Questions tagged [time-series]

statistical techniques for application to data whose observations concern an entity or phenomenon at different points in time.

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Replicating a state-space model

I am trying to replicate the results of Cochrane, 1998. Most of the paper is just describing the theory behind The Fiscal Theory of the Price Level. But from p. 42 he begins the econometrics aspect. ...
WoodfordJr's user avatar
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Max Likelihood Estimators of a stable Gaussian VAR$(p)$ process. Are the Lutkepohl formulas correct?

In «New Introduction to Multiple Time Series», page 90, we have the following formulas for the ML estimators of a stable Gaussian VAR$(p)$ process: where $\tilde \alpha = vec(\tilde A_1,...,\tilde ...
An old man in the sea.'s user avatar
4 votes
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R reproducible example, restrictions on cointegrating equations

The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
london's user avatar
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Non parametric and parametric tests of martingale?

A martingale is a model in which the expectation for the next value is equal to the presently observed value, even given knowledge of prior values, ie $E(X_{n+1} |X_1, X_2, ..,X_n)=X_n$ What tests ...
user157623's user avatar
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How to combine labor market time series when there is a methodological change that creates a break?

Any suggestions on how to combine time series of labor market variables (such as, for example, labor force participation) when there is a methodological change in the way the variable is calculated by ...
night_owl89's user avatar
3 votes
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Quantifying treatment effect in multivariate interrupted time series

I have a multivariate time series dataset, from which I am building an ITS (Interrupted Time Series) model by using facebook's Prophet to construct the counterfactual. Let's say I have a y variable ...
Arthur Langlois's user avatar
3 votes
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AR(q) Strongly Stationary

Consider an AR(q) process, $u_t$. If the roots of a characteristic polynomial are outside of the unit circle, the AR(q) process is weakly stationary. I've seen this proof that proceeds by showing the ...
Michael Gmeiner's user avatar
3 votes
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Extract residuals from Uhlig's rejection method - Lag selection

I wanna determine the number of lags for a Baysian VAR/FAVAR model, which I implement based on R's VARsignR package. To compute the AIC/BIC I'd need the residuals of the model estimation. How can I ...
HPMinsky's user avatar
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Help Finding Information on "Power Trends" or "Polynomial Trends"

I need to prove some facts about the asymptotic OLS estimator, $\hat{\delta}$ in model: $ y_t = \alpha_t + \delta \cdot t^b + \epsilon_t $ where $\epsilon_t \sim iid(0,\sigma^2)$. I've looked at ...
hipHopMetropolisHastings's user avatar
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Wold Decomposition and autocorrelations of AR

Is it possible to retrieve Autocorrelations ( value or any other info) up to a certain lag for an AR(2) stationary model using the Wold decomposition? Example: $$X_t=0.32X_{t-1}+0.51X_{t-2}+ \...
Clemente Cortile's user avatar
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Applying the Martingale central limit theorem to the score process of an autoregressive model

This question is a natural continuation of the following question: How do I construct the score process of a Markov model and verify that it is a Martingale? In this problem, we set up as follows: ...
jmbejara's user avatar
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How do I set up a staggered difference-in-differences design in R?

I have data which looks like this: ...
econdid's user avatar
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Regression OLS estimator with $x_t=1/t$

I found some questions in a book and wanted to train for my upcoming exam (expect to see some more posts from me idk), anyhow this is the question. To solve point A I rewrote the whole equation in ...
Blipo's user avatar
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2 votes
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Time series question from book (ma)

I'm trying to understand this subject and I'm stuck in a question found in a book. I understand white noise characterization, but I'm having some problems with this... maybe it's too much theory? I ...
Blipo's user avatar
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Applications of a certain type of stochastic processes in macroeconomic, macroeconometric or finance

A compound Poisson random vector $Y$ is well defined in this site in wikipidia. Nothing prevents me from compound strictly stationary stochastic processes instead of compound random vectors. The ...
Letícia Fagundes's user avatar
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A conceptual question about the limitation of the MA processes

We know that linear time-series techniques are frequently used in macroeconometrics. The Wold Representation Theorem states that any covariance-stationary process may be expressed as an MA process ...
Fam's user avatar
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Taylor rule estimation with OLS serial autocorrelation

I'm estimating the equation: $$i_{t}=\beta_0+\beta_1\tilde\pi_t+\beta_2\tilde y_t+\varepsilon_t$$ Where $\hat\pi_t=\pi_t-\pi^{target}$ and $\hat y=\ln y_t-\ln y^{\ast}$, are the inflation deviations ...
manifold's user avatar
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Do you know how to compute the IRF of a GARCH (1,1)

We have the following model (GARCH (1,1) ) $y_t=\sigma_t\epsilon_t$ $\sigma_t^2 = \omega + \beta*\sigma_{t-1}^2 + \gamma*y_{t-1}^2$ Note that we can rewrite the latter as: $\sigma_t^2=\frac{\omega}{1-\...
Borja Urrea's user avatar
2 votes
0 answers
41 views

How to choose information criterion?

In time series analysis, it is often important to determine the optimum number of lags in order to remove serial correlation. For example, in VAR, Dickey-Fuller unit-root test or Granger causality ...
csilvia's user avatar
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2 votes
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On Cointegration with Structural Breaks

I am slightly confused about the requirements necessary to conduct a cointegration test with structural breaks such as the Gregory-Hansen test. Suppose I have two I(1) variables. Variable 1 follows a ...
user29937's user avatar
2 votes
1 answer
127 views

Data analysis with GARCH modeling

I'm currently analyzing the relationship between stock, bonds, and real estate returns in Germany. I've gathered my data and am planning on estimating this equation: $\sigma_t = \beta_0 + \beta_1 R_{...
Peter V's user avatar
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Obtaining Wold Representation of VECM Model

I'm attempting to replicate Beaudry & Portier (2006), and I'm having trouble coding up the long-run restrictions in the VECM model. Specifically I'm having a hard time finding a clear explanation ...
hipHopMetropolisHastings's user avatar
2 votes
1 answer
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Why don't Time Series books talk about exogeneity like in classical linear regression models?

Consider the following linear regression: $$y_t = \beta_0 + \beta_1 x_{t} + u_t$$ Typically, we need to assume (assuming a random sample): \begin{equation}\label{I}\tag{I} E[u_t]=0, \quad cov(u_t ,x_t)...
André Goulart's user avatar
1 vote
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Help with Simulating a Time Series Process in R

I'm having difficulty expressing the following process in its most reduced form. Every time I try to simulate it with the arima.sim function, I end up with a non-stationary AR part that cannot be ...
NoNameBoyy's user avatar
1 vote
0 answers
10 views

Normalization for model comparisons

I have a time series applying the Markov Switching model, which is estimated in about 15 different versions. One or two of the time series had to be normalized in order to converge. That is 1-2 out of ...
David K's user avatar
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Is there a good catalogue of time serries available from the Federal government?

I have two closely related questions that I will present here in separate postings. It seems that lately I have spent a great deal of time looking for particular time series that may or may not exist. ...
andrewH's user avatar
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1 answer
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Analysis of seasonal adjustments and moving averages: seeking guidance

I'm looking to seasonally adjust the price data I have using a moving average with a 12-month window size. As window 12 is being used, the first 11 values in the 'Oil_adjusted' column are being filled ...
waka 's user avatar
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Does discount rate and cost of capital mean the same thing to compute levelised cost of energy (LCOE)?

I came to understand that cost of capital and discount rate are two different parameters, although they are also used ...
hbstha123's user avatar
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Deriving ADF unit root test form for the time series with quadratic deterministic trend

I have the following time series process $y_t $ $$\Delta y_t = \delta + \gamma t + \epsilon_t$$ where $e_t$ is white noise process with the variance of $\sigma^2$. I guess that whereas $\Delta y_t$ is ...
studentp's user avatar
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Is there granger causality that can be applied to panel data with structural breaks?

I have panel data containing various macroeconomic variables (for example: interest rate, output, unemployment). I would like to run a Granger causality test on some of them, but there are structural ...
csilvia's user avatar
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1 vote
0 answers
12 views

Time series: predicting covariates for missing years from historical values

I'm working with a time-series dataset where my dependent variable is measured annually from 2018-2021 but my covariates are not all measured over the same period. For instance, $x_1$ is measured from ...
akm's user avatar
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What is difference between Interrupted Time Series (ITS) and Regression Discontinuity in Time(RDiT) analysis?

Can anyone give some details on the difference between Interrupted Time Series (ITS) and Regression Discontinuity in Time(RDiT) analysis? How to choose between them? which one is more robust? Or some ...
Afrouz Hojati's user avatar
1 vote
0 answers
64 views

Detrending multiplicative model

I have a GDP quarterly series and IND.P monthly series, which I need to detrend. I am following Bernanke et al. paper from 1995 and the way they do it is: ...
NotaNewUser's user avatar
1 vote
0 answers
65 views

What is the importance of moving seasonality in seasonal adjustment?

Both Stable and Moving Seasonality are computed in Sliding span test (or D8 F-Stat test) and M7 statistics. But what is the purpose of finding out the presence of moving seasonality in seasonal ...
Peter's user avatar
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1 vote
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230 views

Modelling GDP growth rates with an AR(1) process

I am trying to model the growth rates of real output per worker. I read that GDP growth rates are often assumed to be stationary and are modelled using an AR(1) process, so I took logs and then took ...
Ben's user avatar
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Does GMM have any assumptions that you can't test empirically (and must instead argue qualitatively for)?

My understanding is that you can empirically test some of the main assumptions required for using a GMM estimator. Namely, I understand that you can test over-identifying restrictions with Hansen's J ...
leecarvallo's user avatar
1 vote
0 answers
50 views

What type of econometrics is practised most?

This might sound like a weird question, but what type of econometrics is most common in academia and / or the private sector? Here I am thinking about time series econometrics (Bayesian and ...
ArOk's user avatar
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Intuitive/Practical meaning of non-stationarity of GDP Data

As i just read in a time series book that a particular GDP data under consideration is non-stationary verified through various tests. From non-stationarity definition this means that the process has ...
pkg7724's user avatar
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1 vote
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Correcting high AR(1) coefficients in dynamic Gordon model

I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis. However after receiving some feedback there is one last issue I want to resolve. I'm using ...
Niek de Meijier's user avatar
1 vote
0 answers
60 views

What would be the mean of a finite aggregation of AR(1) processes?

What would be the (expected) mean at each period $t$ of a (in)finite aggregation of $AR(1)$ processes generated by the same data generating process? How would the resulting plot look? For $i.i.d.$ ...
Beck Batucada's user avatar
1 vote
0 answers
8 views

Evaluating the impact of US federal grants

There are a number of challenges with evaluating the impact/effectiveness of federal grants in the U.S. In particular, it's easy to obtain a (somewhat comprehensive) record of transactions between ...
Martin Van der Linden's user avatar
1 vote
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23 views

GARCH data modeling

I am analyzing three time series returns for stocks, bonds and real estate, and have done prelimanary tests including Engle's ARCH test which came back as not rejecting the null hypothesis. IF there ...
Peter V's user avatar
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1 vote
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Is there such a thing as resonance in economic underliers?

In physics the occurence of resonance is explained and widely understood in its linear form and subject to research in nonlinear resonance. Example for instance are resonant frequencies of objects. ...
AndiAna's user avatar
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Can the CPIH be used to find the real terms rise in price of a component of the basket of goods?

I want to calculate the real terms rise in UK private rent prices since 2011 using the CPIH measure. The indexes of nominal rent prices and the CPIH rose by 14.7% and 13.5% respectively, so I can say ...
John Smith's user avatar
1 vote
0 answers
47 views

Would it be appropriate to include state level variable with MSA model?

Greetings I am running a time series which will use vector error correction model. My dependent variable is economic base which is comprised of manufacturing, mining and construction sectors. I have a ...
gr8694's user avatar
  • 21
1 vote
0 answers
31 views

Indicator variables over unequal periods?

I'm comparing the volatility of capital flows using a panel data regression. I would like to examine changes in volatility over different periods (e.g. before financial crisis, financial crisis, ...
Vhakazar's user avatar
1 vote
0 answers
78 views

Sources of Growth and co-integration: production function approach

I am experimenting with time series data to gauge the importance of factors of production i.e. labour force, capital stock, energy, land, etc. in output growth. One venue I am looking into is the ...
london's user avatar
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1 vote
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61 views

Can a MS-VAR(1) be discretized to a Markov-chain the same way a VAR(1) has a discrete approximation?

It is well known via Tauchen (1986) that a VAR(1) process can be approximately fairly well (in the absence of persistence) by a discrete Markov-chain if the innovation is distributed standard normal. ...
hipHopMetropolisHastings's user avatar
1 vote
0 answers
29 views

How to compute standard errors for Blanchard-Quah-restricted SVAR?

People tell me that the way of bootstrapping standard errors in the original paper is incorrect, but then how should I do it? Is there a convention of how to compute standard errors for Blanchard-...
J Li's user avatar
  • 291
1 vote
0 answers
75 views

Absolute Value of Log in stocks returns

Well, i'm interested in model a GARCH for a serie. The original serie is $y_t$ (price index of a Stock Market), which has a unit root. So i create the returns: $x_t = ln(y_t) - ln(y_{t-1})$. Now, i'm ...
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