# 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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### 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 time series, where the model is some auto-regressive function $$y_t=f(y_{t-1},x_{1t},x_{2t})$$ is it a valid approach to use sections of historical data to ...
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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 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 ...
1 vote
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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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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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### 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 ...
1 vote
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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 ...
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### 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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### How could I find the prediction interval of a future observation given the present dataset?

I am given a dataset from an unknown distribution and asked to find the 99% approximate prediction confidence interval for the future observation. I'm afraid I do not understand what making ...
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### Prediction interval for a Weibull distribution

Suppose I am producing units and have tested the failure time of some proportion of them (say 10%), possibly with some right censoring if they didn't fail within the testing period. I'm able to fit a ...
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### Question regarding GARCH modeling using RUGARCH package in R

I have 2 questions regarding ARMA-GARCH modelling using rugarch package In R Question 1 This may be an elementary statistics question . But i couldn't find out a way to do this. I have simulated ...
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### Forecasting a year ahead using annual vs daily data

Suppose, as an example, that you would like to forecast a share price in a year's time based on the past 20 years of data. You can either use annual data and forecast 1 period ahead, or use daily data ...
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### Predicting an interval by deep learning or other machine learning methods

I have a distribution built on an interval for example [v_min, v_max], given a good estimate on the interval, the performance of the model can be good. If the ...
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### Prediction interval for summed dependent variable from multiple linear regression

I have performed a multiple linear regression to forecast 12-month sales from 6-month values (for various predictors) per customer. I obtained y-values per customer and respectively summed the ...
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### Prediction interval of Y given AR model for log(Y) [duplicate]

I have been given an AR model with seasonal variation. $$(1-\theta_1B)(1-\theta_2B^8)(log(Y_t)-\mu)=\epsilon_t$$ Setting $X_t=log(Y_t)-\mu$ one gets the following \begin{...
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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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### Calculating forecast intervals for user adjusted forecasts?

My demand forecasting solution generates point forecasts and forecast intervals for millions of time series (# of products × # stores for a large retailer) using statistical models. Business users (...
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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? [duplicate]

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 ...
1 vote
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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

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 $\overline{R}_{N+1}, \overline{R}_{N+2}, ... , \overline{R}_{N+j}$,...
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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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### 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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### 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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### 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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### 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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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 $\log(y) = a + b_1 x_1 + b_2 x_2 + e$, ...