Questions tagged [decomposition]

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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 ...
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Decomposition of oil price

For a project I want to recreate the graph "Cumulative Weekly Decomposition" from: https://www.newyorkfed.org/medialibrary/media/research/policy/oil_decomposition/oil-decomp_2022-0328.pdf?la=...
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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 ...
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Select the best period value to visualize clearly the Trend and Seasonality

I have a daily data for 4 years range between 2016 - 2019. I used statsmodels.tsa.seasonal.seasonal_decompose to decompose the seasonality and trend but I should ...
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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 ...
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Decomposition methods - example and question of other available methods

I'm working on a model that includes a variable I want to decompose into parts explained by two other variables. For example, in a sport complex there is a suite of kiosks for purchasing a variety of ...
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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 ...
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How to understand Blinder–Oaxaca decomposition second terms

Blinder–Oaxaca decomposition I could understand the first term, but I have trouble understanding the second term interpretation, why would this second term be regarded as the "differential not ...
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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 ...
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adfuller test say its stationary but decomposition shows signs of seasonality

I am working with this time series and i got confused; adfuller test says it is stationary as p-value(1.1125518783299598e-29) is less than 0.05, acf and pacf shows no significance(see image), ...
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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}=\...
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2 answers
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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)...
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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 (...
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1 vote
1 answer
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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 $X_1$...
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Just adding control variable instead of Oaxaca-Blinder decomposition?

Let's say I am interested in the extent to which a wage difference between men and women is caused by different levels of education between men and women. I know one would typically use Oaxaca-Blinder ...
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Can it be shown analytically that the sum of squared semipartial correlations is bounded by r-squared?

Two related questions: I have read in different texts that the sum of squared semipartial correlations is "typically" less than $R^2$, except when supressor variables, or rather a supression ...
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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 & \...
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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 ...
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Decompose industry-region stock returns into industry + region components

I have equity returns by industry and region (29 industries x 10 regions = 290 data points). In my model I assume that the returns are driven by two correlated systematic factors: 1/ industry and 2/ ...
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12 votes
2 answers
1k 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 ...
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1 vote
0 answers
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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 ...
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3 votes
1 answer
207 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, ...
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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 ...
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1 vote
0 answers
33 views

Elaborate Primers (books) on time-series decomposition and factorization?

I am looking for masters or PHD level books and flagship papers on time-series decomposition including mathematical notations/theorems. I recently did a biology bachelor's thesis on singular spectrum ...
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How to configure function "stl" to produce the same result as function "decompose"?

I'm doing prediction for a time series with function decompose. Unfortunately, the object returned by decompose is not ...
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2 votes
0 answers
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How to compare the results between decomposition and SARIMA for a time series?

I was asked in an exercise to compare the results of function decompose and the model SARIMA. I only know to plot the results of function ...
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1 answer
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Decomposing a probit/logit regression

In an econometric work, I want to assess the causal effect of n variables on a binary character variable y, while I highly suspect that the relation between one of these regressors, say x (which is ...
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How does LOESS work in STL Decomposition Algorithm?

I am trying to write a SQL program to calculate STL Decomposition of monthly time series data. In going through the algorithm in the original paper, inner loop step 2 has the detrended series grouped ...
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1 vote
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How to decompose the intercept of a linear regression? [closed]

Problem I'm given a linear regression model. I need to to obtain the decomposition of the intercept coefficient in the form of $$ \hat{\beta_1} = \beta_1 + \sum c_i u_i$$ where $c_i = 1/n - a_i\bar{X}$...
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1 vote
0 answers
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STL decomposition of a daily time series (only business days)

I'm currently working with a daily (business days) time series which has a monthly seasonality and an overall positive trend over the last two years. I want to estimate the error component of the time ...
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1 vote
0 answers
60 views

How do you decompose conditional MSE?

I'm trying to decompose the conditional mean squared error but I'm not exactly sure how to expand the terms. Is it the same as just decomposing the general mean squared error?
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3 votes
1 answer
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Why does NMF of a symmetric matrix yield orthogonal matrices which are not transpose identical?

Consider the non-negative factorization of a positive, real symmetric matrix A. Non-negative factorization of this matrix yields ...
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8 votes
0 answers
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statsmodels seasonal_decompose(): What is the right "period of the series" in the context of a list column (constant vs. varying number of items)

Assume having a list column so that your time series is nested, see Convert pandas df with data in a “list column” into a time series in long format. Use three columns: [list of data] + [timestamp] + [...
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1 vote
1 answer
112 views

Time varying Shapley Decomposition

I have read a lot on Shapley decompositions for relative contributions of regressors in linear regression. I was wondering if there is a way to do time-varying relative contributions. For example: If ...
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2 votes
1 answer
53 views

Eq. (7.12) in Elements of Statistical Learning

I'm looking the snippet below from ESL. I'm a hard time deriving the variance term (last term in Eq. 7.12). I started with \begin{align} \frac{1}{N}\sum_i ||h(x_i)||^2\sigma^2 \\ = \frac{1}{N}\...
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1 vote
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Time series decomposition: should seasonality be tested prior to decomposition?

Some time series decomposition methods (e.g. decompose and stl), do not perform any statistical test to test the presence of ...
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0 votes
2 answers
192 views

Time Series Decomposition: Is it necessary (or wise) to remove outliers beforehand?

Do outliers change the outcome of time series decomposition? As far as I understand it, outliers occur in the residual-component. In the residuals plot they can be visually identified as spikes. ...
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2 votes
1 answer
2k views

How to interpret seasonal component of a time series decomposition plot?

I would like to know how to interpret the graph of the seasonal component of the time series decomposition plot. For example, for this chart: What does zero mean on the seasonal component graph? ...
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Real-time anomaly detection for online time -series

I am new to the anomaly detection world and am dealing with a project to detect real-time anomalies for a time-series in a fraud detection schema. I read the answer by Rob Hyndman here and like the ...
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1 vote
1 answer
161 views

Does SVD provide the best low rank approximation for any matrix regardless of shape?

Wikipedia states (link below) that by the Eckart-Young-Mirsky theorem, the SVD provides the best low rank matrix approximation (on the basis of Frobenius norm of the error matrix) for any matrix A in ...
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115 views

Why feasts::STL in R can only extract trend and remainder from global_economy dataset?

Out of my curiosity, when trying to learn forecasting from fpp3, I found that I can't extract seasonal info from global_economy but I can't explain why. My assumption is that the dataset doesn't have ...
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2 votes
0 answers
64 views

Decomposing change over time and choice of reference period

Suppose you observe an aggregate outcome at time 1 that is made up of $k$ components: $$Y_1=w^1_1 \cdot y^1_1+w^1_2 \cdot y^1_2+...+w^1_k \cdot y^1_k=w^1y^1.$$ You can think of $w$ vector as a set of $...
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0 answers
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Sum of pure errors

We know that in a simple linear regression model that the sum of all the residuals is 0 but why is it that the sum of all the pure errors is also 0? Is there a relation between them?
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0 answers
25 views

Examine the below time-series plot of data. With reference to the graph, justify the chosen method for the analysis that has been started on the table

Please can I be provided with a good answer/justification for the question? I think there is one method and it is moving average? I am not sure though.
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Is a Time series' Model always an Additive or Multiplicative one?

A Time Series consits of four components trend, seasonality, cyclical and an irregular component. Now a time series can be decomposed in an Additive or Multiplicative Model. Are there other ...
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0 votes
1 answer
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Based on the graph & table, what method is used for the analysis that has been started on the table pictured?

Looking at the time-series plot of data (pictured), and looking at the table (pictured), what method and why has been chosen for the analysis that has been started on the table shown? I'm struggling ...
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1 vote
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Method for decomposing time-intervals of univariate Time-Series

I am no expert in time-series analysis but trying to get a more of a grasp of it. So, during a Light/Dark transition test the activity of animals is tracked. During the light-phase, usually low to ...
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1 answer
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Does it make sense to fit an ARIMA model to the remainder component of a timeseries?

Suppose I have a timeseries, something like this: ...
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1 vote
0 answers
40 views

time series decomposition and multivariate models

I have a series of time series data which looks like: ...
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3 votes
1 answer
454 views

Decomposition of Mahalanobis distance: Where's my mistake?

Kim (2000) gives a formula for the decomposition of the (squared) Mahalanobis distance for $d$ variables for a random vector $\mathbf{x}$ with mean vector $\mathbf{\mu}$ and covariance matrix $\mathbf{...
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