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# 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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### Approximate AR(p) with a product of AR(1) and AR(2)

Literature suggests that any AR(p) ARIMA model can approximated as a combination of AR(1) and AR(2) processes. For example, one book suggests that an AR(3) model with the following coefficients: ...
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### Fit ARMA model to ACF

If I have the autocovariance function $\gamma_\tau$ (numerically over a given set of lags $\tau = 0 \ldots n - 1$) of a stationary linear stochastic process, is there an efficient way to determine the ...
127 views

### Stationary Distribution of Multiplicative Autoregressive Model

I know for the additive autoregressive model the stationary distribution of $\{X_t\}$ can be found, if it exists, in the following way: \begin{align} X_t &= \alpha X_{t-1} + \epsilon_t\\ \...
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### Transforming a multivariate binary time series to be stationary

I have a multivariate (multi-response) dataset with, for example, 10 different binary responses. I'm interested in an AR(p) model, determining how the responses at previous time steps relate to the ...
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### Bayesian autoregressive model with second peak at 1 in posterior distirbution of AR parameter

I am trying to run a Bayesian hierarchical AR1 model for a set of fairly short time series. In some of the series I get a second peak around 1 in the posterior distribution of the AR1 parameter. ...
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### Solve For ACF/ACVF of An AR(3) Process

I am currently doing an online course on Time Series and this is a self-assessment question from the homework, I won't see the answer until I submit, so I would appreciate hints/leads. I have made ...
1k views

### Why is the dickey fuller test different from a simple t-test

I am trying to understand why should there be different distribution for t-statistic, in case of AR model, Dickey-Fuller test For e.g. Say, the model is $Y_t = \beta_lY_{t-1} + \varepsilon_{t}$. ...
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### Stationarity of AR(1) model

Okay this might be a stupid question but, I understand that a (weakly)Stationary Time Series is one where 1) $E[X_t]$ = constant 2) $Var(x_t)$ = constant 3) $cov(x_t,x_{t-h})$ = constant, at any ...
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### Proving stationairty of AR(1)

Let me set this up. We have an AR(1) process: $x_1 = w_1$ and $x_t = \frac{1}{2}x_{t-1} + w_t$ for $t \geq 2$ and where the $w_t \sim N(0, \sigma^2)$. I have read that this process is stationary - ...
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### Why do the fundamental time series model explain many dynamical phenomena

What is so special about the way Moving average models, Autoregressive models and their combinations (ARMA, ARIMA) are defined that they seem to fit many of the univariate time series we observe in ...
768 views

### How do I Estimate Joint Entropy Using a Histogram?

I am trying to estimate the entropy for two time series, defined by random variables $X$ and $Y$, each distributed according to an unknown PDF which is to be estimated empirically (using a histogram ...
478 views

### ACF and PACF of AR(p)

Why does the PACF of AR(p) model cut off past the order of the series? Why does the ACF tail off to zero? What is the intuitive reason behind this?
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### Conditional maximum likelihood of AR(1) UNIFORM PROCESS

Let $Z_t = \phi Z_{t-1} + u_t$ where $u_t \sim uniform[-1,1]$ and $|\phi|<1$ I I am facing problems coming up with conditional maximum likelihood estimate of an AR(1) process with uniform errors. ...
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### Would multiple-regression give the same results as auto-regression?

From looking at textbooks, I see that the equation used for estimating auto-regression is different from the equation used to estimate multiple-regression. But, if I used successive values from a ...
156 views

### Convert Spatial Weight Matrix File?

I want to create a spatially lagged version of my response variable to estimate a spatial autoregressive model in R. To quantify the spatial relationship that exists among the features in my data I ...
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### How to fit an Autoregression model in Spark? [closed]

I'm having a look at the implementation of Autoregression model in Scala https://github.com/sryza/spark-timeseries/blob/master/src/main/scala/com/cloudera/sparkts/models/Autoregression.scala Now if I ...
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### Could somebody help me read these ACF and PACF plots?

So, I have this time series that I have already forecasted using an ARMA model, but I am new to this and am therefore not at all sure whether or not I did this (somewhat) correctly. I got the best ...
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### How to simulate a time-dependent AR(2) model?

I'm working with time series and I need to simulate a time-dependent AR(2) model like this: $Y_t = a_tY_{t−1} − 0.5Y_{t−2} + \epsilon_t ,t =1, 2, ..., 1024,$ where $a_t=0.8*cos(t)$ How can I ...
905 views

### External regressors in mean or variance equation of AR(1)-GARCH(1,1)?

What is the difference between entering my external regressors in the mean equation and entering them in the variance equation in an AR(1)-GARCH(1,1) model? I get more explanatory results with the ...
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### How to randomly generate a data with an error which is not normally distributed but follows an empirical distribution $(0, \sigma^2)$

I have this model AR model for multiple time series $Y_{it} = \phi y_{it-1} + \delta_1y_{i-1 ,t-1} + \delta_2 y_{i+1 , t-1} + \lambda_i + \epsilon_{it}$ where $\epsilon_{it}$ is a function of ...