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.

Filter by
Sorted by
Tagged with
0
votes
0answers
19 views

How to calculate uncertainty for predictions coming from cascade of models?

I have developed a bunch of models to predict house prices. It is a 3 fold process: I fit a gbm (first_model) and get the first prediction (first_pred), there are some sub-models (simple lineer ...
0
votes
1answer
27 views

Likelihood that a prediction falls above (below) 110% (90%) of the prediction

For my client I have to predict some products' prices with gbm (scikit). So in the production, I am to give prediction intervals. That is, I need to provide how likely a real price falls above 110% or ...
0
votes
0answers
12 views

Prediction intervals for location scale model

Regarding the example below from Chapter 3 of A.C. Davison's Statistical Models, I'm wondering why $Q = (Y_+-\bar Y)/S$ depends only on $g$.
1
vote
0answers
52 views

Why does prophet produce much tighter prediction intervals than ETS?

I'm currently working on a forecast problem, where narrow prediction intervals are preferred. When I look at the prediction intervals of ETS and prophet forecasts, I'm surprised that the prophet ...
2
votes
1answer
71 views

How to calculate prediction interval in GLM (Gamma) / TweedieRegression in Python?

I have checked much source from webs about conducting the prediciton interval, especially in GLM function. One of the approaches is about Prediction Intervals for Machine Learning https://...
0
votes
0answers
20 views

Prediction interval for linear regression with autoregressive error

Suppose that ${y_{t}}$ and ${x_{t}}$ are time series variables. A simple linear regression model with autoregressive errors of order ${p}$, say AR(P), can be written as \begin{equation} y_{t}= \...
0
votes
1answer
32 views

Prediction of Variance vs Variance of Prediction

Is the prediction of the variance the same as the variance of the prediction? I know the concept of prediction intervals, used to specificy the variance of the prediction. I also know (G)ARCH models, ...
0
votes
0answers
44 views

Generic Prediction Interval Methods

I'm trying to implement a generic method to calculate prediction intervals for univariate forecast methods. While the literature is quite clear on how such a prediction interval is define (e.g., here ...
1
vote
0answers
17 views

How to intuitively understand the shapes of confidence and prediction intervals in simple linear regression [duplicate]

Assume the linear regression $Y=b_{0}+b_{1}X$ The $100(1-a)$% prediction interval for $x=x_{*}$ is given by whereas the The $100(1-a)$% confidence interval for $E(Y|X=x_{*})$ is given by What I don'...
1
vote
2answers
40 views

How to interpret confidence interval and prediction interval in simple regression “in/with the context of sampling distribution”?

With the context of sampling distribution, in regression analysis, is the following an appropriate interpretation? Assumptions : X & Y have a linear relationship sample size is large enough for ...
0
votes
0answers
124 views

Prediction of Mean and Variance with remlscore?

I would like to do a prediction of the mean and variance with confidence and prediction intervals using remlscore in statmod, i....
0
votes
1answer
22 views

Is it possible to calculate the prediction intervals for top down, bottom up, and middle out reconciliation of hierarchical time series?

I have read in several places (heres one) that we can not calculate prediction intervals for the classical reconciliation approaches, top down, middle out, and bottom up, and hence optimal ...
1
vote
1answer
56 views

Accounting for multiple layers of uncertainty in a model

Let's say I have data on 10 stores that sell widgets, each of which received num_orders number of orders in a certain timeframe, and sold a total of ...
1
vote
0answers
34 views

What is the probablity the y value produced in a linear regression is correct?

Apologies in advance if I am using the wrong terminology. Is the y value produced by a linear regression model assumed to be the mean of a normal distribution? Meaning there is a 50% chance the actual ...
1
vote
0answers
34 views

Prediction interval for regression with time series data

Suppose that ${y_{t}}$ and ${x_{t}}$ are time series variables. A simple linear regression model with autoregressive errors of order ${p}$, say AR(P), can be written as \begin{equation} y_{t}= \...
0
votes
0answers
41 views

Calculating the quantile of random forest test cases

I want to calculate the quantile of the observed value of a test case with respect to the prediction interval generated from a random forest, so for each test case I want the proportion of the ...
1
vote
0answers
77 views

Prediction intervals from Linear regression and Arima for DYNAMIC forecasting

I am comparing prediction intervals from linear regression and ARIMA for a simple AR(1) model: p = lag(p) The models were built on monthly data from 2003-2013 years. Predictions were made for 2014 ...
1
vote
0answers
21 views

Calculate prediction interval with stats::predict

I'm forecasting for the first time, so please for some patience. I want to calculate lower bound of 95% interval on my point forecast. I have the following model for estimation and forecasting a ...
0
votes
0answers
13 views

Сonfidence interval mean response and prediction interval for Instrumental Variables regression

I evaluated the regression model using the 2SLS method which is presented in the ivreg R package. Using predict can get fitted ...
0
votes
1answer
47 views

Utility of the whole distribution (other than the mean) in Bayesian posterior predictive

In prediction task, when using Bayesian fashion of predictors, I think in most the cases, people just use posterior mean for each individual estimate. I wonder if there's any utility of the higher ...
1
vote
0answers
18 views

Using AIC weights to determine prediction intervals for a single model structure

I am working with fitting regression models to data, and producing prediction intervals would be useful. Unfortunately, the data often has few data points, and is reported as mean rather than ...
4
votes
1answer
94 views

Quantile regression vs probability density estimation

If you want to predict a range for a regression problem using a deep network, you can do quantile regression and go with (for example) 5% and 95% quantiles. The other option is predicting a ...
0
votes
0answers
25 views

Bootstrap and prediction interval (Kumar & Srivastava 2012)

I am reading the paper Kumar & Srivastava (2012) and I am trying to understand it. However, I have some difficulties to understand some elements in the paper. First of all, let me present you some ...
0
votes
1answer
42 views

How to Derive Prediction Intervals for Orthogonal Distance Regression using `scipy.odr`?

Questions How can I derive prediction intervals for predictions based on new observations from the output of scipy.odr? Is it also possible (or necessary) to take ...
1
vote
0answers
15 views

Marginal mean after OLS, where X is a combination of seen and unseen observations

Looking for advice on a package in R or Python and an approach to help me construct a confidence interval for a marginal mean (or maybe we'll call it a prediction). Say I run OLS regression with $y$ ...
1
vote
0answers
45 views

Prediction Intervals (Conformal Predictions) for Regression Problems

So I've been looking into the idea of looking into conformal predictions, or to obtain prediction intervals instead of just single point predictions. Basically my take is that I would have my deep ...
2
votes
0answers
43 views

How do I calculate confidence level or interval?

I have this data for exam grades in English Literature: 2019: the numbers achieving (A*, A, B, C, D, E) are (1, 5, 4, 7, 2, 0, 0) 2018: the numbers achieving (A*, A, B, C, D, E) are (2, 4, 3, 7, 0, 1, ...
1
vote
0answers
20 views

Significance of datapoint outside prediction band

With linear regression I am plotting 25 bodies of text with their vocabulary count (independent variable X) and occurrence of a particular word (for example: "this"). I have a linear ...
0
votes
0answers
18 views

Why do different divisions of the same text corpus result in different regressions?

Background I am comparing a small text of 169 words to a bigger text consisting of 19.000 words. I am trying to plot a linear regression of different texts that can result from the different ways of ...
1
vote
0answers
22 views

How to calculate the prediction interval for regression through the origin?

I know the predicative interval for a single value of Y for a given Value of X_0 is: However, what would this formula be if the regression was forced through the origin?
0
votes
1answer
34 views

variance of theoretical mean of y at given value of x in regression [duplicate]

Could someone tell me where I might find information on deriving the standard error used in confidence and prediction intervals of y at a given value of x on a regression line. I can't find anything ...
4
votes
2answers
299 views

Prediction intervals for a single random variable

Prediction intervals seem to be talked about most in the context of regression, but I want to reduce it to one random variable to understand the reasoning. Assume you are sampling from a normal ...
5
votes
3answers
294 views

Why are the ends of the prediction interval wider in the regression? [duplicate]

Usually, the prediction interval has this shape in the image. I don't know why the end of the interval is wider than the center.
0
votes
1answer
112 views

Neural Network Assumptions in a Time series

I was wondering whether an artificial neural network regression, like ARIMA, requires statistically insignificant residual autocorrelation -- and, if so, why? I presume that, if I am using the ANN ...
1
vote
1answer
32 views

Project time series from previous time series examples and characteristics

Say I want to open a shop but first I want to project the likely sales in the first 5 years to see if it is a viable option. I have data pertaining to 100s of other start ups, including their success ...
0
votes
0answers
53 views

How do I compute the prediction interval by hand for a multiplicative time series decomposition model?

Say, I use a simple multiplicative decomposition on a time series dataset as defined in Chapter 6.8 of FPP2: $y_t = \hat{S}_t \times \hat{A}_t$, where $\hat{A}_t = \hat{T}_t \times \hat{R}_t$, so ...
1
vote
0answers
12 views

Predicting Rare Events (Incidents) from Sequence Data: Using RNNs

I have a problem I am interested in, and I am thinking of it in the context a neural network sequence model (any appropriate variation of RNN) BUT please correct me if another model is more apt: Data:...
0
votes
1answer
45 views

add linear trend back into time series prediction (in R)

I have the following GARCH(1,1) model ...
1
vote
1answer
51 views

How is modeling the time series error/variance, e.g. ARCH or GARCH models, different from modeling time varying forecast intervals?

I'm having a hard time understanding the intuitive difference between modeling the volatility or variance of a time series as it is done in ARCH and GARCH models: $$Y_t = c+\epsilon_t+\phi_1Y_{t-1}+....
0
votes
1answer
30 views

Understanding plot for stats::predict

I created a time series for 15 years (in each year 123 days), and I created a forecast using stats::predict for the next 5 years. ...
1
vote
1answer
29 views

OLS Prediction Error of sum of m future observations

A paper I'm reading states the "The prediction error of a sum of m future observations (as is needed for determining energy savings) is given by Theil (1971)" Due to covid I don't have access to the ...
0
votes
0answers
15 views

Bootstrap method for the construction of PI

I did physical measurements with a machine. There I could set 3 independent input variables and got 10 dependent output variables (qoi) per measurement. I did 1000 measurements. Thereby the shape of ...
1
vote
1answer
46 views

how to get predicted intervals? code no giving me those values [closed]

I am doing a cross validation in a training data and I am getting my predicted values with my test data. I want to do a plot with predicted versus observed with the predicted intervals but my code is ...
0
votes
0answers
5 views

Business-driven regression metric interpretation

I'm working on a model for income prediction and use RMSE as a metric for it. The desired output is the true_income±delta i.e. ...
0
votes
0answers
15 views

Prediciton interval estimation for GBDT and sum of prediction

I want to create an estimate of the prediction interval for the sum of predictions n-steps ahead for a general estimator f(X) in the presences of auto-correlation in the residuals, and less training ...
0
votes
0answers
44 views

Does the length of a prediction interval decrease with sample size?

For a general prediction interval given by $x_{0}^T\hat{\beta} \pm t_{n-p,\alpha/2}\times s \sqrt{1+x_{0}^T(X^TX)^{-1}x_{0}} $, I have been taught that as n tends to infinity we can approximate this ...
1
vote
0answers
18 views

Estimation of out of sample confidence interval

Background: I have estimated the following logistic function y(t) = a/(1+bexp(ctime)), where a, b and c are the estimated coefficients, and time = 1,2,3,,,T. I want to project y into the future t = T+...
0
votes
0answers
24 views

Average Coverage Error (ACE)

This paper mentions ACE. It is defined as following ACE = PICP - PINC where PICP and PINC stand for Prediction Interval Coverage Probability and Prediction Interval Nominal Confidence, ...
0
votes
1answer
118 views

Calculating Prediction Intervals for multistep univariate time series forecasting using Bootstrapping

I understand the way to compute the prediction interval at 5% and 95% for one step forward forecast based on Bill's answer to the question at Bootstrap prediction interval. The idea being that based ...
1
vote
0answers
230 views

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 ...

1
2 3 4 5
9