# 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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### PC-Vector Autoregression (PC-VAR)

When using PC-VAR model for forecasting purposes, can we define it in the following manner? where a k-dimensional vector of intercepts is denoted by φ0 , Φ represents a k × k matrix of coefficients ...
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### Identifying positive and negative shocks in impulse responses

Dear StackExchange community, I'd have a question on impulse responses that I have not found an answer to in econometrics textbooks. Specifically, I would want to know how to interpret impulse ...
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### IRF of Structural VAR equal to Standar VAR?

I´m doing a traditional Phillips curve approach with a VAR model, in particular, I used the methodology of Blanchar and Quah (1989) to obtain the structural VAR, but when comparing the IRF graph of ...
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### Constrained Matrix Decomposition

I am working on a structural vector autoregression that requires imposing constraints on a matrix factorization. In particular, I have an N-dimensional positive definite matrix $\Sigma$ that I need to ...
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### Differences between Static Factors, Dynamic factors and Exploratory factor analysis in Time Series

I came across many types of factor analysis techniques in the context of time series data. I am not sure whether exploratory factor analysis refers to the same static factor analysis methodology. If ...
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### Residual Diagnostics in Vector Autoregression (VAR) model

My target is to forecast GDP and I have 5 predictors. I estimated a VAR model and the reason why I employed a VAR is that since it considers all variables as endogenous. Since I am only interested in ...
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### Forecasting using PC-VAR

I am trying to forecast an index by using a PC-VAR. When performing the PCA, can I exclude the response variable from the dataset and find the PCs and later build a VAR with the response variable and ...
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### Why forecast accuracy is very high in Restricted VAR but not in individual OLS estimate?

When a VAR is estimated and tested on the test data the RMSE of the model was around 25. However when I estimated a restricted VAR by setting coefficients of the lagged terms of the dependent variable ...
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### How to estimate a Vector Autoregression model using ARCH estimation (VAR-GARCH)?

I estimated a vector autoregression (VAR) model using 3 lags and 5 variables. However, when I estimated the equation using OLS, heteroskedasticity was present. In this sort of a situation, what is the ...
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### What is the coefficient that shows whether there is a positive or negative relationship between variables in vector error correction models? [closed]

I am trying to estimate the long-run and short-run relationship between variables. Based on the Johansen cointegration analysis it was concluded, that there is one cointegrating relationship. The next ...
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### How to compare which variable has more effect in VAR model?

I am using VAR model. I have six endogenous variable and I am using pairwise Granger causality tests to identify the causality, but I am interested also which one has biggest effect in one endogenous ...
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### How to estimate moderators of persistence in a panel?

I have a panel dataset of $n$ groups (i), observed at a given time (t), where we observe a DV (...
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### Multivariate TS analysis for Carbon Prices

I am new here so please pardon me if I make any mistakes. I am trying to understand the determinants of carbon RGGI prices from 2012-2021, using quarterly data available from the website. Basically, ...
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### Multivariate forcasting when variable observations are not contemporaneous: lag logic

I am looking at various VAR models for several time series, doing one-ahead forecasts. Within each period of observation there are sub-periods. Variable x is ...
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### How to deal with a mix of I(1) and I(2) variables?

I have one dependent variable which becomes stationary after the first difference I(1). There are 4 independent variables, out of which 2 become stationary after the first difference and the other two ...
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### Transforming a generic $ARIMA(p,d,q)$ process to make it stationary

I am trying to build a VAR model with 6 variables. In addition to performing the ADF and KPSS tests for stationarity, I thought it might be interesting to use the ...
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### Using a VAR model to predict stock prices

I ran into an issue while trying to predict stock prices using a Vector Autoregression (VAR) model. After noticing that all the series are non-stationary (see example below): I took first differences ...
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### Why does the prediction of a VAR dgp diverge from the test set?

I'm working on a multivariate data set consisting in 44 observations (which have to be splitted: the first 34 observations are in the training set, the remaining ones in the testing set) of 9 ...
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### Quantifying the significance of impulse response functions

I use Stock and Watson's classic reference on vector autoregressions for this question. They carry out a VAR on inflation, unemployment and the interest rate and thereby produce the following matrix ...
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### Predictive or Error Tests for Vector Autoregressive Models (VAR)

I have two questions relating to VAR and would kindly appreciate any assistance/opinion: Question 1: I am having difficulty finding a proper predictive ability test for my VAR model to conclude if my ...
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### Do we need stationarity for non autoregressive time-series models?

Most of the literature around time-series models focuses on models with AR terms. Here I have a slightly different and potentially less complicated case. Suppose you have a time-series model with the ...
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### Problems with VAR: Autocorrelation when imposing restrictions, ARCH effects and non-normality at all times

I am estimating a VAR model for log-returns of: copper prices, USD/local currency exchange rate, and the local stock market index. Using VARselect I estimated a VAR(...
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### What is the effect of robust estimators of covariance variance (Newey-West) on the VAR model?

What will change in VAR model if I will introduce robust estimators of covariance variance (Newey-West)? Will only the interpretations change and the properties of the model remain the same? Or maybe ...
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### How to create a VAR model with robust estimators of the covariance variance in $R$? [duplicate]

I have a problem with autocorrelation in my VAR model, even when I raise a lag order. How can I introduce robust estimators of variance and covariance matrices into the model? How do such estimators ...
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### How to fit a scalable Bayesian VAR model in Stan/JAGS

I am trying to fit a Bayesian vector auto regressive model but I am struggling with the computation. I tried both JAGS and Stan to fit the model but I have never been able to fit it successfully. It ...
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### VAR model selection: is AIC an appropriate measure given that the sample size changes depending on the number of lags?

Given that the sample size of a VAR (or a similar model: VARX, SVAR etc.) reduces by $1$ for each extra dependent-variable lag that I introduce (since we need to drop the empty rows, or ...
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### A new method for processing music scores?

I have developed a method and python script: https://github.com/githubuser1983/algorithmic_python_music which allows the user to input a midi file and then chose a few numbers as parameters, and the ...
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### What units are the cumulative response functions of a VAR measured in, and why does orthogonalisation appear to change the scale?

There are quite a few questions on this site regarding the interpretation of the impulse-response-function plots of a VAR, but none answer my query directly. I will attempt to be as concrete as ...
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### VAR - VARX model selection

Suppose I have three stationary economic time series $y_i$ that are not cointegrated and I want to investigate the relationship between them. I happen to be unsure about the "endogenousness" ...
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### Impulse response function of the exogenous variable in a VARX model

I am learning about VAR models "by doing", so to speak. I am using statsmodels; comparing the documentation on VAR and VARX models, I would like to ...
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### Lag choice for a VAR model

There is something confusing (for me) about this question. I'm working on a VAR model (7 time series) where i've checked for Granger causality (yes) and stationarity (yes). Now, according to the AIC ...
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### Forecasting with unscaled data using coefficient estimates from a penalized regression on scaled data

This is an embarrassingly basic question, but I keep producing absurd estimates from a pretty well-fitting model, so I think I’m making some fundamental mistake. I have a longish time series that I am ...
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### VAR model and impulse response function

Can we run a var model on the first difference instead of the levels as variables when in levels seems to be non stationary. Also the variables are not cointegrated and I hv to run the impulse ...
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### IRF for VAR GARCH (Impulse Response Function)

When there is ARCH effects on VAR residuals $\varepsilon_t$, we can use a GARCH model to remove them : $\zeta_t = \Sigma_{t|t-1}^{-\frac{1}{2}} \varepsilon_t$. Following [Lutkepohl, New Introduction ...
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### VAR in levels or differences for generating impulse response functions

My end goal is to do impulse response analysis. My dataset is non stationary. However, it becomes stationary after first differencing. Also, it is not cointegrated. Could I carry out a VAR analysis ...
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### VAR Regression and seasonal adjustment

I am doing a VAR regression, using jobs data by industry from QCEW. I have two questions. Firstly: Is it necessary to have seasonally adjusted data for VAR. Secondly: if so, why is it necessary
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### Best approach to Quantile Vector Autoregression

So I have a system of endogenous variables in panel form (24 Stock over 52 weeks). I would like to use quantile regression of one variable (Trading Volume) upon another (Social Media Sentiment). The ...
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### VAR model and robust estimators of covariance matrix

I have a VAR(2) model which has autocorrelations (since lag = 8 mostly), even when number of lags for this model are bigger. I got and advice that robust estimators of covariance matrix will help with ...
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### Error in solve.default(Sigma) : system is computationally singular: reciprocal condition number = 3.56435e-18 [duplicate]

Im getting the above error when i try to run a VAR. My data sample is small. but im not sure how to use my small sample for this equation. PLEASE HELP ASAP
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### Include exogenous variable in both level and first-difference

I am wondering if I could include, in a VECM, exogenous variable in both level and first-difference, such as : $\Delta X_t = \alpha \beta^{'} X_{t-1} + \Delta X_{t-1} + Y_t + \Delta Y_t + U_t$ Is ...
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### Structural VAR model and Long-run restriction

I studied SVAR and tried to do it using STATA. In STATA manual it explains in long-run restriction we constrain A to be identity matrix. I can't understand why. If A=I matrix then it is not SVAR(no ...
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### VAR Model with different integration order

I am trying to create a VAR model with 4 variables. 3 of them need 2 differences in order to be stationary, while 1 needs only 1. When I take differences I loose one row of data, so there is one ...
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### Insignificant impulse response function - does this really mean that there is no effect?

I estimated a VAR-model and the result was this impulse response function that shows the 95% confidence interval as the red dotted lines. The effect is clearly not significant. But does this mean that ...
Consider $n$ time series stored in an array $y_t = \begin{pmatrix} y_{1,t} \\ \vdots \\ y_{n,t} \end{pmatrix}$, assumed to follow a vector error correction model: for some matrix \$\alpha \in \mathcal{...