Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [variance-decomposition]

A decomposition of variance explained by a model into additive contributions from each predictor.

3
votes
0answers
68 views

Decomposing R^2 into independent variables

Consider a linear regression model: $$y = β_0 + β_1X_1 + β_2X_2 + ... + β_kX_k + ε$$ where $R^2 = 1 - (SSR/SST)$. I would like to determine the contribution of a factor $i$ (call it $R^2_i$) into ...
1
vote
0answers
34 views

Correcting for ARCH effect in VAR and impulse response results

I find significant ARCH effect in my series when running a VAR analysis $Y_t=(y_{1,t};y_{2,t};y_{3,t};y_{4,t};y_{5,t})^\top$ I have two questions: Does the ARCH effect impact the impulse response ...
2
votes
1answer
50 views

Graphical proof of variance decomposition for linear regression

Suppose we aim to predict $Y$ from $X$ using the linear regression model $Y = mX + b$. There is a standard variance decomposition: $$\operatorname{Var}[Y] = \operatorname{Var}[\widehat{Y}] + \...
0
votes
0answers
27 views

Find contribution of various features/input variables to the variance of the dependent variable / Attribute variance of dependent variable to features

I am working on this problem where I have 20 odd features (input variables) and two dependent variables. The objective is to find the variance structure of one of the dependent variables. More ...
1
vote
0answers
127 views

STL decomposition - independence of components

Let's suppose we have 3 vectors $U_1$, $U_2$ and $U_3$ we construct another vector $V=U_1+U_2+U_3$. If $X$, $Y$ and $Z$ and independent, we can expect that $VAR(V)=\sum_{i=1}^3 VAR(U_i)$, right? Now ...
3
votes
1answer
4k views

Interpretation of Impulse Response and Variance Decomposition Graphs

I am finding it difficult to interpret the following Impulse response and variance decomposition graphs-basically studying the effect of currencies on each other(I know the results from the Granger ...
2
votes
0answers
211 views

Calculating orthogonalized impulse response functions for vector error corrrection models

Background: I am working on orthogonal impuls response functions (OIRFs) for vector error correction models (VECMs). Its an exercise to develop understanding. I am given a bivariate VECM: $$ \Delta ...
1
vote
1answer
338 views

Is there a way to “decorrelate” autocorrelation?

Just as how Principal Component Analysis tries to "decorrelate" the signals, is there a way, given a time series potentially with autocorrelation with unknown lag length, to transform that time ...
1
vote
0answers
161 views

Granger causality and variance decomposition yield conflicting results

I am analyzing a VAR model with 8 variables and 12 lags. When analyzing Granger causality test - it seems there is no relationship between some of the key variables, monetary policy rate and loan ...
1
vote
0answers
319 views

Vector Autoregression Historical Decomposition

I would like to perform a historical decomposition of my VAR model that is identified with timing restrictions, similar to that in figure 10 of this paper: http://pubs.aeaweb.org/doi/pdfplus/10.1257/...
0
votes
1answer
245 views

Variance decomposition (svar)

I was reading the paper by Gromping (2007) about variance decomposition. I was refering to page 141 (LMG) but I do not know what is meant in statistics by $\operatorname{svar}\left(\{1\}| \emptyset \...
0
votes
1answer
338 views

Share of variance explained by individual predictor [duplicate]

I am interested in how to calculate portion of explained variance of each individual independend variable in regression equation. So regression model is $y=b_{0}+b_{1}x_{1}+...b_{n}x_{k}+\epsilon$ ...
1
vote
1answer
322 views

How to calculate variance contribution in a Zero-Inflated Poisson regression?

I was wondering if anyone has an idea on how to calculate the contribution to variance of each independent variable in a Zero-Inflated Poisson. How would it even work if you actually have two models ...
1
vote
0answers
388 views

Compute Forecast Error Variance Decomposition for variables outside the Vector Autoregression

I am replicating the paper of Ang and Piazzesi (2003) in the Journal of Monetary Economics (link: here) where they estimate a Vector Autoregression for both unobservable factors and observable ...
0
votes
0answers
17 views

Are there behavior genetic models for multinomial outcomes?

I am thinking of the standard behavior genetic model of decomposing the variance in an outcome variable into ACE components. I will have outcome variables of different kinds: linear, dichotomous, ...
2
votes
0answers
380 views

Decomposition of variation into cross-sectional and time series variation

I have a panel dataset covering 20 counties and I have 150 monthly datapoints for each country. Specifically, my data consists of stock returns from each individual country. I want to dig deeper into ...
1
vote
1answer
242 views

Is there a method similar to commonality analysis but can be applied beyond the scope of multiple regression?

I got one dependent variable and six independent variables. All of them are continuous. First, I built a linear regression model, but the R2 was only 0.22. Then I tried to build a random forest model ...
8
votes
2answers
1k views

Interpretation of Total Law of Covariance

let $X,Y,Z$ be random variables defined on the same probability space and let covariance of $X$ and $Y$ be finite, then the law of total covariance / covariance decomposition formula states: \begin{...
0
votes
0answers
105 views

Random Variable Decomposition Standard Error

I have a decomposed random variable $X$ into partitions $A_1,A_2,\dots A_m$. I know how to compute the expected value of X and the variance of X given the variance and the standard errors of $X$ ...
1
vote
0answers
492 views

How to explain to laypeople that in a VAR model some variable explaines its own variance?

Background: I observed that people not familiar with vector autoregressive (VAR) models often struggle with the interpretation of a forecast error variance decomposition. I am frequently asked, why a ...
1
vote
0answers
29 views

Varaince decomposition without stochastic variance

I am working on an analysis that doesn’t feel natural until now. I am trying to analyze a dataset that consists of the prediction results of forest growth simulators, so actually I’m trying to make a ...
3
votes
1answer
876 views

Sum of Square decomposition

Question about the Total, Explained, and Residual Sum of Squares. I am in the simple linear regression model. Could you help me clarify why the residual sum of squares (SSE where E stands for errors) ...
2
votes
1answer
72 views

Question about an expectation

Let $x$ and $\gamma$ be vectors. Here it says that $$E[y-x'\gamma]^2 = E[(y-E[y|x])^2 + (E[y|x]-x'\gamma)^2]$$ However, I don't see why $$E[(y-E[y|x])(E[y|x]-x'\gamma)] = 0.$$ By the way, $E$ is the ...
1
vote
0answers
160 views

Decomposition of a random vector into uncorrelated components

I have a set of random vectors $Y_i$ and their correlation matrix $C_{i,j}$. Each vector can be thought of as a sum of two uncorrelated vectors $Y_i=A_iX+B_iY$, where $X,Y$ are the same vectors for ...
9
votes
1answer
14k views

Additive vs Multiplicative decomposition

My question is a really simple one but those are the ones that really get me :) I don't really know how to evaluate if a specific time series is to be decomposed using an additive or a multiplicative ...
4
votes
1answer
2k views

Meaning of covariance matrix row sums

Say I have an $n \times n$ covariance matrix for a sample set of $n$ random variables. Is there any meaning if the sum of the rows of this matrix? Is it a meaningful measurement of the contribution ...
13
votes
3answers
22k views

How to split r-squared between predictor variables in multiple regression?

I have just read a paper in which the authors carried out a multiple regression with two predictors. The overall r-squared value was 0.65. They provided a table which split the r-squared between the ...
24
votes
2answers
7k views

Collinearity diagnostics problematic only when the interaction term is included

I've run a regression on U.S. counties, and am checking for collinearity in my 'independent' variables. Belsley, Kuh, and Welsch's Regression Diagnostics suggests looking at the Condition Index and ...