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Questions tagged [decomposition]

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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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1answer
59 views

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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16 views

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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31 views

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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1answer
112 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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32 views

How to fit a regression model with ARIMA errors on the seasonally adjusted component of a time series (in R)?

I want to do these two things (combined) with a time series T: forecast the seasonally adjusted component of T (STL used for the decomposition) and "add back" the seasonality (I assume that the ...
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144 views

Neural Network regression on time series

I want to predict the trend values of a time serie [Y] based on the effect of other 10 input variables which can also have interaction. Since the combination of interaction between the inputs is ...
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31 views

Independent Component Regression using sklearn's FastICA

I am trying something along these lines ...
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38 views

Closest ARIMA models to Holt-Winter's Mixed Model and Time Series Decomposition Models

Can you please tell which ARIMA model will be closest to Holt-Winter's mixed model and Time Series Decomposition (additive/multiplicative) models And that ARIMA model maybe used in replacement of the ...
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38 views

Name for decomposition of joint probability into product of conditional probabilities

Consider a set of events $A_1, \dots, A_n$. By definition we have $$\mathbb{P}[A_1 \cap (A_2 \cap \dots \cap A_n)] = \mathbb{P} [(A_2 \cap \dots \cap A_n) | A_1] \mathbb{P}(A_1).$$ Applying the ...
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36 views

What is Effective Hypothesis Decomposition

My girlfriend used the program Statistica and in the ouput of ANOVA test, there is a graph with label "Effective Hypothesis Decomposition". We are lost what this means. There is even a help page on ...
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27 views

Decomposition random variable with conditional expectation [closed]

Why given some information set $I$, any random variable $x_t$ can be decomposed into the sum: $$x_t = E(x_t | I) + v_t $$ where $E(v_t | I) = 0$. I'm looking for a clear proof.
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65 views

Should I decompose time series before applying DTW

I have two time series which I want to compare by using the 'Dynamic Time Warping' technique. However, I am only interested in comparing the trend component of them (i.e. excluding the seasonal and ...
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1answer
138 views

Why doesn't the Wold's decomposition theorem imply a good AR(p) fit?

I'm trying to fit an AR(p) process to the standardized, 10 years long time series of monthly logreturns of a stock index and get extremely poor fit. I'm not surprised, because if I had a good fit, ...
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42 views

classical decomposition method(without seasonal component)

I understand the following points: When decomposing, the trend is obtained from the data by a regression line.=> T A cyclic component containing irregular variations is obtained(series/linear ...
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403 views

How to choose between additive and multiplicative decomposition in time series

I have a time series which is the number of weekly flu cases from 2010 to early 2018 in one county. I want to remove seasonality from my data so I can have a clearer data to infer the relationship ...
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1answer
187 views

How to decide whether to model a time series additively or multiplicatively?

I've been reading a lot of theoretical content on additive and multiplicative decomposition, but when it comes to deciding what type of decomposition to use on my own data I find it kinda hard to do ...
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43 views

Observed very different from Trend, decomposed time series

using simple R lines, I have plots of decomposition of a time series. ...
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49 views

Should I include gender dummy for the probit regression in Heckman?

I'm estimating the wage equation for a selected sample which contains both males and females, afterwards which will be decomposed using the Oaxaca command in stata, by gender. The wage equation for ...
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107 views

If $X=Y+Z$ with known pdf of $X$, are $Y$ and $Z$ unique?

Say there are random variables such that $X=Y+Z$ with $Y$, $Z$ independent; knowing the pdfs of $Y$ and $Z$, one can (technically) find the pdf of $X$. Taking it from the other side: if one knows the ...
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34 views

How to decompose data into specific frequency-range components?

I have a 20 year daily wide area distributed weather data-set I would like to analyze as a part of my master thesis in engineering. Different frequency events impact my system in different ways and ...
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30 views

Is it common to decompose many time series in a business?

I am working in a industry. Most of the time I do statistical reports on sales. I'm new to time series analysis, so please be patient: the question might be obvious. I would like to monitor the sales ...
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1answer
609 views

Decomposing a time series with some zero values

There are many techniques to decompose a time series into trend, seasonal, and remainder components. I was wondering if these techniques can be applied without worry to time series which have some ...
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311 views

Time series forecasting and decomposition

I have a project about time series analysis. My data are not stationary and they have daily seasonality as shown in figure below. Is it correct to do the following steps? Decompose Time serie into ...
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1answer
61 views

3-way interaction not signficant; how to interpret subsequent 2-way interactions.

I know there are similar questions on this topic but I have checked all of them and haven't found the specific answer to my (simplistic) questions. There are 3 explanatory variables: A(3 levels, ...
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1answer
71 views

After decomposing my data, should I fit an ARIMA to the remainder or the trend?

I've decomposed my data to get rid of the seasonality. Now I want to use the arima function to fit an ARMA(p,q) model. Do I fit the model to the "random" component of the decomposition? That ...
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1answer
281 views

Even after seasonality adjustment, seasonality still remains. Why?

I'm trying the classic AirPassengers dataset in R and tried removing the seasonal component using deSeas <- forecast::seasadj(decompose(d,"multiplicative")), but ...
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1answer
289 views

Approximate AR(p) with a product of AR(1) and AR(2)

Literature suggests that any AR(p) ARIMA model can approximated as a combination of AR(1) and AR(2) processes. For example, one book suggests that an AR(3) model with the following coefficients: ...
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103 views

Bias variance dilemma (derivation in Haykin's Neural Networks)

I have a question regarding a certain derivation of the bias variance dilemma. Generally, I guess I have understood the derivation in, e.g., Geman's Paper, or in books like Bishop's Pattern ...
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1answer
179 views

Decomposition of single variable into mean and dispersion around mean

Consider a survey of firms of size $n$. This survey includes, among other variables, the average wage of workers in firm $i$ ($x_i$) and the number of workers in the firm ($L_i$). Both are random ...
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1answer
483 views

Seasonal trend loess (STL) decomposition around holidays

I am seasonally adjusting a weekly transaction time-series. The seasonal adjustment works great, except for on and around closed days. At and around these points there are serious errors. What is the ...
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1answer
152 views

Conditional expectation and variable decomposition

Suppose that $X$ and $Y$ have an uknown joint distribution $f_{XY}$. How can I formally demostrate that it always exists a unique decomposition of the form : $$ Y = E[Y|X] +\epsilon $$ without ...
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372 views

Determining Seasonality nature of a time series i.e additive or multiplicative

I have 4 years of data starting from 2014-Jan to 2017-Dec, I am trying to extract seasonality component from that series, to do this I am using decompose function in R, one of the parameters to ...
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1answer
25 views

Decompose growth of variable

This is probably an elementary question. Let's see. Say variable $y_t$ depends on two other processes, as follows: $$y_t=x_tz_t$$ I observe these variables in period 0 and period 1. I want to ...
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36 views

Seasonality for monthly period

The question is simple but I am having a trouble to figure it out. If I have a monthly data of 5 years how could calculate the seasonality for each month not quarter. I found this example online and ...
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158 views

Why does stl() decomposition require integer frequency?

I need to decompose and forecast weekly series with around 10 years of data. In this data leap years play an important role so I need the have non-integer frequency, frequency = (365.25/7) By ...
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89 views

Elimination of Trend and Seasonality Using Classical Decomposition Model

Brockwell and Davis (2016, page 26) have illustrated the classical decomposition model for elimination of trend and seasonality. the assumptions for this model are: $X_{t} = m_{t} + s_{t} + Y_{t}, ...
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1answer
2k views

How to perform variance decomposition?

suppose I have the variable X, and I simply want to know how much of the variance of X is explained by the other variables Y, Z and W. How can I do this in Stata? I have in mind a simple linear model, ...
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1answer
150 views

How to treat days when shops are closed in sales time series?

I am working on a time series that contains daily sales data. The aim of the project is to estimate the impact of marketing expenditure on the sales, while accounting for seasonality and trend. I ...
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116 views

How to decompose seasonality of a time series with a limited time span?

I am working on a time series that contains daily sales data over 2 and a half years. The aim of the project is to estimate the impact of marketing expenditure on the sales, while accounting for ...
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1answer
44 views

Can quintile/dispersion ratios be decomposed according to subgroups?

I'm try to decompose inequality/dispersion ratios (top 10% to bottom 10% or top 20% to bottom 20%) according to subgroups. I would like to say something like e.g. males are responsible for x% and ...
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2answers
305 views

TBATS Decomposition with High Residuals

I have an msts time series, hourly data of electricity prices that have daily, weekly and yearly seasonality. I am decomposing the data using TBATS. Data I am using covers 365 days. Residuals have ...
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60 views

What are the decomposition based forecasting methods?

I would like to learn that all forecasting methods are doing decomposition initially. For example, as I know, MAPA method is decomposing the time-series data first, then apply forecasting. If not all ...
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430 views

How to choose the best time window using structural times series with loess

My question is about the Cleveland et al. 1990 paper STL: A Seasonal-Trend Decomposition Procedure Based on Loess. The full citation is: Cleveland, RB, Cleveland, WS, McRae, JE, and Terpenning, I. ...
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62 views

Using one stock price as a predictor for another stock price

I have two stock prices with a strong trend which are non-stationary. I want to calculate the correlation between one stock say $x$ and another stock say $y$, but lagged 7 days back. Why should I ...
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1answer
2k views

Seasonal decomposition or Holt-Winters methods for forecasting?

When you have a time series that contains both trend and seasonal components, I learned that either seasonal decomposition (e.g., forecast the deseasonalized series, then add back the seasonal factor ...
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1answer
184 views

What would happen if we perform Time Series Decomposition on a data that only has trend and irregular components?

I am performing Decomposition of a Timeseries data. It appears that the data does not have a seasonal component and possess only trend and irregular components. However on still performing the ...
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122 views

Decompose Covariance by Observations

Suppose I observe $n$ iid realizations of two random variables $X$ and $Y$, denoted respectively $x_i$ and $y_i$. Observations can be groupped into two subsamples, with $n_1$ and $n_2$ observations. I ...
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1answer
4k views

How does loess decomposition work? [duplicate]

I actually read a lot about times eries and there I often read about "loess decomposition". But what is that exactly? It exists in package STL or packages about outlier-detection. Can someone give me ...
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254 views

R interpretation of STL() or decompose() results

How can I interpret the results of the decomposition of a time series, especially from the seasonal results? Example: ...