# how to estimate a variable's upper limit with 95% confidence level?

Suppose I have a variable, $S(t)$, for stock price. So always have $S(t) > 0$.

$S(t)$ is a random variable, with some volatility $\sigma$ and trend.

Now the requirement is to estimate $\hat S(t+1)$ with at 95% confidence level, or: estimate $\hat S(t+1)$ based on $S(0)$, $S(1)$, ..., $S(t)$, so that 95% of the time $S(t+1) < \hat S(t+1)$.

If it's not for the 95% confidence level, it's easy, I could just use regression to genereate a formula something like $$S(t+1) = a_0 + a_1 S(t) + a_2 S(t-1) ... + a_m S(t-m+1)$$ .

But such estimation is only predicting the "trend", not considering the volatility and 95% confidence level.

If it's not for the trend, it's also easy, I could just get the 95% percentile value from history S:

$\hat S(t+1) = 95 %$ percentile value of $S(t), S(t-1), ... S(t-m)$

, maybe could choose $m = 36%$, using 3 years' data.

But such prediction would not cater the trend -- if there is a trend in the market that the Stock price rises, the estimation will always be lower than the future realized.

How could I have a $\hat S(t+1)$ that could cater both "trend" and "95% confidence level"?

Please notice here we didn't assume any parametric model about Stock price's distribution.

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