# 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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### How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

The question is a bit similar to question 147242 . I'm dealing with a multiple linear regression model, say:
$$
y = \beta_0 + \beta_1 x_1 + \beta_2 x_2
$$
and I'm looking for an algebraic equation to ...

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### Estimate an error bound for an estimate

I have two datasets regarding historical data (say, quarterly revenues for companies over time). The first is the actual results of this data and the other is available estimates for these results ...

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### Good proportion of training data to get prediction interval using bootstrap

I am trying to get prediction intervals thanks to bootstrap: I train 1000 linear regressions with different subsets of my training data.
Say I have 1,000,000 rows in my dataset, what would be a good ...

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### Does it make sense to propensity scores for re weighting samples in prediction tasks?

When reading the literature on propensity scores, the focus is mainly on estimating treatment effects (be it ATE, ATT, or else).
But that, in linear models terms, is equivalent to asking questions ...

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### Is there a possibility to combine WLS with bootstrapping methodology for prediction purposes in R?

This is my first post, so here I go: I used R to create a bootstrap prediction interval for a one-predictor logarithmic regression model. Here are the steps for the creation of the bootstrap ...

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### Buld prediction intervals for glmmTMB

I'm using glmmTMB to build a mixed effect logistic model from which I want to draw predictions.
The predict() function applied to a glmmTMB model allows extracting the ML prediction and the relative ...

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### Standard Error of prediction for Logistic Sigmoid function

Standard Error of prediction for Logistic Sigmoid function
(previously: Finding the prediction interval for logistic regression)
Update 2:
This paper describes what I am looking to implement.
...

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### Implementing Bayesian Linear Regression using PyMC3

I am learning a Bayesian Approach towards implementing Linear Regression.
The motivation is that Bayesian Approach gives you a range on predictions which might be useful when investing money in ...

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### (G)LM prediction interval with heteroscedasticity

I am trying to get prediction intervals from some non-linear data which also exhibits heteroscedasticity.
...

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### Prediction and confidence intervals interpretation for nonlinear data and linear model

I have a bunch of features that have an approximately simliar pattern. I've plotted a confidence interval and a prediction interval for one of them and I wonder weather CI and PI are meaningfull for ...

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### Prediction interval for OLS with non-normally distributed residuals

I'm estimating a multiple linear regression model (found in equation 19 of "The volatility of realized volatility", Corsi et al. http://www.econstor.eu/bitstream/10419/25467/1/515328057.PDF) using ...

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### Predictions on transformed series post intervention analysis

I have taken this logged data and performed an intervention analysis:
...

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### Regarding Hyndman's approach to estimating prediction intervals for forecasts generated by neural networks

I'm currently looking for ways to estimate prediction intervals from an LSTM generated forecast. Several advanced methods are suggested in the literature (e.g. SQF-RNN), but as a first pass, I'm ...

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### Upper 95% Prediction Bound

I understand calculating a two-sided 95% confidence interval for Beta1 of a simple linear regression model. Now I am stuck trying to calculate an upper 95% Prediction bound for y_star at the value of ...

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### How to compute the prediction interval with poisson GEE?

How do I compute using R the prediction interval for poisson GEE via geeglm? I prefer geeglm because of the "waves" argument.
Aside: I'm trying to predict what future counts of an event will be in ...

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### Forcasting with only total sale of product?

is it possible to make a forecast when you only have the total sale (of last year) per product variant? I would like to make a forecast for the next year 2021.
So for example, if last year's sale per ...

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### Can you use relative prediction intervals to compare models trained on a different response

Is there a reason not to use a relative prediction interval ( PI/target_value, for a constant PICP) to compare models with different target variables?

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### How to deal with Non-Linear prediction intervals with horizontal asymptotes?

I'm using a weibull regression on a data set which reports % total expenditures over time. Time is measured by % of project total completed, therefore neither the dependent or independent variable can ...

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### learn prediction intervals (variance, noise)

The problem:
I'm looking to emit prediction intervals for each predicted value (the mean) in regression. I need that these intervals cover say 90% of true values and be as narrow as possible. In other ...

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### Predicting the variance of a future sample

Suppose that I have the dataset for wealth distribution for 50 different countries. Each country's data consists of the wealth figures for 100 random individuals in that country. Some countries have ...

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### Predictive density via LOOCV

I am looking for a way to generate a density prediction (in contrast to a point prediction or a prediction interval) in a multiple regression setting without relying on stringent parametric ...

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### Interval and density forecast in R with both heteroskedasticity and non-normality in time-series data

We tried to get both an interval and density forecast based on time-series data, which we found to be both non-normal and heteroskedastic, in R.
We know that for non-normality, forecasts can be ...

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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 http://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 ...

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### 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 ...

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### 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 ...

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### 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 š 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 ...

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### 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 ...