In a person who is elderly, what causes rises and falls in oxygen saturation?

Many. If there is underlying lung disease(such as empysema) the lung is already prone difficulty extracting o2 out of the blood. As we age our lungs and chest get stiffer and there is more unusable space- with resulting low o2. Also, central or obesity related sleep apnea can contribute to low o2 levels. Pickwickian syndrome related to morbid obsesity can also decrease the amount of o2 levels.