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

I am trying to predict the total sum of donations that Monica will receive on https://www.gofundme.com/f/stop-stack-overflow-from-defaming-its-users/ I copied the data and summed for all days the ...
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### Is always true that in the simple linear regression the width of prediction interval corresponding to new observationx=xo increases linearly with xo

Is it always true that in the simple linear regression model the width of the prediction interval corresponding to a new observation x=xo increases linearly with xo? Thanks in advance
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### 95% prediction interval for an ARMA(2,2) model

What would the formula for a 95% prediction interval for an ARMA(2,2) model be? The specific model I am using is: an ARIMA(2,0,2) with non-zero mean, with the following parameter estimates: ...
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### Using T -test results to find probability of an event occurring

Given two samples, one consisting of a different number of times someone made sales calls to different potential clients who ended up buying the product. the other one consists of a different number ...
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### Predictions in time series

I am working on project about the kitchen sink method and the lasso. My objective is to make in the sample predictions by, of course, taking part of the database as historical data and the other part ...
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### How to calculate seasonal naive quantile forecasts?

I was reading a chapter on prediction intervals and saw that the standard deviation is used to calculate "prediction" intervals. Earlier today I was reading some results from GEFCom2017 where ...
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### Confidence intervals for non-parametric statistics

I have a positive random variable $X$ (say, price or latency or energy) and I want to be able to say something like I am 95% confident that $P(X<42)>0.9$ (percentile) or $P(X<22)\ge\frac12$ (...
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### WMAPE / WAPE for the evaluation of time series with positive and negative values

I have a time series y that has both positive and negative that I want to predict. For the prediction I normalize the values to a range between 0 and 1. If I give ...
40 views

### Prediction interval for multi step forecast

If I have a multi-step forecast of some timeseries, where the model is some auto-regressive function y[t] = f(y[t-1],x1[t],x2[t]) is it a valide approach to use sections of historical data to train ...
49 views

### Estimation of prediction confidence interval

I have a linear model $Y=\hat{\alpha}X+\hat{\beta}$ fit on a bunch of samples $(X_i,Y_i)$. How can I compute the prediction confidence interval for a given $X'$ ? Assuming than $X'$ does not belong to ...
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### Should I use a confidence interval or a prediction interval around the LOESS fitted curve?

A Freakonometrics blog post shows how to use a LOESS regression of the residuals of a logistic model on the predicted values of the logistic model to assess the linearity of the predictors used in the ...
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### How to address impossible values in a regression prediction interval?

Background I've performed a regression analysis on a toy data set to predict GPA from height. I want to compute the predicted GPA value for a given height value and also compute a confidence interval ...
34 views

### Forecast interval for VAR model predictions

I have been looking at VAR models for doing multivariate time series analysis. What would one need to do to also estimate forecast intervals for the predictions from a VAR model?
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### Gamma GLM - Derive prediction intervals for new x_i

In a Gamma GLM, the statistical model for each observation 𝑖 is assumed to be $Y_i \sim Gamma(shape, scale)$, where $E(Y_i) = \mu_i = f(X_i\beta)$, and $f$ is the link function. I've used MLE to ...
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### If prediction intervals become narrower when less historical data is provided, how do you justify using a full range of data?

In forecasting (ets) annual data, I notice that when I use the full data set of 10 years, the prediction intervals are much wider than when using an abridged version of the data set (5 years). I ...
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### Bootstrap Prediction Interval: which residuals to use and which method?

I ask this question referring to the post: Bootstrap prediction interval, where a step by step method for calculating the prediction interval for linear regression models is explained. In the ...
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### RSME, MAE and prediction interval [closed]

Could someone please clarify, whether it is appropriate to define a prediction interval or an equivalent for an RMSE and MAE measure. If so, could you please suggest how such an interval is defined.
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### Can I give continuous rank probability score (CRPS) to Diebold-Mariano (DM) test?

I would like to use DM test for probabilistic forecasting case. My initial thinking was to give CRPS of two forecasting methods instead of raw forecast errors, where CRPS is calculated using ...
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### Are the conditional expectation values of y and f necessarily equivalent in Gaussian processes?

Suppose $y$ is a Gaussian process given by $y \sim f + \epsilon$, where $\epsilon$ is a Gaussian noise model with zero mean, and $f$ is a deterministic yet unknown mean function (or a Gaussian process ...
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### How to calculate confidence interval for prediction

I have model with k = k0/(1+((distance/r0)^alpha)). I have parameter value for r0 = 0.019 with std.err = 0.0042 k0 = 0.00605 with std.err = 0.00043 alpha = 0.2608 with std.err = 0.0058 and ...
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### Regression Output Acuracy

Suppose I have a logistic regression formula that takes x as input and y is the estimated output. The regression is based on a historical set of x and y values. How can I give an accuracy percentage ...
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### Penalize predictions with larger prediction interval

Suppose I am building a model for regression problems. I am quite curious about the following questions: Are there relevant theories that can confirm/disprove the following intuition: we should ...
52 views

### Confidence % on a single point estimate

I am working on a business case problem for my company (CPG) and was asked to come up with a way to predict Customer Order Fill Rate (CFR) based on the amount of inventory we hold. Now I have come up ...
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### Estimating prediction interval of ARMA process using R forecast function

the theme is forecasting with ARMA models. I'm trying to understand how the R forecast function works if applied to an ...
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### How to find the Prediction Intervals of a Gaussian Process Regression via caret kernlab packages?

I am trying to use a Gaussian Process Regression (GPR) model to predict hourly streamflow discharges in a river. I've got good results applying the caret::kernlab train () function. Since the ...
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### Slicing prediction interval at a certain level

Suppose your given some data to which you fit a linear regression with its prediction interval (on level $\alpha$, here 5%) like so: Now I fix a certain threshold $\tau$ at a y-level (blue dashed ...
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### Forecasting time point not value

I have a simple question. when we want to forecast a time series, we always focus on the value of series in future. But could we forecast time point of spesific value? For example I would like to ...
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### Prediction Interval , Confidence Interval , Standard error

What is the relation between Confidence Interval and prediction interval and, standard error for a point estimate? Please explain with an example. As per my understanding, the standard error is a ...
52 views

### How to find prediction interval when there is >1 response variable

I have been working on a data set where there is more than 1 response variable (multi-output). I used random forest for this model. The data set has 17 predictor variables and 2 output variables. I ...
122 views

### Can MAD (median absolute deviation) or MAE (mean absolute error) be used to calculate prediction intervals?

From my understanding, RMSE (root mean square error) estimated through cross-validation can be used to calculate the prediction interval of a mixed-effect linear model with gaussian error. In my case, ...
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### Estimating probability density for forecasts

I've used a handful of algorithms for forecasting future values in a time series. But sometimes what I'm really interested in is not the predicted value, but the probability that some future will be ...
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### How do the forecast intervals from an AR model behave when the time series is inherently stationary?

I'm trying to wrap my head around two contradictory intuitions behind how forecast intervals should behave when we use an AR process to model a stationary time series: (a) On one hand, since the time ...
26 views

### Confidence in Forecasted Median

Suppose I am measuring the time it takes to complete tasks, and I am looking across a year period, say 2019. At the end of the year, I will report on the median time taken across all tasks. Assume ...
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### Predict periodic event with multiple guesses and re-alignment

Suppose there's a metronome set to 60 bpm. Without hearing or looking at the metronome, we need to predict when it ticks. A prediction is considered correct if it ...
48 views

### How to test whether individual fits to regression line or not

I have a defined regression model for the healthy control (HC) group, with corresponding CIs of coefficients and of E(Y). I would like to test whether individuals belonging to another population (...
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### Deming regression prediction interval using jackknife resampling

I am trying to write a custom Deming function following the maths in Linnet (1993): https://www.ncbi.nlm.nih.gov/pubmed/2281234 Using jackknife resampling I calculate the standard error for the ...
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### Predictive value of a predictor - model choice

I have been stuck on this for a while. I am supposed to find the "predictive value" of a predictor - entrance exam score. Together with the entrance exam score also grades from the first semester are ...