# 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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### If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$?

Q: If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$? Attempted solution: $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + W_t$, where $W_t$ is white noise. \begin{equation} \begin{split} Y_t &:...
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### interpretation coefficient sign dynamic model

Screenshot of a paper under a section about dynamic interpretations. Source: https://doi.org/10.3200/JECE.36.1.77-92 Does anyone care to explain this to me. Are they stating that the negative ...
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### Statistically significant AR(1) coefficient, but insignificant coefficients when calculating ARMA(1,1). Why?

I'm using the library statsmodels with a simple financial time series to calculate the coefficients for an AR(1) model, and a ARMA(1,1) model. In the first case the L1 coefficient is statistically ...
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### Partial autocorrelation significant at regular lag distance

I am trying to forecast inflation with a simple AR model. I took the natural logarithm of the CPI and subtracted the 12th lag, thus obtaining a measure of inflation. The PACF is significant at the ...
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### Do autoregressive coefficients obtained with the Durbin-Levinson algorithm, the Yule-Walker system of equations, and OLS coincide?

I am applying the sieve bootstrap for time series introduced by Kress (1988), which requires the estimation of autoregressive models with the Durbin-Levinson algorithm (generalized to the multivariate ...
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### Can any Model be Modified into an "Autoregressive Model"?

In one of Data Science classes, we were given a dataset to explore that contains medical/health information on patients and whether they missed their last doctors appointment or not (e.g. most of the ...
Let $\Phi (\cdot)$ be the cdf of the standard normal distribution. Given $(y_t)_{t \in \mathbb N}$ a time series. Suppose $F(y_t | \mathcal{F}_{t-1})$ is the conditional cumulative distribution ...