# How to predict future data points with probability distribution associated, given past few samples?

I have a column vector with about 40,000 points. The plot of the vector looks like this:

Now, I decided to fit a normal distribution across these points which looks like this :

My question is the following, how can I predict future data points using the knowledge of the normal distribution function parameters and a fixed number of samples, say 25. The prediction should not be a fixed data point, rather it should be a normal distribution with certain mean and standard variation. References on MATLAB commands to facilitate this will be very helpful.

• The characteristics of the series appear to be changing over time (the variance at the least, seems to be changing, and possibly the mean as well), so that fitted marginal distribution wouldn't be informative. You might consider ARCH or GARCH models as a first step. – Glen_b Oct 11 '15 at 22:34
• ARCH model looks promising. Unfortunately, I am not from statistics background, but I can work on it. Just, a question, can ARCH/GARCH give me the desired output, like a range with confidence on prediction increases as the range increases? – GKS Oct 11 '15 at 22:52
• It can give what you asked for in your original question - a predicted mean and standard deviation on the assumed normal; I don't know what you meant in your comment. If you're learning ARCH/GARCH from scratch, you'll want to have learned about ARIMA models first. – Glen_b Oct 11 '15 at 23:26