Rating rise: luck or actual increase in playing strength? The FIDE rating of very active chess players can vary a lot: rating fluctuations of 50 rating points are not unusual.

Is there a way to distinguish whether a rating rise/drop can be explained by random factors, e.g. "(bad) luck", being "in/out form", etc..., or an actual increase/decrease in playing strength?

Does it make sense to say "a rating increase of X over minimum Y games is statistically significant"? If yes, what is the value of X and Y?
Is there a way to distinguish whether a rating rise/drop can be
  explained by random factors, e.g. "(bad) luck", being "in/out form",
  etc..., or an actual increase/decrease in playing strength?


No, would be my answer, at least there is no easy way to distinguish.

The problem is that there are very many factors affecting ratings. 

For instance, about 5 years ago FIDE changed the system. I'm not sure if it was lowering the minimum rating, changing the k factors or a combination of these but the net effect was a rating deflation. Talking to a range of players it seems that there was an influx of very underrated juniors into the system. One disgruntled player complained of losing or drawing to juniors who were, in his opinion, as much as 400 points underrated.

Over the following 2 years I noticed a 150 point drop in my rating and anecdotal evidence is that many other older players who have had stable ratings for many years noticed the same kind of drop. Over the last year these same players have reported that their ratings are rising back towards their old averages and attribute this to the system regarding rating of junior players (perhaps with their higher k value) as "settling down". I have to admit I haven't noticed this effect yet ;-), but then I played very few games in the last year. I hope this means I have something to look forward to if I go back to playing a lot more games!

You can also have anomalies due to the average strength of the players you play against. If you play a lot of players who are much, much weaker or much, much stronger than you then this can also distort your rating due to the way they are calculated.

Finally, I would just add that FIDE only attempts to measure my rating "sitting down". My rating "standing up" is at least 300 points higher ;-).