Absolutely not! It is a very bad idea. The filter is the life and soul of your pond, especially when you have koi or goldfish. changing the water once or twice a week is far too little to keep your fish alive without a filter--you would have to change it everyday, and even then there would be no guarantee as to how long they would last. Even if they stayed alive, that amount of water changes would not keep your pond beautiful nor presentable, and your water would most likely be a nasty brown-green color.
If you are willing to change the water every week or biweekly, you pond really must not be all that big--certainly not large enough for koi, who need thousands of gallons as adults--no joke. I would definitely recommend goldfish if you decide to get anything, because koi have a massive growth rate. Goldfish can be just as beautiful, colorful, and rewarding.
I know this may be a question of money, but the filter is too often the part that hobbyists try to skimp on, and this is very unwise. Even with a great filter, ponds are still a lot of maintenence to keep them looking right, so without one, you would probably find yourself with a huge headache and massive amounts of work on your hands. Filters were invented to do some of this work for us. good luck, i hope you come to a good decision.
