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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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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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What is the implication of using joint versus conditional probability in this definition of a prediction interval?

I quote an excellent answer from @whuber here on the interpretation of prediction intervals. A prediction interval (for a single future observation), given by endpoints $[l(\mathbf{x}), u(\mathbf{x}...
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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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Prediction Interval for linear model with fixed effects

I've got a panel data and I'm using a linear model with fixed effects for individuals and time, along with other covariates to explain the variation in a dependent variable. I'm clustering my standard ...
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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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How to predict how many customers are going to purchase based on population purchase frequency?

I am trying to calculate a metric "frequency of purchase of a customer" to determine when I would expect a customer to then purchase an item next. Say, the distribution of my customer base looks like ...
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Exact definition of very short term load forecasting(VSTLF) and short term load forecasting(STLF)?

In the research papers, I have read that VSTLF is for minutes and hours ahead, whereas STLF is for days and weeks ahead. However, If I do a week ahead prediction of load data with a 5 minute ...
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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. \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 ...