# Tagged Questions

"VAR" stands for *vector auto-regression*, which is a multiple time-series model / method. VAR is common in econometrics, & allows each time-series to be modeled based on its own previous values, & also the previous values of each of the other series, simultaneously. Thus, the series are given equal ...

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### Granger causality in a trivariate system

I am working on testing Granger causality, in particular with the Toda & Yamamoto approach as in Dave Giles blog post "VAR or VECM When Testing for Granger Causality?". Can I consider more than ...
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### A model similar to vector autoregressive (VAR) model with different explanatory variables

VAR models do not allow the flexibility of having different explanatory variables in each equation. Are there any alternative models which allow this flexibility and written in a VAR form?
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### VAR model: good diagnostics but poor forecasting performance

I constructed a VAR model of order 4 where some of the variables are statistically insignificant. The model is based right in terms of diagnostics (no autocorrelation of residuals, normal distribution,...
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### Vector Autoregressive Models with Non Stationary Variables [duplicate]

I am beginning to study VAR models, and I have a simple question. If I have three variables and one of them is nonstationary, can I estimate a standard VAR model? If not, what should I do?
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### Error with predict function in var model with exogenous variables [on hold]

I am trying to get a 1-step ahead forecast in a VAR model with exogenous variables using the predict function in R. The code is a ...
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### How to forecast from VECM (in R)?

I am interested in forecasting with a vector error correction model (VECM). I am facing a problem of not being able to transform a cointegrated series into a VECM model using the stationary series. ...
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### Rescaling the Implse-Response Function of a Structural Vectorautoregressive Model

I'm thinking about the Impulse-Response Function (IRF) of an Structural Vectorautoregression (SVAR). According to the Enders Book we can write the IRFs with help of the Vector MA-Representation as: \...
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### Joint evolution using VAR model and pairwise correlation plot in R

I have data for three commodities for which I conducted a time series analysis using VARselect and VAR functions in "vars" ...
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### Are there any methods for fitting “interconnected” AR with cross-lags at times older than 0?

I'm not really sure how to explain this, so any advice about the terminology would be very welcome! So let's say that I have two independently driven AR(2) models that are connected together, for ...
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### VAR model with different time period for each series

I am trying to fit a Vector Autoregression model to forecast GDP growth Rate. I have 2 series, monthly GDP growth rate and a monthly economic indicator. For the monthly GDP growth rate, the latest ...
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### Number of coefficients in a VAR($p$) model

How do you determine the dimension of a let's say VAR($p$) with 3 time series $(x,y,z)$ with a lag of $p=2$? From what I understand, the dimension depends of the number of time series and the lag size ...
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### What is lm() compared to VAR()

What's the difference between # Fit Model # fit1 = lm(var$1 ~ var$2, data=data) and ...
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### Difference between Granger Causality and AR1

Here are my questions: is there a difference between "VAR(1)" and "AR(1)"? Granger Causality inspects the direction of causality. In return, we receive a p-value on how much a time series is likely ...
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### VAR and coefficients with OLS

I have a model like $Y_{it}=\beta_{0it} +\beta_1x_{1it}+\beta_2x_{2it}+\beta_3x_{3t}+\beta_4x_{4t}+e_{it}$ I have the data for all the variables and I know that $x_3$ and $x_4$ follow an AR(1) process....
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### Difference between VAR model and simple vectorial regression

So I am aware of VAR models. Specifically for the VAR(1) case: $X = A_1~LX +\epsilon_t$ where $L$ is the lag operator. A simple regression between vectors would be: $Z = A_2~Y+\epsilon$ where $Z$ ...
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### Variance of stationary VAR process

Suppose we are given stationary VAR(p) process. How to estimate variance of its components: $y_{1t}, y_{2t}...y_{mt}$? Will be very grateful for help!
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### Stationarity of time series and VAR model

I have two variables, one is stationary I(0) and one is non-stationary I(1). Is it possible to make VAR model for these two variables if the non-stationary variable will be differenced to obtain ...
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### autoregressive models vs simultaneous equations models

I know that when the model is a simultaneous equation, you can't always use OLS to estimate the parameters. You will get biased estimators and most important inconsistent. But if all the variables are ...
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### Can a cointegrated variable be exogenous in first difference in a VEC model?

If I have a variable C that is cointegrated with both variables A and B separately, can I use it in first-differenced form as an exogenous variable in a VEC model involving A and B?
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### Does all variables in a VAR/VEC need to be normally distributed, or only the target variable?

Well? Does all variables in a VAR/VEC need to be normally distributed, or only the target variable? It is very hard to get all of them to meet criteria of normality without deleting too many outliers.
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### VAR lag length vs Johansen cointegration test outcome?

First puzzle: I am taught that the lag order of VECM does not affect the cointegration rank because the lag order is for the differenced regressors. But, I see the contrary: I experimented with sample ...
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### What models for Rahbek and Mosconi method for exogenous variables in VECM?

I'm not very good at algebra, wich caues problems for me when reading econometric articles.Â Now, I'm reading the Rahbek and Mosconi (1998) paper on how to introduce exogenous variables in VEC models. ...
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### Why Are Impulse Responses in VECM Permanent?

The usual interpretation of impulse response functions in standard vector autoregression (VAR) models is that they represent the response of a variable, say $y_t$, to a shock of one standard deviation ...
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### Is ARCH test mandatory for VAR?

Is ARCH test mandatory for VAR? If so, what lag length of the ARCH test should I use? The same as the lag length of my VAR or VEC model?
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### Why do VAR forecasted values radically change depending on which month historical data end?

I am building a model to forecast housing variables using vector autoregression. I am encountering spurious results. My forecasted values change dramatically depending in which month the historical ...
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### Testing for cointegration and building a VEC model

I have 3 variables which are all stationary at 2nd order difference. I want to check for cointegration using the piece of code below. If I run pairwise cointegration analysis then I get these results: ...
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### R: vector autoregression with penalty for non-cointegrated factors

I can perform a vector autoregression using the "vars" package in R. library(vars) data(Canada) VAR(Canada, p = 2, type = "none") But as I understand it, vector ...
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### Testing for differences in variation between variables

I am trying to find out whether it is true that variation in expenditure is greater, for more narrow subsets. e.g. is it more likely that an individual buys an orange instead of an apple, than it is ...
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### VAR model interpretation: Coef vs Impulse response functions

In courses such as time series analysis, we learned that the relationships derived from impulse response functions or Granger causalties are more interesting than the estimation output. I was ...
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### VAR model selection, auto-correlation specification issues

I am encountering the following problems and I don't really know which model a should pick. All model selection criteria indicate that I should take the model with 1 lag. After building the VAR(1)-...
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### How to impose exclusion restriction on cointegrating vector? R reproducible example

The code given below estimates a VEC model with 2 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
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### Comparing unit root tests

When comparing the results of different unit root tests (in this case DF-GLS test with and ADF test), should I keep the lag length fixed for both tests, or am-I allowed to use predefined/suggested ...
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### VAR model: include all lags up to AIC-suggested order or just the significant ones?

I'm building a regression model in which I have a dependent variable OSE, and two independent variables, MSCI and Brent. In this model I wish to include lagged variables. I performed an AIC for my ...
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### Global VARX model?

I am looking for a way to compute IRFs for the following setup. Cross country dimension (country level data) Time dimension (60 periods quarterly data) 3 endogenous variables (VAR) 1 Exogenous ...
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### Should I use a VAR or VECM to model a time series in which one variable is stationary?

I was wondering which of the above two models would be most suitable. I'm modelling the relationship between interest rates, unemployment, CPI, GDP and London house prices (all UK data). I was going ...
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### Compute Forecast Error Variance Decomposition for variables outside the Vector Autoregression

I am replicating the paper of Ang and Piazzesi (2003) in the Journal of Monetary Economics (link: here) where they estimate a Vector Autoregression for both unobservable factors and observable ...
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### Breuschâ€“Godfrey test under heteroskedasticity

Do I need to account for heteroskedasticity when performing the (vector) AR1-2 test? The Autocorrelation (AR) 1-2 test is defined as follows - often reffered to as the Breuschâ€“Godfrey test (Wiki link)...
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### VAR impulse response interpretation when differencing

I am trying to formulate a way of how to think about differencing when interpreting impulse responses produced by VARs. There are two different views I came up with. First view is that a temporary ...
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### Impulse response stablity in a VAR model

I am trying to fit a 3 variable VAR model and I need to check if the qualitative features of impulse responses are approximately stable across subsamples. But I am not sure what impulse response ...
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### Estimating a restricted (sparse) VAR in R [closed]

Assume that I want to estimate a VAR or SVAR model for some monthly economical time series without a long history (i.e. in the range of 2000-2016, which consists of only ~180 data per variable). ...
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### Replicate cointegration rank statistics using a 9 variable VAR(2)

I am trying to replicate Tables 3 and 4 from the paper "A Long Run Structural Macroeconometric Model OF the UK" by Garratt et al (2003). Using the Akaike criterion the authors decide to proceed with ...
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### Autocorrelation of VAR residuals

I am fitting a VAR model on 50+ timeseries that both have two variables, x and y. I am trying to identify if my bivariate VAR model has sufficient amount of lags. AIC nad SBIC both suggest using 2 ...
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### How to code dummy variables for structural breaks in VAR

This question is really 2-in-1: 1) How do I code dummy variables for the following series that has 2 structural breaks in trend; an initial upward trend, then a much flatter upward trend, then ...
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### Variance of a multivariate AR(1) process

I have a multivariate AR(1) process (first-order vector autoregression, VAR(1)) of the form $$\pmb X_{t+1} = A \pmb X_t + \zeta_t$$ where $\pmb X_t$ is a vector, $A$ is a matrix and \$\zeta_t \sim N(...
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### Nonstationary (but not I(1)) components in VAR model. What should I do?

I have several time-series, which are non-stationary, but it looks like they have a number of structural breaks, resulting in different trend coefficients. I need to estimate a VAR model and make ...
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### lag length selection in VAR model

I want to study the impulse response function and the variance decomposition by fitting a var model. The lag length criteria gave me this result. What's the problem ?
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### Choices of priors for time-varying-parameter VAR in Primiceri (2005)

The main idea of the question is how to choose priors' parameters for the time-varying-parameter VAR model. I am really confused in the way Primiceri (2005) constructed priors in his paper under the ...
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### GARCH Markov representation

I'm studying the Markov representation of a GARCH(p,q) process, i.e. $$\boldsymbol{v_t} = \boldsymbol{u_t} + M_t\boldsymbol{v_{t-1}}$$ where \boldsymbol{u_t} = \begin{pmatrix} \...