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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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Prediction interval of Y given AR model for log(Y)

I have been given an AR model with seasonal variation. \begin{equation} (1-\theta_1B)(1-\theta_2B^8)(log(Y_t)-\mu)=\epsilon_t \end{equation} Setting $X_t=log(Y_t)-\mu$ one gets the following \begin{...
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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 ...
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Making a model to predict the error of another model

So basically I have a machine learning model where I want to have a prediction interval, the model is XGBoost so it is tricky to do Quantile Regression and I was looking for an alternative method to ...
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using attribute outcomes to define variable limits

I am working on developing a specification for peel strength of a package (looking for a minimum value, higher is better). The limit of where it is considered "good" is determined by a leak test (pass/...
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Posterior predictive distributions and predictive intervals

I'm confused about the role of posterior predictive distributions in Bayesian inference and predictive inference. As I understand it, the frequentist approach would typically involve fitting the MLE,...
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Evaluation metric for prediction interval?

In quantile regression (https://en.wikipedia.org/wiki/Quantile_regression), what are some suitable evaluation metrics? Intuitively, I think a good model should have: good accuracy, i.e. the ...
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Interpreting prediction intervals, and prediction intervals for a specific parameter?

Can someone correct my thinking if I'm off course here? Confidence intervals provide an estimate of precision$^1$ for a specific parameter, but they can also be used for a regression equation (i.e., ...
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How to get prediction interval from a model obtained in h2o?

From an AutoML Leaderboard on H2O, I selected a Stacked Ensemble model. I used this model to predict, using a new data set, and now I would like to obtain prediction intervals in addition to point ...
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Linear Regression: Calculating a treatment effect directly in regression vs. averaging potential outcomes

Suppose I have the following true model, where an individual $i$ at a particular point in time $t$ is either treated ($W=1)$ or untreated ($W=0$). The outcome for individual $i$ at time $t$ under ...
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Can I assume the normality of prediction interval?

Can I assume the normality of the prediction interval for an arbitrary machine learning model? Or in general, the prediction error can follow any distribution?
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Prediction intervals exponential smoothing statsmodels

I've been reading through Forecasting: Principles and Practice. I am working through the exponential smoothing section attempting to model my own data with python instead of R. I am confused about how ...
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Quantiles of transformed series

Possibly stupid question, but I need to ask. Let's have a time series $S_{n}$ of a same market asset. Let's $R_n = ln(S_n/S_{n-1})$ be an asset returns. So, I could forecast same $\overline{R}_{N+1}, \...
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Forecast Confidence intervals for for AR(P) [duplicate]

I want to contruct 12-step ahead forecast confidence intervals (CI) for AR(2) models and above. However, the CI calculation seems extremely tedius for forecasts above 2 periods as iteration process ...
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How to calculate a prediction interval for the mean of multiple new responses

I am using a Neural Network to estimate Ecosystem Respiration (ER) and Gross Primary Productivity (GPP) from Net Ecosystem Exchange (NEE) observations where. NEE = GPP + ER I've used the model to ...
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Forecasting and prediction intervals for aggregates

I have monthly time series and I need to make predictions for the next quarter. However, for operational reasons, the forecast must be made one month before the quarter. That way, I need, in practice, ...
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Prediction Interval on a Product

As a (perhaps) less offensive twist on this question, suppose that $z_i$ are independent $p$-variate standard normals: $z_i \sim \mathcal{N}\left(0, I\right).$ Let $a$ be an unknown $p$-vector. ...
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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 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 ...