# Time series forecast. Probability of forecasted value exceeding a threshold value?

#### downthesun01

##### New Member
OK. Let's say that I have several years of monthly sales data. How would I go about finding the probability that monthly sales, three months in the future, will exceed a threshold value?

Is this something that's commonly done? I spent some time searching on the internet for this, but haven't found anything. Maybe, I'm not describing what I want properly or something.

In any case, if anyone has any references, examples, etc. on this, I'd love to check it out. Thanks.

#### staassis

##### Active Member
Re: Time series forecast. Probability of forecasted value exceeding a threshold value

Several years of monthly data is too little for accurate estimation of tail probabilities (probabilities of exceeding or going under certain thresholds). In general, a statistically efficient approach would involve modeling the underlying process (sales) directly. You would use a time series model in which residuals are not normal but bootstrapped from the data. Incorporating the empirical (bootstrapped) distribution of the residuals would allow you capture the tails of the distribution more accurately... Then you could simulate the estimated model 100,000 times and estimate the probability of exceeding any threshold at any point in the future.

In your specific case, it is possible to estimate only very simple models, like

deterministic (non-)linear trend + AR(3) + bootrstrapped residual.

No point to try adding any stochastic volatility effects

#### Stu

##### New Member
Re: Time series forecast. Probability of forecasted value exceeding a threshold value

This sounds a bit like simulation, or even worst-case scenario analysis. I like staassis's of using bootstrap.