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May I please ask the community's support with the following problem?

I have 2 time series, with approximately 1000 observations each (same number of observations for both). They represent the daily closing prices for 2 stocks: asset A and asset B. Assuming we are currently at time t, I'm interested in computing (forecasting) the probability that, (at anytime) over the next 5 days (i.e. t+1, t+2, t+3, t+4, t+5), either stock A's or B's price will fall by at least rloss%:

Pr( PAt+i < PAt (1-rloss) or PBt+i < PBt (1-rloss) ) = ?

where:

i = {1,2,3,4,5}, periods for which I want to forecast ahead (not yet observed)

t = current time

PA, PB = price of stock A, price of stock B

rloss = loss threshold, e.g. rloss = 0.03 => PAt+i < PAt (1-0.03)

mihnea_11235
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  • If you consider this probability (let's focus only on asset A) as a ratio between the number of stocks for which this situation happens and the total number of stocks you can iterate to check how many times the situation occurs in the series. This can be done with a simple iteration (the implementation depends on the ds used to represent the data i.e. `list`, `pd.Series` etc.). If you want add your code so somebody could answer precisely. – Nicola Fanelli Jan 08 '22 at 11:51
  • @Nicola thank you very much for your reply! Just to make sure I understand correctly, you suggest to compute the frequency this event takes place in the sample I have (i.e. the empirical probability). And then use this probability as a naive forecast for the next 5 days no? My fear is that this method will not capture market regime changes (good times vs bad times, when markets are more correlated) quickly enough. I'm curious if maybe there are any established methods from quant risk management, such as copulas (I'm not sure how to use them for this case), that can be applied to this problem? – mihnea_11235 Jan 08 '22 at 13:08
  • Hello @mihnea_11235. So now I clearly see your question, I understood from the problem statement that you needed to find the empirical probability. Exactly as you wrote, that won't give you any "temporal" information about the series, since in that case the source would be treated as a combination of several independent symbols. I don't know about specific ways to solve this problem, maybe you could look into Markov chains (but I'm not sure). – Nicola Fanelli Jan 08 '22 at 13:25
  • @Nicola Thanks! Added clarifications in the question right now in order to avoid future confusion. – mihnea_11235 Jan 08 '22 at 14:15

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