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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 ...
citizenfour's user avatar
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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 ...
Bilal Khan's user avatar
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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 ...
Drew Brady's user avatar
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How can I decompose this VAR equation?

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{...
Anna's user avatar
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Is there such a thing as a geometric series of a non-constant?

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 ...
hendogg87's user avatar
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Questions on coin tossing and AR(1), martingale & Markov chain

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)....
Celine's user avatar
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Generating synthetic multivariate time series with stable VAR model

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 ...
Eti JS's user avatar
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3 votes
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What's the point on using logarithms before differencing a time series in ARIMA? [closed]

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 ...
Daniel Limia Perez's user avatar
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Two correlated AR(1) series [closed]

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

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 ...
Almostsurely's user avatar
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Simulate autoregressive model

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 $...
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Smooth autoregressive model

I am trying to build 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 $p &...
newbie's user avatar
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Understanding Moving Average Models

Can someone explain why we use past errors to predict future data values in Moving Average models? It just doesn't make sense why we use past errors to make predictions. Using past values, as in $\...
Seller Central's user avatar
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1 answer
568 views

Precision matrix of AR(2) matrix

I am trying to construct the inverse covariance matrix of an AR(2) process of the form $X_t=\theta_1 X_{t-1}+\theta_2 X_{t-2} + \epsilon_t$ with i.i.d. $\epsilon_i$, $\mathbb{E} \epsilon_i =0$, $\...
Conny's user avatar
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2 votes
1 answer
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Random Coefficient AR(1) and Kalman filtering

I am interested in a process such that \begin{align*} &x_{t+1}=\rho_{t} x_t+\varepsilon_t, \varepsilon_t\sim \mathcal{N}(0, \sigma_{\varepsilon}^2)\\ &\rho_t=\lambda \rho_{t-1}+(1-\lambda)u_t,...
Terry's user avatar
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4 votes
2 answers
118 views

How do I derive the following expression for the sum of orthogonal matrices?

In Johansen's book 'Likelihood-based inference in cointegrated vector autoregressive models', in order to get the expression for the Granger's representation theorem he claims that: $$\beta_\bot(\...
Alchemy's user avatar
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Running coint_johansen cointegration test gives : LinAlgError: Matrix is not positive definite

I am pretty new to mulltivariate time series, I am trying to make a VAR model with 108 predictors and 1 target variable. While performing the Johansen Cointegration Test, I am getting an error ...
Dravidian's user avatar
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High F-Statistic Value and negative Probability for Granger Causality Result, Interpretation?

I tested the hypothesis: SwissFranc/USD does not Granger Cause S&P500 and received an F-Statistic of 69.1 and a probability of 2E-51. How do I interpret this result and can the probability be 2E-...
CleverseekerRover1's user avatar
2 votes
1 answer
694 views

AR(1) to Ornstein-Uhlenbeck for AR(1) process of the form $\ln z_{t+1}=\rho \ln z_t+\sigma \sqrt{(1-\rho^2)}\epsilon_t$

I have the AR(1) process of the following form: $$\ln z_{t+1}=\rho \ln z_t+\sigma \sqrt{(1-\rho^2)}\epsilon_t$$ And need to find its continous time corresponding Ornstein-Uhlenbeckprocess. I have ...
user469216's user avatar
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36 views

Can an autoregressive process of order $k$ be expressed as a $k$-step Markov chain?

I am curious if an autoregressive process of order $k:$ $X_{t}= c+ \sum_{i=1}^{k}\phi_i X_{t-i} + \epsilon_i$ can be expressed as a $k$-step Markov chain with transition probability $$ P_{ij}^{k} = ...
Arbiturka's user avatar
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Collinearity in Vector Autoregression and Impulse Response (Time Series)

I am sort of new to time series, and I am jumping right into modeling one time series in terms of past values of itself as well as other time series. Simply from visualizing the predictor time series, ...
Jane Sully's user avatar
1 vote
1 answer
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Determining first element of an AR1 model

I have an AR1 process of the well-known form: $y(t) = a*y(t-1) + e(t)$ And, in any computational software the elements of the time-series $y$ will be stored in a vector. Now, how can I calculate $y(...
Fabio Capezzuoli's user avatar
1 vote
0 answers
48 views

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 ...
A.Sah's user avatar
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1 answer
103 views

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 $t=1, \dots ,T$. ...
wrong_path's user avatar
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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 $$\Delta \vec{y}_t = \vec{\mu} + \Pi \vec{y}_{t-1}$$ ...
Lagerbaer's user avatar
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137 views

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, ...
RAMM's user avatar
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3 votes
1 answer
436 views

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 $\gamma(0)$ ...
Eren's user avatar
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341 views

How to generate power spectra of AR-1 process in matlab?

I have a time series x1 as 3600x1 double. I need to fit AR-1 spectra on the power spectral density of x1. Well, I am not an expert and this is the first time I am studying time series. If AR-1 ...
Vid's user avatar
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