# 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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### Unit root stationarity and modelling AR(p) process

I'm reading through Introduction to Econometrics by Gary Koop. I'm a little confused on the process for modelling AR(p) processes. Hopefully someone can help clarify things for me. Let me set out my ...
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### Covariance stationarity for an AR(1) with squared terms?

I have a simple, but surprisingly mind-numbing, problem. I am familiar with determining stationarity for an AR(p) process: look at the roots from the characteristic equation. What if we had higher-...
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### Autoregressive cross-lagged models

I'm working on a research project with an autoregressive cross-lagged model with two measures three time points. The paths from $t_1$ to $t_2$ were significant, but $t_2$ to $t_3$ were all not ...
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### Difference in coefficients between ar() and lm() using R?

When I use ar(method="ols") it should return the same as lm(), right? It doesn't: ...
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### Calculating the fitted values from a gls() object in R

I have created a gls() object to create a linear model with AR(1) errors. By all indications this model is a good fit for the data and the resulting model appears ...
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### Estimate of the intercept is off in a simulated AR(1) model

I've been working with a SARIMAX model for forecasting and found myself struggling to accurately interpret its long-term forecasts. To better understand the underlying mechanics and perhaps pinpoint ...
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### Does white noise guarantee that $X_{t-1}$ is uncorrelated with $u_t$?

I have a question about the properties of white noise in a time series context. Specifically, I want to know: If we assume that the error term $u_t$ in a time series model is white noise, does this ...
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### Block length in time series bootstrap of AR(1) model, biased AR coefficient

I'm using block bootstrapping for some simple autoregressive time series models, and I'm running into pretty high bias in the bootstrapped estimates of the autoregressive coefficients, even from large ...
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### Covariance matrix of autoregressive process

I am learning about autoregressive processes and there is something that I find unclear about the structure of their covariance matrix. Some sources (e.g. Box and Jenkins, 2016) describe the ...
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### Is it legit to estimate an AR(1) model for non-stationary time series?

Suppose ${X_{t}}$ is a non-stationary process. The goal is to estimate the following AR(1) model: $$X_{t}=\alpha +\beta X_{t-1}+\epsilon_t.$$ From classical time series analysis, we know that ...
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### Which Forecast Evaluation Metric To Use?

It is a forecasting problem. I need an evaluation metric which penalizes under-predictions more than over-predictions. Also I want it's range in certain interval (say 0-100), so that it becomes easier ...
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### Designing a random factor in a linear mxied effect model to combine repeated and single exposure datasets to prevent p-hacking

I currently have data that can be split into two categories: one is a repeated measures data (collected at multiple time points), whilst another is a single measure dataset (one single time point out ...
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### Repeated measures of multiple time series processes

I am struggling with a comparison of temporal processes, which are observed in several time series. The problem is as follows: Suppose there are some semi-experimental conditions, with several ...
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### Lag operator and stationarity [duplicate]

I just study about time series. I want to ask about in AR(1), why the lag operator, L, need to be bigger than 1 for zt become stationary. And also when |L|>1, it is lie outside of the unit circle ...
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### At what circumstances will the difficulty for the tasks of density evaluation and sampling be different?

In this tutorial video of normalizing flow, the presenter mentioned that for the original autoregressive flow, the density evaluation is fast and the sampling is slow. In contrast, for the inverse ...
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### Is my motivation for ARMA accurate?

I think I finally understand the point of the 'moving average' part of ARMA/ARIMA, but I wanted to confirm here, just in case I am still off. Idea 1: Autoregressive processes are easy to motivate - ...
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### Can a covariate also be a random effect in glmmTMB model with ar1 [closed]

I have data consisting of catches of insects at weekly intervals over 2 years, repeated with the same methods at the same location 3 decades later. My main question is, have numbers (total and for ...
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