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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3answers
114 views

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 https://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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1answer
37 views

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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1answer
39 views

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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1answer
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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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15 views

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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1answer
26 views

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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1answer
31 views

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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1answer
70 views

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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40 views

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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1answer
49 views

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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1answer
40 views

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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27 views

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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34 views

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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1answer
130 views

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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49 views

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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1answer
59 views

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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1answer
100 views

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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106 views

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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50 views

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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30 views

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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1answer
56 views

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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1answer
52 views

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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182 views

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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39 views

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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16 views

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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1answer
110 views

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 ...
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1answer
52 views

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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1answer
122 views

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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30 views

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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1answer
59 views

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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1answer
26 views

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 ...
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65 views

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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1answer
48 views

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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1answer
84 views

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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16 views

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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1answer
115 views

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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1answer
120 views

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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0answers
27 views

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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30 views

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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22 views

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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1answer
41 views

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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0answers
21 views

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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22 views

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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31 views

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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0answers
37 views

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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1answer
181 views

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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0answers
18 views

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/...