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What weighted average is OLS?

How can we find what sort of weighted-average a covariate is from a linear regression fitted with least squares? Consider the model $$ Y = \beta_0 + \beta_1 \tau + \sum_{j = 2}^k \beta_{j} X_{j} + \...
num_39's user avatar
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Difference between weight matrix and loading matrix in PCA

Currently I am working with PCA techniques (specifically sparse PCA techniques) but my question revolves around obtaining the weight matrix in PCA. This reference provides the following representation ...
Aryan's user avatar
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1 answer
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Matrix decomposition with constraints and weighted least squares

We have a matrix, $\mathbf{X}$, of probability distributions between 6 different results, so each row $\mathbf{x}_i$ sums to 1. We want to perform dimension reduction so that each row is a linear ...
jgf1123's user avatar
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Inconsistent Results with SEATS and X-11 Decomposition Models in R using fpp3

I’m experiencing inconsistent behavior when applying time series decomposition models in R using the fpp3 package and would like some guidance. I have a time series of Broad National Consumer Price ...
Fam's user avatar
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Can I instrument multiple (related) variables with a single instrumental variable?

I have a valid instrumental variable, $Z$, for my endogenous variable $DeathRate$. I can decompose the latter into components, e.g.: $$ DeathRate = DeathRate^{GroupA} + DeathRate^{GroupB} $$ Could I ...
Martin Georg Haas's user avatar
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Can we use decomposed time series in a test set to obtain models accuracy metrics?

Currently I'm cross validating (rolling time window, different test lengths) several forecast models to obtain performance comparison on highly skewed time series (due to true ocassional outliers). My ...
Tom's user avatar
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when doing an STL decomposition, is is possible to take the first derivative and get a confidence interval around it to test if different from zero?

when doing an STL decomposition, is is possible to take the first derivative and get a confidence interval around it to test if different from zero? I know this can be done with GAMS as shown in this ...
Justin Murphy's user avatar
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variance decomposition in factor models

Consider a linear model $\textbf{y} = \pmb{\beta}'\textbf{x} + \pmb{\varepsilon}$ with $\textbf{y}$ a $N \times 1$ vector of random variables, $\pmb{\beta}$ a $N \times K$ vector and $\textbf{x}$ a $K ...
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Why use integrals when building exponential composite functions?

I recently read this paper, which describes a generalisation for statistical exponential decay models used in ecology. Essentially, the parameter $k$ of the exponential decay function $f(x) = ce^{-kx}$...
Luka Seamus Wright's user avatar
1 vote
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37 views

Decomposition time series

I am studying a daily dataset from a game which contains informations about the peak of players from 2013-2023. This is my first try applying decomposition to see how time series components behaves. ...
Racamposx's user avatar
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50 views

Can we interpret residuals in trend-seasonality decomposition?

General case: to build a model of market for further quality estimation of our algorithms. (Predicting optimal price, demand prediction etc.) Current approach: take two features of a product - price ...
taciturno's user avatar
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2 answers
339 views

As Brier Score = MSE, does MSE in a regression have a calibration-discrimination decomposition?

When the outcome of a supervised learning problem is binary and probabilities are predicted, Brier score can be decomposed into a measure of calibration and a measure of discrimination. ...
Dave's user avatar
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Unpack the notation used in Wikipedia's decomposition of the Brier score

Wikipedia has an article about the Brier score whose notation confuses me. The article starts out easy enough by defining the Brier score to be: $$ BS = \dfrac{1}{N}\overset{N}{\underset{i = 1}{\sum}}\...
Dave's user avatar
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Can I use the residuals of a time series decomposition to estimate the effect of a covariate?

Context I work for a company that has an e-commerce website. Regularly we make specific campaigns in order to sell more. For example: We can make a campaign for fathers day, black Friday, crazy August,...
Guilherme Parreira's user avatar
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462 views

How to obtain seasonally-adjusted time series data using STL in Python

On the section "STL decomposition" in the 2nd edition of Forecasting: Principles and Practice, it says that the seasadj() function can be used to compute ...
Luca Guarro's user avatar
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30 views

Empirical Mode Decomposition(EMD) + CNN for time series forecasting

I'm currently working on a time series project, and I intend to employ the EMD+CNN technique for forecasting the output. Upon applying EMD to the training data, I obtained a total of 14 Intrinsic Mode ...
Shahin's user avatar
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How can I back transform the residuals of a decomposed time series , where I used log(x+c) transformation on the original data?

I did a time series decomposition on a series of Twitter activity data into trend, seasonal and residual component. I checked the distribution of the residuals when fitting a linear model to the time ...
Mim_Tauch's user avatar
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27 views

Seasonal component inconsistency in X-11 method using R

I am learning about time series decomposition using the X-11 method in R. I am following the book “Forecasting: Principles and Practice (3rd ed)” by Rob J Hyndman and George Athanasopoulos, which uses ...
Rony Golder's user avatar
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11 views

When to Split Data for Time Series Forecasting using Ensemble Empirical Mode Decomposition?

I want to forecast a time series data by using Ensemble Empirical Mode Decomposition (EEMD) and LSTM. However, I'm unsure about when to split the data into training and test sets. Should the data be ...
bella_pa's user avatar
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compute the Wold representation of this process

I want to find the Wold representation of $y_t = e_t + \alpha e_{t-1} e_{t-2}$, but I'm having difficulties with the product. For instance, I tried: $$ y_t = e_t + \alpha e_{t-1}e_{t-2} \pm e_{t-1}^2 ...
R__'s user avatar
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Theoretical analysis of STL decomposition

I would like to know if, for some specific models, the STL ("seasonal-trend decomposition using LOESS, see here) algorithm for time series analysis is proved to converge (in some sense). For ...
Plop's user avatar
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2 votes
0 answers
69 views

Why are Square Integrable Functions important in Statistics?

I'm reading a paper by Giles Hooker on Functional Decomposition through the use of Functional ANOVA. In the paper he defines a function: $$ F(x) : \mathbb{R}^k \rightarrow \mathbb{R} $$ and explicitly ...
Connor's user avatar
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Better default prior for non-negative canonical polyadic decomposition of counts than Exp(1)?

Suppose I have a instance of a random $k$-mode tensor $X_{n_1 \times \ldots \times n_k}$ of count data. I would like to perform non-negative canonical polyadic decomposition of this tensor using ...
Galen's user avatar
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Decomposing prices into different independent components

Are there any known algorithms that can split up the prices into it's components? I have a pseudo-competitor dataset that looks like the following: Prices Fuel Type Brand Doors 15,000 Gas Audi 4 23,...
Tan Guan Quan's user avatar
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0 answers
42 views

Can you decompose a wave approximately?

I have data which looks like composition of sine waves. I need to decompose it to fewest possible sine waves that would give me tolerable error. The picture is of a half-period. Each half-period ...
Boppity Bop's user avatar
1 vote
1 answer
1k views

Seasonal Decompose Interpretation

Q1) How to interpret the Seasonal Decompose (Additive V/S Multiplicative) plotted against the same dataset? Q2) And, on the basis of the below plotted Observed data-points, which decomposition one ...
fast_crawler's user avatar
3 votes
2 answers
339 views

What is multilinear principal components analysis?

I've gotten a lot of usage out of principal component analysis, and after recently learning the basics of performing canonical polyadic decomposition I was intrigued to learn that there exists a ...
Galen's user avatar
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1 vote
0 answers
21 views

How to decompose the component that is influenced by X from time-series Y?

There is a time series Y, which is the remaining part of the initial time series after removing the trend and seasonal periodic components. And there is also a time series X, which represents the ...
Sebastien J.'s user avatar
1 vote
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43 views

How do I find a mapping f : X -> Y to characterize the relationship between 2 time-series X and Y? [closed]

I have a time series Y, and another time series X related to Y. The value of Y is affected by X and some noise. How can I separate the effect of X on Y ? That is, how do I find a mapping f : X -> Y ...
Sebastien J.'s user avatar
1 vote
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106 views

How to select ranks to search for CP decomposition of 4-mode tensor of experimental gene expression data?

I have a sparse (0.625 percent non-zero occupancy) data tensor with shape (118, 16, 5009, 10). I would like to try exploring the data using CP decomposition. The ...
Galen's user avatar
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1 vote
2 answers
184 views

How to obtain uncentered factor scores from Factor analysis

The Exploratory Factor Analysis has the following mathematical formulation as in the screenshot from wikipedia (https://en.wikipedia.org/wiki/Factor_analysis): That means the factors in F are ...
gnm's user avatar
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1 vote
1 answer
452 views

What does it mean that the decomposition is based on the linear systematic component? And how can I interpret my result?

I'm using the oaxaca package to implement a Blinder-Oaxaca decomposition on a logistic model with binary outcome. The vignette says that: Note that, if a non-linear function such as glm() is chosen, ...
robertspierre's user avatar
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0 answers
53 views

Decomposition of the mean squared error

In this blogpost given a probabilistic binary classifier, with prediction $\hat{p} \in [0,1]$ and label $Y \in \{0,1\}$, the authors claim the following decomposition of the mean squared error. $$\...
user1337's user avatar
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1 vote
0 answers
220 views

Using statsmodels.tsa.seasonal.seasonal_decompose, my trend line does not cover the entire time period of the data. any words of advice?

I am trying to do a time series decomposition using this1 article as a guide--it uses statsmodels.tsa.seasonal.seasonal_decompose. However, the trend line I get does not extend to the beginning or end ...
Maria's user avatar
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1 vote
0 answers
275 views

Seasonal component of STL decomposition looks like the original data

I am doing STL decomposition on Kaggle dataset. Below is just example for one region. I have summed up the values for type (conventional, organic). So data is grouped on date and region. My question ...
IamLearning's user avatar
2 votes
0 answers
207 views

decompose function show a seasonal graph but there is no correlation in the correlation plot past lag 12 for a monthly dataset. What does it mean?

I generated a TS out of a monthly data. TQ_volume_ts <- ts(csv_file[4:39,"Volume"], start=c(2019,01), frequency = 12) When i apply the decompose function I get the following result: Now ...
Paulo Britto's user avatar
0 votes
1 answer
426 views

R: how to interpret the gray bars in the plotted output of the decompose function for time series?

In order to do some time series analysis, I used the decompose() function, to retrieve the adjacent plot. However, I was asking myself about the meaning of the gray bars at the right side. If the show ...
LGe's user avatar
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0 answers
266 views

Can you shift a time series and multiplicatively decompose it afterwards to not have negative/zero values

THis question refers to the last unanswered comment in this question: Decomposing a time series with some zero values I see, thank you for the explanation. Let's suppose that the time series follows ...
Fenrir's user avatar
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0 answers
27 views

How can I determine best fit for a time series decomposition? [duplicate]

I’m new to time series decomposition and have been doing Seasonal and Trend decomposition using Loess (STL) in R. My data is reported monthly and it appears that seasonality is annual. From what I’m ...
Melanie Shebel's user avatar
1 vote
0 answers
83 views

Wold Decomposition -- summation to infinity

In Wold's decomposition we have $ Y_t = \sum_{j=0}^\infty b_j \varepsilon_{t-j} + \eta_t $, where the variables have definition as in the Wikipedia page. I'm confused about why the summation goes to ...
user221772's user avatar
1 vote
1 answer
529 views

Wold Decomposition of an AR(2) process: Expanding a product of geometric series

In the last step of this answer, the author writes that to obtain Wold Representation of an AR(2) process, you need to expand the geometric sequences in the fractions on the right hand side: $X_{t}=\...
borninthenorth's user avatar
0 votes
2 answers
39 views

Is it possible to decompose the model evidence?

Assume I want to apply Bayes theorem with some state variable $x$ (scalar or vector, doesn't matter) and an observation vector $\mathbf{y}=[y_1,...,y_N]^T$:: $$p(x|\mathbf{y})=\frac{p(x)p(\mathbf{y}|x)...
J.Galt's user avatar
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3 votes
0 answers
683 views

Blinder-Oaxaca decomposition, logistic regression and unbalanced dataset: fitted probabilities numerically 0 or 1 occurred

I have a binary y outcome, a dummy variable gender for gender, and a set of covariates x (...
robertspierre's user avatar
2 votes
1 answer
207 views

How to decompose the determinants of an outcome

I was looking at this graph about the gender pay gap. I have a similar problem. I have an binary outcome $Y$, a binary covariate $D$ for gender (with 1 meaning female), and a series of covariates $X_1$...
robertspierre's user avatar
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0 answers
195 views

Decomposition of normal standard distribution with equicorrelation matrices

Suppose $x_{ij}\sim N(0,1)$ such that $Cov(x_{ij},x_{il})=0$ for $j\neq l$, $Cov(x_{ij},x_{kj})=\rho$ for $i\neq k$, and $$[E[x_{ik}x_{jk}] ]_{ij} =\begin{bmatrix} 1 & \rho & \cdots & \...
Atina Husnaqilati's user avatar
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0 answers
141 views

Decomposition of a time series based on another time series

I have a general question about decomposition of time series. I have a time series for electricity consumption of one building in hourly resolution for 1 year. This building also has an air ...
PeterBe's user avatar
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15 votes
2 answers
5k views

Why Time series decomposition is performed

I am new to time series forecasting. In most of the forecasting blogs that I have read so far, the time series is decomposed first. As per my current understanding it is suppose to help us in figuring ...
MonkeyDLuffy's user avatar
1 vote
0 answers
31 views

What is the most suitable classical decomposition model for the time-series graph? [closed]

To decompose time series data using the classical decomposition method, we have additive as well as multiplicative model. What is the most suitable decomposition model to be used to decompose the time ...
Anonymous M's user avatar
3 votes
1 answer
337 views

How to account for shifting seasonality arising due to differences between gregorian and Islamic calendars?

I am trying to predict time series through decomposition, my time series is as follows, As islamic calendars lag the gregorian calendar by 10 days after each year, so my seasonality is also changing, ...
abubakar ilyas's user avatar
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0 answers
95 views

How to interpret regression results when the data have been detrended?

I am planning to build a linear regression model where I explain flight ticket demand with airfares, lagged airfares, GDP etc. based on monthly data from the past 15 years. This is my first time ...
econocat's user avatar