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A prediction interval (also forecast interval) is an interval that covers the future (or otherwise unknown, but *observable*) value of a random variable with some prespecified probability.

0 votes

learn prediction intervals (variance, noise)

To make the prediction interval for a particular forecast point , one needs to efficiently separate the data into signal and noise thus providing the "smallest model error variance" . Now the model mi …
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1 vote

Calculating forecast intervals for user adjusted forecasts?

You could simply adjust the limits by the difference between the two values. More generally one could include a predictor variable reflecting the user's specified probability of a particular event hap …
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1 vote

How to do prediction from a linear regression?

You have taken count data ( i.e.the number of failures in the first interval , the second interval , the nth interval ) and added them to create a cumulative series which is autocorrelated as a result …
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7 votes

The "sum" of prediction intervals

In order to compute the variance of a sum of forecasts you need to incorporate the covariance between these forecasts. Thus compute the varriance and covariance of the observed series for as many lags …
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9 votes

Simple method of forecasting number of guests given current and historical data

There are simple methods to use but they are probably profoundly wrong as daily data presents a ton of opportunities . Simply striking daily averages is both simple and useless BUT I guess if there is …
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1 vote

Forecasting/predicting total sum of donations (following GLM with poisson family and log link)

I took your 29 days (oldest to newest) and found that there were 3 unusual days thus the following equation with Actual/Fit and Forecast here All models are wrong ... but some are useful .... . It …
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1 vote
Accepted

Forecasting/predicting total sum of donations (following GLM with poisson family and log link)

ROUND TWO: You asked “how do I do this with the log-link function and quasi(Poisson) errors?”. I say put aside your priors suggesting a particular fixed model and use a data-driven empirical process t …
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0 votes

ARIMA forecasting using exogenous variables with their own forecast intervals

Generate a family of forecasts for each point in the future for all input series allowing for identified unusual values in the past of all input series to have an effect on the forecasts for these exo …
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6 votes

Bootstrapping with quantiles of data instead of SD*z?

A possible alternative is to identify and form an efficient model generating a set of iid residuals. Generate a forecast using the model and then use the distribution of residuals as the basis of the …
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1 vote
Accepted

Choosing model to predict next value in a sequence

You have a time series problem requiring a time series solution. The preferred method is an optimized weighted average of the past ... this method is called ARIMA or univariate Box-Jenkins. Concern ha …
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0 votes

95% prediction interval for an ARMA(2,2) model

you have to generate the psi weights which can be obtained by expressing the model as a pure long-lagged ma model https://rdrr.io/cran/tswge/man/psi.weights.wge.html . You also need the estimate of th …
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1 vote

Confidence Interval derivation

Another way to pose your question is to ask "What is the probability of making a year-end number given that we have cumulative sales of xxx so far ?" . At a baseball game , after 3 boring innings I …
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1 vote

Which formula does the forecast package in R use to calculate variance/ standard error for p...

Whereas @javlacelle did a great job in developing the forecast variance for a particular case as he stated "The expressions of the variances vary with the order of the model", it is interesting to pur …
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