About 5% more probability in one direction is also what I'm currently getting, hoping to improve the score but I don't think it's realistically possible to go much further, or the markets would notice. Also base on my calculations there's about 90% confidence that that 5% edge is systematic and not purely random, so that's another area to improve on. Is it to much to dream on 10% edge with 98.5% confidence? And then there's the question how to profit from that? Even when there's 5% probability that the market will go one direction, there's always a significant probability that it will go the reverse way ... and if you also add magnitude, it may very well obliterate any profits you made from figuring the direction when you do. If you ONLY trade when you have the indicator, then indeed you should perform better than the market AT THE RESPECTIVE MOMENTS, but this doesn't mean you'll outperform the market in general coze you'll miss the other times when it goes up. So it's more likely about allocating your investment amounts: more when you "know", less when you don't. Gotta do more research on that.
The US stock market has a general up bias, so if I predict "up" I should have a > 50% probability of been correct. I analyzed buy on open sell on close and had positive results in general. Of course it had to be: Long term SPY returned ~7% per year. So if I am a day trader, in a bull market I should be profitable in general?
Just some food for thought: Suppose the probability is 50/50. Then that would mean the up days tend to be more in absolute value than the down days. Suppose I flipped a coin 100 times, and 54 times, it was heads. Could I properly conclude that there is a bias towards heads? Statistics, likelihoods, and probabilities can be tricky sometimes. https://www.crestmontresearch.com/docs/Stock-Yo-Yo.pdf
You are right, again. Though, I noticed for the past decade, the % of up day was ~55%, same as OP's predictor algo. Flipped a coin 100 times in a ~50/50 setting is insufficient to establish statistical significance? On the other hand, if you flipped a coin 1000 times, perhaps?
Mathematically the answer to your question is no, because in 68.2% of the cases we'll encounter a number of heads between 45 and 55 (1 standard deviation). From a statistical point of view, any (supposedly) random event that exceeds 3 standard deviations (SD) is considered abnormal. The sudden down moves (crashes) in the stock market routinely exceed 3 SD, another proof that the stock market is not random.
Off the top of my head, no, not with a fair coin. Each toss is independent of prior tosses. No memory is involved. What are the odds of getting HTHT? Toss 1: 1/2 H Toss 2: 1/2 T Toss 3: 1/2 H Toss 4: 1/2 T =1/16 What are the odds of getting HHHH? Toss 1: 1/2 H Toss 2: 1/2 H Toss 3: 1/2 H Toss 4: 1/2 H =1/16 So, any random sequence of 1000 flips, has the same probability of showing as does a sequence of 1000 heads in a row.
Right, if coin flips were normally distributed. Coin flips are discrete, not continuous. So there distribution is uniform, not normal. Just as lottery numbers are uniformly distributed.
Based on weekly data for 10 years, that's about 500 samples and indeed the index was up about 55% of the times. My up indicator triggered some 150 - 200 times and up times were about 60% in this case. Assuming probability really is 55%, if you test 200 times, you will get 60% up some 10% of them. This is "confidence level". More margin (10% instead 5%) and more confidence (99% instead 90%) is best. But even so, there's still volatility so even if up 60%, you can lose it all on one bad down. Don't really know right now how one could exploit knowing the up prob.
A lot of traders do that. Even I am trying to learn from the experienced traders the various tools that they use which aids their predictions. UMPI so far seems to be really popular.
Since we're at it, just got some 7% edge in predicting an up move with 99.98% confidence, still no idea how to exploit this or even if it can be done.