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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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### Stationarity of ADL(p, q) with heteroskedasticity

Suppose I have the model $$y_t = \alpha_0 + \alpha_1 y_{t-1} + ... + \alpha_p y_{t-p} + \beta_0 x_t + ... + \beta_q x_{t-q} + \epsilon_t,$$ where $\{x_t\}$ is a stationary process and $\epsilon_t$ has ...
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### Forecast Confidence intervals for for AR(P) [duplicate]

I want to contruct 12-step ahead forecast confidence intervals (CI) for AR(2) models and above. However, the CI calculation seems extremely tedius for forecasts above 2 periods as iteration process ...
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### Spatial Temporal Autoregressive Regression and implication on Fixed effects assumption in Difference in Differences

I am currently planning on testing the effects of marginal price change of properties based on an exogenous event using Spatial DID model. The model has a spatio-temporal lagged variable (y) which ...
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### (multiple) fractional outcomes & autoregression

Let me start with a broad description of the problem and I will then describe my approach (that might be totally inappropiate). The big goal is to predict the distribution of population of a given age ...
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### What is an autoregressive model - terminology with respect to machine learning

In Wikipedia, an autoregressive model is defined in terms of an AR(p) linear process as The autoregressive model specifies that the output variable depends linearly on its own previous values ...
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### Tests for predictive models with autoregressive neural networks

I'm working with time series predictions with NNAR autoregressive neural network models (p, P, k) and I'm doubtful for the validation of my models. After making the predictions, I'm selecting those ...
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### Approximating AR(1) by finite order MA process - convergence results

I am currently struggling with a result pertaining to the finite order MA approximation of a simple AR$\,(\,1\,)$ process defined on a double sided time-index set $\,T=\mathbb{Z}$. I would be very ...
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### VAR Model using Stata

I'm relatively new to the VAR model and have been using Sean Becketti's 'Introduction to Time Series Using State' as reference and wanted to check if I am on the right track. As of now, I have 5 ...
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### Is conditional r-squared ever zero?

I am using multivariate auto regressive modeling (MAR) to assess a complex data set (MAR is a form of vector auto regressive modeling, VAR). The output of the MAR method is >1 response variables and >...
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### How to deal with auto-correlation in generalized linear modelling?

I've built a generalized linear model by using glm.nb function (my response is a count type of data) using a single predictor. The model summary is given below. <...
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### What's the variance of an AR(1)/ARCH(1)

The main question is: an AR(1)/ARCH(1) process has the variance of the ARCH(1)? I've tried to compute the unconditional variance of an AR(1)/ARCH(1) model, so an AR(1) in which the noise is modelled ...
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### How to adjust confidence interval

I am reading a journal where it is written "Time series are based on annual-mean translation speeds from 1949-2016. Trends are estimated by linear regression. The P values of the regression are based ...
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### mean of autoregressive process [closed]

An autoregressive process of order p, AR(p), is of the form $x_t=\phi_1x_{t-1}+...+\phi_px_{t-p}+w_t$ where $x_t$ is stationary, i.e. $E[x_t]=\mu$ for all $t=0,1,2,...$, and $w_t$ is white noise, i.e....
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### ARCH testing and Stationarity

I have a time series y and I need to build the "best" autoregressive model for it i.e. y(q*). What I do: 1. Start with y(1) and test for serial correlation in the errors until I find an AR lag -lets ...
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### Recommended tests to determine whether threshold autoregression is suitable

I was wondering if anyone had suggestions about the best sort of test to determine whether a SETAR model is a reasonable specification. I've come across some portmeanteau tests, but I'm not sure ...
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### Proof of contemporaneous exogeneity, and its implications for an AR(1) model

It can be shown by contradiction that exogeneity fails to hold for an AR(1) model. Is there any proof that contemporaneous exogeneity does not fail to hold? All I've come across is assuming it does ...
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### Biasedness of ML estimators for an AR(p) process

Do you know any derivations (or references) which quantify the biasedness of ML estimators of an AR(p) process?
This is very basic, but I have been stuck here for a while. Consider an AR(1) model $Y_t = c+\phi Y_{t-1} +\epsilon_t$, where $c$ is a constant. If $\epsilon_t \sim i.i.d. N(0, \sigma^2),$ then \$...