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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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### 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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### What guarantees the existence of a finite representation of the Wold decomposition? Mechanics and Intuition

Every covariance stationary process can be written as a linear, infinite distributed lag of white noise. In other words, every covariance stationary process has a Wold representation. Then we go on to ...
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### Computing Standard Errors in EM algorithm

I'm applying the EM to a hidden markov chain (the $\mathbf{Z}=\{Z_1,...,Z_n\}$ variable), with observations(the $\mathbf{Y}=\{Y_0,...,Y_n\}$ variable) dependent not only on the hidden markov chain, ...
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### How to interpret the characteristic roots of moment equation of a AR(2) model?

I am learning the financial time series using the book 'Analysis of financial time series' by Ruey Tsay. In chapter 2, they introduced AR(2) models. The moment equation (which is the function between ...
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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-...