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Questions tagged [decomposition]

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2answers
26 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
38 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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0answers
34 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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0answers
118 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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24 views

Decomposition Difference Between Twitter and STL Method

I am having a lot of trouble understanding the difference between the two decomposition methods: twitter and stl. https://www.rdocumentation.org/packages/anomalize/versions/0.1.1/topics/...
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0answers
45 views

Anomalize Package time_decompose

I am trying to figure out what the meaning is behind each of the different compositions of the time_decompose function in the ...
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1answer
78 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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0answers
28 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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0answers
33 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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1answer
104 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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0answers
17 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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0answers
12 views

Deconvolution of 2 vectors (1 know + 1 unknown)

I am currently trying to deconvolute 2 vectors (a & b) from 1 (c). Actually, I have access to the recorded data of (a) & (c) but not (b). All are signal vs time with signal totally random. I ...
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0answers
20 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
173 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 ...
2
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2answers
189 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
38 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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0answers
28 views

Variance decomposition on estimated series

I am puzzled on how to achieve a variance decomposition on five estimated series. Each series is I(1), and there exists at least one cointegrating relationship at the 1% level between these five ...
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1answer
24 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
118 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 ...
2
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1answer
58 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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0answers
93 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 ...
3
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1answer
174 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 ...
2
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1answer
350 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 ...
2
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1answer
62 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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0answers
235 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
19 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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0answers
27 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 ...
2
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0answers
100 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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0answers
65 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
1k 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
99 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 ...
2
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0answers
87 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 ...
0
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1answer
38 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
198 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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0answers
50 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 ...
2
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0answers
293 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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0answers
61 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
1k 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
116 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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1answer
105 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
3k 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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0answers
209 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: ...
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0answers
330 views

Remove price and promotion effects from sales time series

I'm trying to measure the effect of an in-store media campaign on the sales. I have sales data along the time for test (treated) stores and control (not treated) stores. Before comparing test and ...
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1answer
1k views

Weekly and Monthly Decomposition of Daily Time Series

I have a data set including daily prices and demand of a commodity. I am sure that, price and demand weekly and monthly changing. So it has a seasonality effect. How can I decompose it by using daily ...
0
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1answer
58 views

decomposition of time series into many time series

I have two time series $x_t$ represents expected default rate from one data provider $y_t$ represent expected default rate from another data provider. Correlation between $y_t$ and $x_t$ is 0.9 ...
0
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1answer
101 views

Shift Share Decomposition for Non-Multiplicative Relationships

Given $$ Y_t = \sum_i \omega_{i,t} \cdot X_{i,t} $$ We can decompose the change in $Y$ from period $t$ to $t + 1$ into: $$ \begin{align} Y_{t + 1} - Y_t &= \left( \sum_i \omega_{i,t + 1} X_{i,...
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1answer
2k views

Analysing some series in R - problems with TS/decompose functions

I am trying to analyze and forecast the European Emission Allowance (EUA) prices by using the data from January 2008 to March, 2016 and also using other series that might be related to that price, as ...
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1answer
123 views

Time series forecasting via decomposition and component-wise modelling

Consider a time series $t_{k} = d_{k} + s_{k}$, where $d_{k}$ is a deterministic series (trend or periodic component, for example) and $s_{k}$ - a stochastic process, for example, ARMA(p,q)-GARCH(P,Q)....
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0answers
95 views

Accuracy of time series decomposition

How to judge the accuracy of time series decomposition provided by R? Because at different level of data aggregation and seasonality different repetitive patterns appear in seasonality index. How ...
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1answer
652 views

Time series decomposition results interpretation

I have a long multi-seasonal time series, and the stl() decomposition got me this: The remainder is definitely not white noise. Then what should be the next step ...