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14 votes
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What is the difference between VAR, Dynamic Regressive, and ARMAX models?

I will focus on ARMAX versus VAR. I am not quite sure what a dynamic regression is. (I have seen a few different interpretations. Funnily, there are textbooks and lecture notes with chapters called "...
Richard Hardy's user avatar
14 votes

Interpretation of Impulse Response and Variance Decomposition Graphs

Impulse response plots represent what they are named after - the response of a variable given an impulse in another variable. In your first graph you plot the impulse-response of EUR to EUR. At the ...
user30978's user avatar
  • 151
11 votes

VAR forecasting methodology

I thought I would add to Regis A Ely very nice answer. His answer is not wrong, but using a VAR to forecast is different than using a VAR to do other VAR type things (i.e. IRF, FEVD, Historical ...
Jacob H's user avatar
  • 922
11 votes

Why are my VAR models working better with nonstationary data than stationary data?

Two facts: When you regress one random walk on another random walk and incorrectly assume stationarity, your software will generally spit back statistically significant results, even if they are ...
Matthew Gunn's user avatar
  • 22.4k
11 votes

Unconditional mean and variance of a stationary VAR(1) model

Taking the variance of both sides of the equation $$ y_t = \nu + A_1 y_{t-1} + u_t $$ leads to $$ \operatorname{Var}y_t = A_1\operatorname{Var}y_{t-1}A_1^T+\Sigma_u. $$ Stationary implies that $\...
Jarle Tufto's user avatar
10 votes
Accepted

ARIMAX vs VAR comparison

From a theoretical perspective, VAR does not include moving-average (MA) terms and approximates any existing MA patterns by extra autoregressives lags, which is a less parsimonious solution than ...
Richard Hardy's user avatar
9 votes
Accepted

Required sample size and degrees of freedom for a VAR

One should not expect there to be a hard-and-fast rule for such thresholds. The reason is that the precision of the estimates does not only depend on the ratio between parameters and observations, but ...
Christoph Hanck's user avatar
9 votes
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Time series data with seasonality using VAR?

VAR models are routinely used with seasonal data, e.g. in macroeconomics where most of the time series (such as GDP or unemployment) are seasonal. Seasonality is handled either (1) outside of the ...
Richard Hardy's user avatar
8 votes

Interpreting VAR impulse response

When you conduct VAR all variables should be on the same scale or same variable transformation basis (or as close as possible). It makes perfect sense that when you multiply your original variables ...
Sympa's user avatar
  • 7,772
8 votes
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Panel vector autoregression models in R?

There is your solution. Code will be available soon. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2896087 Panel Vector Autoregression in R: The Panelvar Package: This paper considers two ...
Michael Sigmund's user avatar
8 votes
Accepted

OLS with Time Series Data - yay or nay?

There are time series models (such as VAR, ARIMA, etc.) and there are estimation techniques (such as OLS, maximum likelihood (ML), etc.). Different models can be estimated by different techniques (...
Richard Hardy's user avatar
7 votes
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VAR in levels or differences for prediction only?

In absence of cointegration, running a VAR in levels is not justifiable, because the dependent variables diverge from any possible combination of the regressors (unless in each equation of the model, ...
Richard Hardy's user avatar
7 votes

Impulse response: Interpreting shock and response for log-variables

The VAR(p) model is defined as $$y_t = \Phi_0 + \Phi_1 y_{t-1} + ... + \Phi_p y_{t-p} + u_t$$ In your case $p=3$ and $y_t \in \mathbb R^2$ with the two variables $y_t =(prod_t,e_t)$. The infinite MA(...
Jesper for President's user avatar
6 votes
Accepted

Least stupid way to forecast a short multivariate time series

I understand that this question has been sitting here for years, but still, the following ideas may be useful: If there are links between variables (and the theoretical formula does not work so well),...
jochen's user avatar
  • 721
6 votes

Why Are Impulse Responses in VECM Permanent?

This is a great question, and I'm learning so bear with me. What would be a correct interpretation of an impulse response that does not go back to 0 in a VECM? Riffing on the drunken walk theme, ...
Ben Ogorek's user avatar
  • 5,387
6 votes

What is lm() compared to VAR()

If var$1 and var$2 are two distinct variables, fit1 = lm(var$1 ~ var$2, data = data) will ...
Richard Hardy's user avatar
6 votes

Unconditional mean and variance of a stationary VAR(1) model

According to Lütkepohl (2005), p. 14-15, if we have a $K$-variate VAR(1) process of the form $$ y_t = \nu + A_1 y_{t-1} + u_t, $$ then the unconditional mean is $$ (I_K-A_1)^{-1}\nu $$ (where $I_K$ ...
Richard Hardy's user avatar
6 votes

VAR model for first differences (not a good idea?)

Think of it this way, when data is I(1), that is interesting. It tell's us something about the underlying process. Further, if you have two I(1) process and they are co-integrated, then this is ...
Jacob H's user avatar
  • 922
5 votes

VAR-model with a contemporaneous variable

A multiple-equation VAR model where contemporaneous dependent variables enter as regressors in other equations is a structural VAR (SVAR) model. When it comes to estimation of such models, there is a ...
Richard Hardy's user avatar
5 votes
Accepted

Find cointegrating vectors and loadings from a trivariate VAR(1) equation

Checking out equation by equation $$ \begin{aligned} X_t &= 1 + 0.5 X_{t-1} + 0.5 &Y_{t-1} & &+ \epsilon_{1,t} \\ Y_t &= &Y_{t-1} & ...
Richard Hardy's user avatar
5 votes
Accepted

Difference between Distributed Lags and VAR Models

I am having a difficulty understanding the actual question, but let me provide some clarification that could be helpful. Take two time series, $x_t$ and $y_t$. Distributed lag DL($q$) model: $$ y = \...
Richard Hardy's user avatar
5 votes
Accepted

How many endogenous variables in a VAR model with 120 observations?

Since vars uses (equation-by-equation) OLS estimation, the number of parameters in one equation cannot be greater than the number of data points used in the ...
Richard Hardy's user avatar
5 votes
Accepted

Selecting lag order for VAR and VECM

Your methodology seems fine. From a theoretical perspective, it broadly agrees with recommendations in time series textbooks. From an empirical perspective, your models have well-behaved residuals, ...
Richard Hardy's user avatar
5 votes
Accepted

How to explain and interpret impulse response function (for timeseries)?

Impulse-response analysis is quite simple. Having estimated a vector autoregressive (VAR) model and expressed it in a vector moving-average (VMA) representation, you are able to see how a shock to ...
Richard Hardy's user avatar
5 votes
Accepted

what does it mean to run a time series model in levels?

VAR in levels just means without taking any differences of the data. If your data in levels (i.e. as-is without any differencing) is $I(d)$, then first-differencing will make your data $I(d-1)$, and ...
dlnB's user avatar
  • 2,289
5 votes

AIC, BIC values keep changing with lag.max in VAR model

If you have a sample of size $T$ and are exploring VAR models with up to $P$ lags, the models being compared (VAR($1$), VAR($2$), ..., VAR($P$)) are fitted on the last $T-P$ data points in the sample. ...
Richard Hardy's user avatar
5 votes

Stationary VAR( 1) process : complex eigenvalues

The process is stationary when all the complex eigenvalues are within the complex unit circle. This implies you are correct in checking that the norm is less than 1. An AR process with complex ...
John's user avatar
  • 2,287
4 votes

Forecasting of highly correlated time series

The AR, MA, and ARMA models are examples of univariate time series models. Each of these models has a multivariate counterpart: Vector Autogression (VAR), Vector Moving Average (VMA), and Vector ...
John's user avatar
  • 2,287
4 votes

Covariance of two time series driven by a restricted VAR(1) model

One direction to go in might be something like: $$ X_n = \rho_x X_{n-1} + \epsilon_n $$ and $$ Y_n = \rho_y Y_{n-1} + \rho_{xy}X_n +v_n $$ Substitute for $X_n$ in the second equation: $$Y_n = \rho_y ...
Matthew Gunn's user avatar
  • 22.4k
4 votes
Accepted

VAR model interpretation: Coef vs Impulse response functions

Interpretability is another issue. While you are of course right that structural responses are generally of more interest, even an orthogonal impulse response generally is more useful than the ...
Christoph Hanck's user avatar

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