# Questions tagged [vector-auto-regression]

Vector autoregression is a stochastic process model used to capture the linear interdependencies among multiple time series.

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### What formula should I use for 1D autocorrelation?

I obtained a list of $r^2_{end-to-end}$ from a Monte Carlo simulation of polymer movement. ...
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### Least squares regression with stable and non-negative constraint

I am trying to fit an auto-regressive model to a time-series where I have some constraints. We have the first order model, $$X_{t+1} = AX_t + \xi_t,$$ which I can pose as a least-squares ...
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### Non-negative autoregressive model

I am trying to fit a linear 1-order autoregressive model to some multivariate time-series data. The model I am using is of the form $$x_t = Ax_{t-1}+\xi_{t-1}$$ and I am solving it in R using the mAr ...
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### Solve VAR(2) for the n-step ahead forecast

I'm trying to find for this VARX*(2) $$x_t=a_0+a_1t+F_1x_{t-1}+F_2x_{t-2}+\Theta_0d_t+\Theta_1d_{t-1}+\Theta_2d_{t-2}+\varepsilon_t$$ an explicit form for $x_{T+n}$, i.e. solve it as an equation for ...
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### Vector-Autoregression: Assertion on the convergence radius of a power series with square-matrices as coefficients

I first want to give some context to understand the setup of my question (but you may provide an answer without knowing anything about time series analysis - I guess). Anyways: In a proof that derives ...
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### In search of vector autoregression models supporting uniform bounds on coordinate-wise derivatives

This question is motivated by the desire to build mathematical models that forecast vector-valued discrete time series while guaranteeing a kind of "continuity" via uniform bounds on the ...
1 vote
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### Autoregressive Gaussian process -- limiting distribution?

Let $x_0 = 0$ and suppose that $x_{t + 1} \mid x_t \sim N((1-\alpha) x_t, \alpha^2)$. That is, $$x_{t + 1} = (1- \alpha) x_t + \alpha w_{t+1}, \quad \mbox{for}~t \geq 1,$$ where $w_{t}$ are ...
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### Spillover and covariance effects in spatial statistics

I have a dependent variable, $Y$, which is made up of several independent uncertain variables, $X$. Independent variables are dependent to each other and there are co-variance and spillover effects ...
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### Partial derivative of matrix-vector product: Least Square

The following is part of an assignment so no full answers please. I am given the following VARX process: $$Y(t) = \mu + \sum_{p=1}^P A_p Y(t-p) + BU(t) + \epsilon (t),$$ with $t=1, \dots ,T$. ...
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### Cointegrated multivariate time series - question about a derivation

Trying to follow a derivation in Lai & Xing's "Statistical Models and Methods for Financial Markets", regarding multivariate time series: Let $$\Delta \vec{y}_t = \vec{\mu} + \Pi \vec{y}_{t-1}$$ ...
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### What are the instruments in a panel p-var? (vector autoregression)

So, I am following Abrigo Love (2015) and I want to write a Matlab code to produce the estimate of a panel VAR (I do know that there is a STATA code already done, but I am trying something different, ...
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### Finding the ACF of a VAR(1) model

I want to know the first order autocorrelation of a VAR(1) model. That can be calculated as follows $\rho(1)=\frac{\gamma(1)}{\gamma(0)}$ where $\gamma(1)$ denotes the covariance and $\gamma(0)$ ...
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