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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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### when fitting a regression model to a time-series, can I use lagged values of the time-series itself?

I'm fitting a regression model $y_t$ to a time series $x_t$ (not a dynamic model involving ARMA terms!). I saw that useful predictors to put in my model are $t$, seasonality variables and lagged ...
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### How to calculate auto-regression with missing values for different surnames in one generation?

I do have a dataset consisting of surnames, years and values y. My aim is to analyze whether the value y is dependent on the corresponding value y of the previous generation. Unfortunately, I do not ...
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### Regression for long tailed time series events

I have a set of values which are a time series and follow a long tailed skewed distribution. I would like to understand what the best method might be to predict the next value in the series. Do the ...
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### Z-score from Skewed Student T

I'm implementing the following method. The text is provided for background, but my question is about line (8). Am I understanding this as "a z-score generated from a standardized skewed Student t?" ...
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### Solving Variance of Time Series AR process [duplicate]

I am trying to solve for the variance of $x[n]$, a time series process. $$x[n] +a_1x[n-1]=w[n]$$where $w[n]$ is white noise with zero mean and variance $\sigma^2_v$. Also $|a_1|<1$. I am aware ...
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### Statistical test for comparing means of two AR(1) time series

Say I have two time series which each follow the AR(1) model: $$X_{t+1} = X_t + (1 - \theta_X) (\mu_X - X_t) + \epsilon_X(t)$$ $$Y_{t+1} = Y_t + (1 - \theta_Y) (\mu_Y - Y_t) + \epsilon_Y(t)$$ ...
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### Nonstationary solutions for stationary ARMA equations

By "stationary" I mean "weakly stationary". Consider a "stationary" AR(1) equation: $$X_t=\varphi X_{t-1}+\varepsilon_t,$$ where $t\in\mathbb{Z}$ are discrete time moments, $\varepsilon_t$ a zero-...
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### Showing 0 covariance for special form of AR(1) time series

This is an exercise I have been trying to solve but have not made much progress. Suppose $\{Z_t\}$ is an AR(1) process with $\rho_1 = \phi$. Define the sequence $\{b_t\}$ as $b_t = Z_t - \phi Z_{t+1}$...
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### AR model throws ValueError on a constant time series

Here's my code: ...
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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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### How to check whether a given ARIMA (p, d, q) process is stationary or not?

I know that a finite MA process $X_t = \Theta(B)Z_t$ is always stationary. Also, whether an AR(p) process is stationary or not can be verified by checking the roots of $\Phi(B)=0$ where the process ...
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### Why do these independant variables have significant explanatory power, when 'theoretically' they should have none? (Self contained example inside)

I am putting together a model which involves a simple linear regression, and to aid the development I have put together a process for generating synthetic observations. The idea is that you have ...
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### Relation between AR(1) and Vasicek model

The discrete time version of a Vasicek model is equivalent to an AR(1) model with opportunely chosen parameters, as showed in this paper: http://www.damianobrigo.it/toolboxweb.pdf. Following this ...
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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{...
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### Moments of an AR(1) Process

Definition of an AR(1) process In an Autoregressive Process, a time series can be generated based on a stochastic difference equation. \begin{align} X_t = c + \phi \, X_{t-1} + \epsilon \end{align} ...
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### How can I estimate autoregression when non-stationary?

I have a series that I believe has one autoregression characteristic under condition A (example: positive) and another under condition B (example: negative). Is there a way (hopefully in Python) to ...
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### Stationary distribution of AR(1) process with AR(1) shocks

I am trying to find the stationary distribution of an AR(1) process, where the shock terms themselves are an AR(1) process. That is, the process moves subject to the following 2 equations: \begin{...
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### AR(1) process can be estimated using linear regression

Can the $AR(1)$ process represented as $$x_t= ax_{t-1}+\epsilon_t$$ be estimated by regressing $x_t$ on its lagged value $x_{t-1}$.
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### What is an autoregressive decoder?

I saw that this was part of a deep belief network I was looking at. I'm not sure what it means. Is it a layer that transforms few inputs into many outputs and has a connection to itself? What is an ...