# 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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### Good Resource For Converting ARIMA output in R to equation form?

I've seen this question asked a few times but I still haven't seen a place where I can get some good examples on how to convert an arima() output in ...
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### When is ARMA(p,q) strictly (strongly) stationary and what is its unconditional distribution?

It seems that the discussions on ARMA are always focused on weak (second-order) stationary, but what about strong stationary? What are the conditions on the coefficients for it to be strictly ...
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### Does stationarity of AR(p) imply innovations are i.i.d.?

My lecture notes give the following definition: A stochastic process $(X_t)_{t\in\mathbb{Z}}$ is called autoregressive of order $p$ if it satisfies: $$X_t=\phi_1X_{t-1}+...+\phi_{t-p}X_{t-p}+W_t.$$ ...
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### Can I use a spatially lagged Dependent Variable while using Spatial Error Model?

I have following issue: I run spatial diagnostics on dependencies for my Log-Log Transformed regression model. LM Tests (including Robust) are highly significant. Since I am using GeoDa, I cannot ...
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### Population autocovariance goes to zero, assuming covariance stationary

In time series context, let $\gamma_j=E[(y_t-\mu)(y_{t-j}-\mu)]$ denote population autocovariance, where $\mu$ is population mean of $y_t$, assuming covariance-stationary. Then, $\gamma_j$ goes to $0$ ...
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### Temperature time series forecasting predictions converging to a certain value

I am trying to forecast the value of the ambient temperature based on given data on Python. The data frequency is 15 minutes. In order to predict future values, I am using a simple autoregressive ...
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### Expected Value of an AR(1) process

I saw the answer on this post and got confused about a couple things in its explanation. Mainly, I am unsure of How the poster immediately knows the process $X_t = c+\phi_1 Y_{t-1} + \epsilon_t$ is ...
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### Forecasting autoregressive model. What's the best linear predictor?

Obviously if $X_t = \phi X_{t-1} + Z_t$, then the best linear predictor of $X_t$ given $X_{t-1}$ is $X_t = \phi X_{t-1}$. But if $\phi$ is unknown, one may attempt to substitute $\phi$ by a Yule-...
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### divergence of beta estimates between OLS and regression with ARIMA error

I have physiological time-series data: ~60k observations per channel, ~100 Hz sampling. I will model individual channels with ~20 regressors. Under OLS, given temporal autocorrelation in the data, ...