Questions tagged [vector-autoregression]

Vector Auto-Regression, a multivariate time-series model / method. Under VAR, each univariate time-series is a linear combination of its own previous values and the previous values of the other series.

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59
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5answers
27k views

What are disadvantages of state-space models and Kalman Filter for time-series modelling?

Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's ...
39
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9answers
81k views

Why use vector error correction model?

I am confused about the Vector Error Correction Model (VECM). Technical background: VECM offers a possibility to apply Vector Autoregressive Model (VAR) to integrated multivariate time series. In the ...
22
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2answers
34k views

VAR forecasting methodology

I am building a VAR model to forecast the price of an asset and would like to know whether my method is statistically sound, whether the tests I have included are relevant and if more are needed to ...
20
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1answer
1k views

Least stupid way to forecast a short multivariate time series

I need to forecast the following 4 variables for the 29th unit of time. I have roughly 2 years worth of historical data, where 1 and 14 and 27 are all the same period (or time of year). In the end, I ...
15
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1answer
2k views

Multivariate biological time series : VAR and seasonality

I have a multivariate time series dataset including interacting biological and environmental variables (plus possibly some exogenous variables). Beside seasonality, there is no clear long-term trend ...
13
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3answers
9k views

Stationarity in multivariate time series

I am working with a multivariate time series and using VAR (Vector Autoregression) model for forecasting. My question is What does stationarity actually means in a multivariate framework. 1) I know ...
11
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2answers
905 views

How to model month to month effects in daily time series data?

I have two time series of daily data. One is sign-ups and the other terminations of subscriptions. I'd like to predict the ...
10
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1answer
2k views

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

I'm using python's statsmodels VAR library to model financial time series data and some results have me puzzled. I know that VAR models assume the time series data is stationary. I inadvertently fit a ...
9
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3answers
16k views

What's a stationary VAR?

What is a stationary VAR (vector autoregression)? Can a VAR with non-stationary variables be stationary? How do you test whether a VAR is stationary or non-stationary? (Example in ...
9
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6answers
8k views

How to estimate vector autoregression & impulse response function with panel data

I am working on vector auto-regression (VARs) and impulse response function (IRFs) estimation based on panel data with 33 individuals over 77 quarters. How should this type of situation be analyzed? ...
9
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1answer
16k views

Interpretation of Impulse Response and Variance Decomposition Graphs

I am finding it difficult to interpret the following Impulse response and variance decomposition graphs-basically studying the effect of currencies on each other(I know the results from the Granger ...
9
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2answers
2k views

VAR in levels for cointegrated data

I have read some paper that expresses that "recent works" show we can use a VAR model with raw data I(1) but there has to be cointegration. This means that there is no reason to difference the data ...
9
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1answer
4k views

Forecasting of highly correlated time series

In time series forecasting using various models like AR,MA,ARMA, etc, we usually focus on the modeling of the data in the change of time. But when we have 2 time series that Pearson correlation ...
8
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2answers
6k views

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

All of these models seem to be used in predicting an endogenous time series variable, using several lagged exogenous time series variables. If it is so, how do we decide when to use which?
8
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1answer
11k views

ARIMAX vs VAR comparison

With a time series Y of interest and another time series X that possible explains a part of Y, I came up with using ARIMAX and VAR models to model. What is the difference? Thanks,
8
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1answer
3k views

Required sample size and degrees of freedom for a VAR

I have read in many textbooks that as the ratio between the number of coefficients to be estimated in a VAR and the number of time periods increases above a certain threshold, estimation becomes ...
8
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2answers
2k views

What is a vector autoregressive model?

I'm looking to understand this from a managerial perspective. For example if I was explaining linear regression I would say it is a line of best fit through some data points and it can be used to ...
8
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1answer
10k views

Fit a VAR model with R [closed]

I have a bivariate time series z_t where z_1t is the change in monthly US treasury bills (maturity 3 months) and ...
7
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2answers
25k views

How to calculate the impulse response function of a VAR(1)? (With example)

How to calculate: 1) Simple IRF 2) Orthological IRF (Y2 -> Y1) Of an unrestricted VAR(1) model: $Y_{1, t} = A_{11}Y_{1, t-1} + A_{12} Y_{2, t-1} + e_{1,t}$ , $Y_{2, t} = A_{21}Y_{1, t-1} + A_{22} ...
7
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4answers
20k views

Time series: one I(1) and one I(0) variable, should I use VAR/VEC, test for cointegration?

Like the title says, I've got two time series, one is stationary to begin with and thus has no unit root, the other time serie is stationary after one-time differencing. I want to create a model out ...
7
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2answers
11k views

VAR or VECM for a mix of stationary and nonstationary variables

I have 4 time series. One of them is stationary and rest of them are not. I need to find relation between them. I will use AIC to decide lag length. Should I use VAR or VECM to find relation between ...
7
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1answer
8k views

Optimal lag length in VECM using vars R package

I have some series that are cointegrated, so I know that I should fit a vector error correction model (VECM). Nevertheless I found no guidance in finding the optimal lag length, say ...
7
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2answers
4k views

Why do we use Vector Autoregressive Models?

Let's say we want to estimate the system $x_{1,t}=\phi_0+\phi_1 x_{1,t-1}+\phi_2 x_{2,t-1} +\epsilon_t$ $x_{2,t}=\gamma_0+\gamma_1 x_{1,t-1}+\gamma_2 x_{2,t-1} +\eta_t$ Do we gain anything be ...
7
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1answer
151 views

VAR() or dynlm() or lm()

Can anybody tell me something about the difference between the functions VAR() and dynlm()? I thought I could do my VAR with OLS ...
7
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1answer
3k views

Understanding vec2var conversion in R

I'm using Bernhard Pfaff's packages {urca} and {vars} to analyze 3 time series. Each is I(1) and cointegrated with $r =2$ cointegrating relationships. The vec2var() command should make the ...
6
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2answers
5k views

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

I am confused while trying to find a general expression for the mean and variance of a stationary VAR model. I am trying to do it for VAR(1). I also can't find it in the literature. Can anyone help ...
6
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2answers
8k views

Time series data with seasonality using VAR?

I have two time series: 1) Which only contains historical data for production 2006-2011 on a monthly basis. 2) Which contains both historical and projected flow data 2006-2057 on a monthly basis. I ...
6
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2answers
341 views

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

Suppose that I have two time series $X_n$ and $Y_n$ where: $$ X_n = \rho_x X_{n-1} + \epsilon_n $$ and $$ Y_n = \rho_y Y_{n-1} + \rho_{xy}X_n +z_n $$ Here, $z_n,\epsilon_n$ are independent random ...
6
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3answers
1k views

Outlier treatment in Vector Autoregression (VAR) Model

Data: Multivariate Time Series, Series Demand of a product Rainfall data both available at monthly level from 2010-2013. Approach: I am trying to estimate the effect of rainfall on demand of the ...
6
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0answers
4k views

Stationary vs Stability

I am searching for an example of an unstable VAR($p$) process (its reverse characteristic polynomial has no roots inside and on the complex unit circle) which is stationary. I come up with this ...
5
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1answer
1k views

How do you simulate two correlated AR(p) time series?

I would be interested in the mathematical framework plus code in R if possible. Basically I want to find out the parameters of the two AR(p) models if I already specificed a certain cross-correlation ...
5
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1answer
144 views

What are good resources to learn about VAR models?

I am looking for websites, books, lecture notes, or research papers to learn about VARs. At the moment I have no knowledge of them. I would greatly appreciate any advice.
5
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1answer
2k views

Open source code for factor-augmented VAR (FAVAR) model

I am looking for an open source package (R, Python, Julia) that has an implemented FAVAR (factor-augmented VAR) class for time-series prediction problem. I've already tried to use several solutions ...
5
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0answers
3k views

VAR model for price forecasting in multiple time-series context. How to get "real figures" as forecasts?

Sorry for the rather long introduction, but since I was (legitimately) critizised for not explaining my cause and questions enough, I will do so now. I would like to conduct a (price)-forecast based ...
5
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0answers
309 views

Restriction matrix for a VAR

In New Introduction to Multiple Time Series Analysis by Luetkepohl (2005), section 5.2.1, it says that one can specify linear restraints for a VAR, $Y = \beta X + U$, in the form $$ \operatorname{vec}{...
5
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0answers
474 views

VAR model with time series of different frequencies

In case I want to see the effect of two or more endogenous time series on each other, I use a VAR model. But how do I proceed if one data set is monthly, and the other one daily?
5
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0answers
4k views

Vector autoregression with exogenous variables

Im dealing with a VAR model where I also want to include exogenous variables. Based on my sampling, the exogenous variables in $t$ are independent from my other variables in $t$, but highly dependent ...
4
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1answer
2k views

Estimating VAR by GLS versus OLS: efficiency

Suppose I have a VAR model with different regressors in different equations (this could be due to restricting some coefficients of a full VAR($p$) model to zero or having some different exogenous ...
4
votes
1answer
10k views

OLS with Time Series Data - yay or nay?

I want to model the relationship between two (time-series) variables by using a Vector Autoregressive model (VAR). Since I am not entirely familiar with time series analysis yet, the following ...
4
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1answer
799 views

How to simulate a bivariate VAR(2) model in R? [closed]

hopefully someone can help! I want to simulate a bivariate VAR(2) model in R using the package containing var.sim (this package is called ...
4
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3answers
2k views

Granger Causality with or without VAR

I would like to test two stationary time series (say a and b) for Granger Causality. I am familiar with the method of running two regressions: ...
4
votes
1answer
3k views

Interpretation of the Impulse Response Function - VAR Estimation

I have some issues while discussing and interpreting this impulse response function (the graphics analysis). What do they mean and represent economically? What can the conclusions be? Basically ...
4
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1answer
2k views

Lead-and-lag test?

What are the simplest methods to check for the lead and lag relationship between two variables? I mean.. how to see, between two variables, which leads the other (and which follows) ?
4
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1answer
5k views

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: ...
4
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1answer
1k views

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(...
4
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3answers
2k views

Does the Granger Causality test in the "vars" package make sense?

We all understand that the Granger Causality test entails constructing two models. The first one is simply an autoregressive model with $y_{t-1}$ being the single independent variable. The second one ...
4
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2answers
947 views

Forecasting with a VAR estimated by GLS versus OLS

Suppose I have a VAR model with different regressors in different equations (this could be due to restricting some coefficients of a full VAR($p$) model to zero or having some different exogenous ...
4
votes
2answers
5k views

Program Impulse Response Functions for VAR

I'm trying to program impulse response functions for a VAR model using Cholesky decomposition. The thing is I do not completely understand how I should do this when I read in the literature. Suppose I ...
4
votes
1answer
4k views

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 ...
4
votes
1answer
3k views

What can be inferred from "covariance matrix of residuals" and "correlation matrix of residuals" after VAR?

I have this VAR: summary(VAR(V6CADModelSt45obs1D.df[,c(5,3,2,6,1,4)], p=5, type="none", ic="SC")) The following is the result of this VAR: ...

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