or windy conditions.
It is also possible that animals might sense an earthquake when it happens by detecting changes in how waves travel through air and water. Some scientists think this might be true because some animals can detect sounds at very low levels -- but we do not know if this is related to earthquakes yet.
If you want your pet to behave differently during an earthquake than other times, teach him commands like "go under my bed" so he will hide there when you tell him now instead of doing whatever else he would normally choose to do during another time.