Questions tagged [vector-auto-regression]

Question 1

Noting first that autoregressive models are for stationary signals and it is assumed an AR fit will not produce accurate results: For the differential equation $m*\frac{d^2x}{dt^2}+b*\frac{dx}{dt}+k*x(...

Question 2

I am writing a dissertation and for one part I want to validate an estimator I derived given different systems. In particular, the most basic system is a VAR(1) model: $$ X_t = AX_{t-1} + \epsilon_t $$...

Question 3

Consider an autoregressive process of the form, $$ x_{t+1} = Ax_t + \xi_t, $$ where $\xi_t$ is sampled from ${N}(0,\Sigma)$, then I have two formulas from the stationary covariance that do not agree. ...

Question 4

(Repost of this thread, as I believe that the answer may be wrong.) An $\text{AR}(1)$ model with Gaussian errors takes the form below: $$x_t = \rho x_{t-1} + \epsilon_t$$ where $\epsilon_t$ are IID ...

Question 5

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 ...

Question 6

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 ...

Question 7

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 ...

Question 8

I have this VAR equation $\begin{pmatrix} s_t\\ f_t \end{pmatrix} = \frac{\begin{pmatrix} 1-0.4L & 0.3L\\ -0.6L & 1-0.1L \end{pmatrix}}{(1-0.1L)(1-0.4L)+0.18L^2} \begin{pmatrix} 0.5\\0.7\end{...

Question 9

I'm an applied social scientist with an interest in time series analysis. I have a question about the behavior of a 'geometric series' of a non-constant, so to speak. If we had a geometric series like ...

Question 10

After $t$ tosses of a fair coin, let $H(t)$ be the number of heads observed so far; $T(t)$ be the number of tails observed so far; $X(t)=H(t)-T(t)$. Which one of $H(t)$, $T(t)$ and $X(t)$ are a) AR(1)....

Question 11

I am trying to generate stable multivariate time series (MTS) using a VAR model. Here I don't try to fit a VAR model on existing data, but to create the data from a VAR process by manually setting the ...

Question 12

I would like to know what's normally the point on ARIMA models, before differencing our time series in order to get stationarity, of applying a logarithm to our series. Does this helps our time series ...

Question 13

I have two AR(1) series that are correlated. $$X_{t,1} = \rho_1X_{t-1,1} + e_{t,1}$$ $$X_{t,2} = \rho_2X_{t-1,2} + e_{t,2}$$ and $corr(X_{t,1}, X_{t,2}) = \rho.$ I want to generate at each time $t$ a ...

Question 14

It is well known that the Wold's decomposition allows that every covariance-stationary time series $ Y_{{t}}$ can be written as the sum of two time series one deterministic $\eta _{t}$ and one ...

Question 15

I am trying to simulate an autoregressive model such that $\mathbf{W}^t = \mathbf{W}^{t-1}\mathbf{M}$ where $\mathbf{M} \in \mathbb{R}^{k \times k}$ and $\mathbf{W} \in \mathbb{R}^{p \times k}$ where $...

Stack Exchange Network

Questions tagged [vector-auto-regression]

Relating Parameters of an Autoregressive Model Back to Physical Parameters of its Equivalent Differential Equation

Can I simply apply non-linear transformations to a VAR model like this? How do I know whether it's stable/unstable?

Covariance of a multivariate autoregression

How to show that an AR(1) process with Gaussian errors is ergodic?

Least squares regression with stable and non-negative constraint

Non-negative autoregressive model

Autoregressive Gaussian process -- limiting distribution?

How can I decompose this VAR equation?

Is there such a thing as a geometric series of a non-constant?

Questions on coin tossing and AR(1), martingale & Markov chain

Generating synthetic multivariate time series with stable VAR model

What's the point on using logarithms before differencing a time series in ARIMA? [closed]

Two correlated AR(1) series [closed]

Wold's decomposition and Gaussian distribution in infinite dimensional Hilbert space

Simulate autoregressive model

Hot Network Questions