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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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Principles behind time-series forecasting intervals

So, this is truly a bit of a general question, but I am not aware of the guiding principles (if there are any) behind forecasting intervals. For whatever time-series model one might be using, whether ...
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Prediction interval for rolling average forecast

In agile software development average of last 3 delivered periods (sprints) is taken to forecast next periods deliverables. I'm not here to discuss if the approach is correct or not. ;) According to ...
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Prediction intervals for THieF

I would like to add prediction intervals to a temporal aggregation using the thief package. Can someone point out either how to automatically plot prediction ...
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Is a comparison between Bayesian and frequentist prediction intervals sensible?

I am aware that frequentist confidence intervals and Bayesian credible intervals have quite different interpretations, and are not comparable. I'm wondering if the same is true for prediction ...
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Reality check: Given $k$ and an estimate of $n$, solve $B(n,p)$ for $n:p\approx1$?

Back Pedaling Honestly, I'm not even sure if this is the right question but I haven't been able to come up with anything that makes more sense so I'd appreciate some help. This is a real problem, not ...
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Compute forecasts and 90% forecast intervals for ARIMA(p,1,q) models

Consider the two models (ARIMA(1,1,0) and (ARIMA(0,1,1)):
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Approximate prediction interval in linear regression

Suppose we have a linear regression model of the following format : $$ y(x) = \beta_0 + \beta_1 x_1+ \beta_2x_2+\beta_3x_3+\epsilon$$ We know that the prediction interval associated with a level $\...
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Returns forecast back to closing price?

I'm working with log returns. I've selected an ARMA-GARCH for mean and volatility forecasting and I would like to get the forecasted confidence intervals and plot expressed in terms of the closing ...
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What is the relationship between the prediction interval of an ARIMA(p,d,q) and the prediction interval of the original variable

The title may be enough, I want to know what is the relationship between the prediction interval of an ARIMA(p,d,q) and the prediction interval of the original variable. Lets say that d = 1, so that I ...
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Is bootstrapping suitable for deriving prediction intervals in models which randomly sample from distributions?

I'm working with a fairly complex predictive model which essentially produces total populations for different groups in future years. Joiners, leavers, and transitions between the groups are modeled ...
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How to get a density from a forecast with prediction interval

Some reproducible code to have in your environment a time series and a possible forecast: ...
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Prediction interval for log transformed variable in Stata [duplicate]

I want to predict $y$ with $x_1$ and $x_2$, including an out of sample prediction interval. However, $y$ has large outliers, so I log transform $y$ and estimate $\log(y) = a + b_1 x_1 + b_2 x_2 + e$, ...
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How to correctly compare the accuracy of different forecasting methods using bootstrapping with time series forecasting

I am currently working on a forecasting project and I have tried several different models to forecast with. Having trained and tuned my models I want to pick which model works best for each time ...
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Machine Learning - Prediction Interval - Cheating?

I work at a company that is trying to use machine learning methods in particular gradient boosting and neural networks to make predictions on stock market data, so using historical data to predict ...
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Quantile-Regression and Grid-Search

i am currently experimenting with quantile-regression in h2o. I am building prediction intervals. For the individual regression models i am looking after R^2, RMSE and also quantile-loss. I performed ...
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Calculating prediction bounds from composite data

I have several (partially overlapping) data curves of oscilloscope-measured detector voltage as a function of time (very simple hypothetical example as follows): There is an underlying physics ...
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Probability for mean of a subpopulation

Suppose I have drawn 21 samples from a population which I assume to be normal, where the sample has mean 3.8 and sample standard deviation 0.7. What is the probability that the mean of the next 210 ...
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How to test whether 2 prediction intervals are statistically different?

I've been struggling with this for a while now, hopefully someone will know how to help me :) Here it is : 1) I'm using a linear mixed effects model on longitudinal data (biological values of many ...
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Is this interpretation of prediction intervals correct?

I have a regression model relating to a ''normal'' population. If a new observation which corresponds to point $x$ is outside the prediction interval at $x$, do I have a reason to suspect the new ...
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Measuring uncertainty of a fitted calibration curve

My question is: how can you compute the prediction interval of a calibration curve, just like you might for any other regression model. A calibration curve maps estimated probabilities to empirical ...
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How to calculate prediction intervals for p values using just the obtained p value (Cumming, 2008)

I've been reading over Cumming (2008) on replication and p intervals. I don't appear to be able to replicate calculation of his p interval for p obtained = .05 following formula B3. I'd very much ...
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How to test whether a prediction interval truly captures 95%?

I want to analyze the 95% prediction intervals for a model. The true values should fall within the prediction intervals 95% of the time (on average) if the interval is well calibrated. If the ...
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Prediction interval for sampled count data

I am trying to get prediction intervals around a sampled count variable. For example, say I want to know the number of letters an apartment building receives every day. Each day I record the count ...
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How to you measure the accuracy of a model that gives quantile forecasts or distributions of forecasts?

I've come across some recent demand forecasting approaches that present methods where instead of generating just a point forecast, the model outputs a set of forecast quantiles, or a distribution of ...
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Confidence or prediction interval for in-sample prediction?

I'm trying to make a plot of the uncertainty interval of in-sample prediction ...
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Prediction of random sum of binomial variables

Let us concider $\xi\sim\sum\limits_{i=1}^v\text{Bin}(1,p):=\sum\limits_v\eta$. Where $v$ is random variable with unknown distribution. Let $\mathbb{E}v^m<\infty \quad\forall m$. We know, that $$...
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Bootstrap intervals for predictions, how to interpret it?

I want to come up with a way to get how confident I am in my predictions. I am not using a Bayesian model so I was thinking a bootstrap confidence interval would be good: I would re-sample my ...
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Do regression algorithms give you a probability associated to each predicted value?

I am looking for an algorithm to predict an amount of money (a real value), therefore I am thinking of using a regression algorithm. However, I also need to know the probability associated to that ...
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which fraction of training set should be contained in prediction interval?

Im using Rs lm function to make a linear regression of some datapoints (10-50 points) ...
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Compare forecast interval between ARIMA and ARIMA/GARCH

I tried to compute parameters of ARIMA/GARCH in two step. The first one is to build ARIMA and then fit GARCH using iid Gaussian MLE estimation. The second one is to construct ARIMA/GARCH ...
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How to interpret forecast output in words

May I ask you guys regarding forecast in R? How should I interpret this graph? Please describe it in easy-understandable words.
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Prediciton interval for lasso regression with time series data

I am currently working with time series data. My objective is to predict the a certain value at time t given some other variables that we will know the same day ( but prior to our objective variable). ...
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2answers
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Plus/Minus Model accuracy from $R^2$

I completed a linear regression for a model I was working on, and obtained that the $R^2$ value was $R^2 = 0.801$. Can one assess a $\pm$ error from this value for future predictions? I.e., if I now ...
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Probabilities of different forecasts from linear regression

Let's suppose for the sake of simplicity that we have the following linear regression: Y=a+b*X Where Y would be the sales of ...
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Bootstrapping Prediction Errors

I'm trying to bootstrap non-parametric prediction errors for a model I'm building. My understanding is that the procedure below should yield bootstrapped predictions and prediction errors, with the ...
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Multistep prediction interval for ARMA(p,q) process

How do I find an $h$-step prediction interval (forecast interval) for a zero-mean ARMA(p,q) process $$ x_t = \varphi_1 x_{t-1} + \dots + \varphi_p x_{t-p} + \varepsilon_t + \theta_1\varepsilon_{t-1} +...
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How to make $h$-step interval forecasts from an ARMA-GARCH model?

I recently wrote various Python functions to fit ARMA models and make forecasts from them. I am now trying to do the same for ARMA-GARCH models. To make $h$-step forecasts from ARMA models, I used ...
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Estimated Mean and Confidence Interval and Predicted Value and Prediction Interval

This question comes from Ramsey and Schafer Statistical Sleuth, Second Edition, Chapter 7: Immediately after slaughter the pH in postmortem muscle of a steer carcass is around 7.0-7.2. For a ...
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Prediction intervals with experimental errors

Engineer here, so apologies for my simplistic stats language. I am missing some experimental data that I would like to "fill in" based on a linear regression to other data. I need to do this because ...
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Choosing model to predict next value in a sequence

Background: I am currently starting to work on a Machine Learning project that might be of use in car racing. The goal of it is to give engineers suggestions about strategies. First thing I am ...
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Prediction interval in simple linear regression; classical v/s bayesian

Is there any conceptual difference in the prediction interval for simple linear regression between classical and bayesian statistics with non-informative prior?
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How to calculate prediction intervals using best-fit parameters when parameters covary?

I'm doing a nonlinear least-squares regression to find best-fit values for two parameters. I then want to use these best-fit parameters and their variances to extrapolate to a predicted value. It's ...
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Plotting $\alpha \%$ prediction bands

After calculating the relative errors of some predicted value vs the real value, I've made a plot of the relative error vs some property of my dataset (in this case the size); As you can see, the ...
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Why does Prediction Interval of lm function in R Return a Static Interval

I am looking for a simple method that will capture the relationship between predictor variables and the variance of the outcome. As a simple reproducible example consider this code where I ...
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157 views

Prediction Interval for Mean of Predictions

This question is about creating a prediction interval for the mean of predictions from a regressor. Let's say I have arbitrary regression function (not necessarily parametric, could be random forest, ...
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Resampling methods in derivation of prediction error

I have made a model which predicts some value $Y_i$ given $X_i$ where $i \in 1,...,N$. My ultimate goal is to predict $Y=\sum_i^n Y_i$ and to be specific the interval in which $Y$ lies within some % ...
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How to calculate prediction Intervals for a sum of predicted values from a mixed-effects model

I have a mixed-effects regression model and have predicted values with their respective prediction intervals. I would like to obtain the sum of these predicted values, and create a prediction interval ...
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179 views

ARIMA-GARCH vs. ARIMA

How do the prediction intervals for ARIMA models compare with ARIMA-GARCH models? Should we expect the prediction intervals for one to be narrower/wider than the other?
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confidence interval for RMSE for out of time forecast

I have built a loss model with my training data and obtain the RMSE. As part of performance monitoring to ensure the model is operating as intended, I performed an out of sample forecast using my ...
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How to create users preferences vectors from clickstreams, presuming the existence of multiple distributions of the preferences

Let's imagine we do have products which are conceptually described by 40 features, with scores between 0 and 1. Let's imagine the first feature is 'color'. 0 would be white, 1 would be black, just for ...