# Questions tagged [prediction-interval]

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.

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### Forecasting costs with forecast interval using past performance

I'm trying to adopt a model for project cost forecasting in agile. Consider the following table of previous costs per sprint, along with story points completed: ...
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### Simple method of forecasting number of guests given current and historical data

I am trying to predict the number of guests a restaurant might serve in a meal period based on the volume of business that same day from prior years (3-5 years of data), trends for the same day of the ...
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### Prediction Interval for Regression Models with Weights

Courtesy Prediction Interval for Neural Net With Hessian :: nnet in R I would like to understand how to manually derive a point-wise prediction confidence interval applicable to neural models. ...
283 views

### Find error interval of linear relationship

I have two sensors of different quality capturing the same process, where one of them is much more accurate than the other. Hence, I want to find out how much better. Let us for example say that the ...
570 views

### Forecast R function : prediction interval is not symmetric across mean

Using forecast function in Forecast package, I am trying to get mean and prediction interval for forecast period (h = 8). But I could not understand why prediction interval are not symmetric across ...
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### Sampling from forecasting interval

Suppose I have an ARIMA model with $n$ step ahead forecasts and forecast intervals. If I want to sample from those forecasts: One way to look at is: take one observation from the prediction ...
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### Are predictive distributions supposed to be distributions of future data?

In frequentist analysis, we define a 95% prediction interval as an interval that will contain the next observation 95% of the time under repeated sampling of the entire experiment and prediction. If ...
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### ARIMA forecasting using exogenous variables with their own forecast intervals

Suppose model <- Arima(y , xreg=cbind(x1, x2), order=(p,d,q)) If I am forecasting $x_1$ and $x_2$, then for forecasting $y$: 1) If I use expected forecasts ...
636 views

### Disadvantage of prediction interval vs confidence interval

I have a linear regression model μ = 4.7937 - 0.0627t with Y ~ N(μ, σ^2), where t is temperature and μ is the expected number of accidents that happen. At t = 50, μ = 1.66 and the confidence ...
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### Heteroskedasticity in a VEC model, adding robust standard errors and plotting forecasts

I'm dealing with a data set which required me to log and take first differences of it to induce stationary. A VECM as a result was prodouced. Everything seemed fine until I checked for ...
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### Calculate original data forecast interval from differenced data forecast interval

How to calculate original data forecast interval from differenced data forecast interval? Please provide formulas or bibliographic reference.
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### Time series: Getting from monthly to semi-annually data by summing - how to determine the forecast interval? [duplicate]

I have to forecast some monthly timeseries 1.5 years into the future and then sum them up to get 3 semi-annual counts. The forecasts give forecast intervals, but how do I get from the 6 monthly ...
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### Predictive maintenace model to identify indication of failure before it happens

Situation I'm working on a problem where I'm using sensor data to predict machine failure before the failure happens and I need some advice on which methods to explore. Specifically, I want to ...
693 views

### Bootstrapped prediction intervals: Quantile, median, SE...?

I am trying to construct prediction intervals for a non linear model via Boostrap. What I do is to apply the usual bootstrap procedure, here you have pseudo-code for 1000 iterations: ...
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### What is a "valid interval" in a prediction?

Learning about linear regression, I was teached that when a linear regression is calculated for a set of points, I can only make predictions with this linear model on the interval setted by the first ...
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### "ARIMA" versus "ARMA on differenced data" gives different prediction interval

I have seasonal time series (with frequency of 30). I am fitting ARIMA models using R library forecast. My first ARIMA model would be (1,0,1)(1,1,0) with ...
208 views

### Prediction interval for single future response

I know the following results: $\frac{RSS}{\sigma^{2}} \sim \chi^{2}_{n-r}$ where $r = rank(X)$ and $k$ is the degrees of freedom. Then, for any $c \in \mathbb{R^{p}}$, and when X has full rank, i.e. ...
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### When calculating a meta-analytic prediction interval is it appropriate to report the back-transformed mean of that distribution?

The Problem I have been working on an epidemiological meta-analysis of prevalence values, measured as proportions but analyzed in logit-space. The conditions I study are quite rare (<5%) so all ...
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### simple linear regression (predictor)

Consider a simple linear regression model $Y = X\beta + \epsilon$ $\$. Let $Y_O$ be the least square predictor of $Y$ at $X = x_o$ , based on $n$ observations $(X_i ,Y_i)$and $\overline X$ = ...
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### Which formula does the forecast package in R use to calculate variance/ standard error for prediction intervals?

I am trying to compare a manual computation for the prediction interval for a forecasted value (one step ahead, at 95% confidence) on this data set, to the given prediction interval from R's forecast ...
I have a multiple regression equation that predicts a trait of interest ($y$) from two measured traits ($x_1$ and $x_2$). I want to measure $x_1$ and $x_2$ for $k$ individuals of a certain plant ...