# Questions tagged [autoregressive]

The autoregressive (AR) model is a stochastic process modelling time series, which specifies the value of the series linearly in terms of the previous values.

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### Modelling auto-correlated binary time series

What are the usual approach to modelling binary time series? Is there a paper or a text book where this is treated? I think of a binary process with strong auto-correlation. Something like the sign of ...
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### Why are we not concerned about the distribution of the $x_t$ in an AR(1) model?

I am trying to investigate the reasons why we don't bother about the distribution of the $x_t$ in an autoregressive model. Why do we concern ourselves about the distribution of $e_t$? And why are ...
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### How to write variance covariance matrix of AR(1) process in R

I'm trying to write autocovariance matrix of AR(1) process in R and I'm having difficulty. The autocovariance matrix that I'm using in my project takes the form as shown in the picture: I also ...
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### Time Series for each customer

Is it possible to create Time Series Analysis for each customer? Say if have 100 customers and I wanted to predict how much amount they are going to spend next. I have done the Time Series for the ...
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### Are all $AR(p)$ processes for which $|a_1|,…,|a_p| < 1$ stationary?

For an $AR(p)$ process $Y_t = a_1Y_{t-1}+a_2Y_{t-2}+...+a_qY_{t-q}$ : Is having the coefficients $|a_1|,....,|a_p| < 1$ just a necessary condition for stationarity, or is it sufficient as well?
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### Unable to calculate the density function for AR

The model is an AR(p) process excited by a white Gaussian noise $\epsilon_t$, \begin{align} Y_t = &c+ \phi_1Y_{t-1} + \phi_2 Y_{t-2}+ \ldots+ \phi_p Y_{t-p} + \epsilon_t\\ \epsilon_t = &\...
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### Is it allowed to reduce a dataset of moving averages to run an AR(1) model properly?

I run a simple AR(1) and AR(2) model with the following code: ar.ols(df$y, order.max = 1) ar.ols(df$y, order.max =2) My dataset is as follows: I do have yearly ...
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### Comparison of GMM and ML estimators for regression with correlated errors

Consider a linear model with normally distributed, autocorrelated errors \begin{aligned} y&=X\beta+\varepsilon \\ \varepsilon&\sim N(0,\sigma^2_{\varepsilon}) \text{ and autocorrelated.} \end{...
I am working on an ARX forecasting problem mostly using feed-forward neural networks in MATLAB. The functional model is of the form $y(t) = f(y(t-1),...,y(t-n),u(t))$. My data is at half hourly ...
I am doing a time series course and in the theory part there are few things I don't understand.In obtaining auto correlation function for AR(p) process it is done as: \newcommand{\Var}{{\rm Var}}\...