# 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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### What's wrong if I fit the auto-regression with OLS?

I am doing auto-regress by usual linear regression package. e.g. $y_t=φx+ε_t$ with $x =y_{t-1}$ My reason is that, Auto-regression does assumes iid errors, same for linear regression. Linear ...
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### Derivation of the distribution of $\hat{\phi}=[\hat{\phi}_1, \cdots, \hat{\phi}_p]$ in AR(p) models

Background Consider the following AR($p$) model: $$\dot{X_t} = \phi_1 \dot X_{t-1} + \phi_2 \dot X_{t-2} + \cdots + \phi_p \dot X_{t-p} + \epsilon$$ where $\dot{X} := X - \mu = X - \mathbb{E}(X)$...
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### How many lags should I include in time series prediction?

I'm wondering: how do I select the number of previous time steps to use to predict the current one? I'm just plotting the autocorrelation plot and picking previous time steps that have statistically ...
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### Difference between different autoregressive models

I am trying to understand the difference between these three different specifications of an autoregressive model for variable var in Stata: ...
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### Conceptual questions: Variance of a process

Wikepedia, at Variance of Autoregressive model, mentions an expression of variance for an AR(1) process. I am learning signal processing (beginner level) and facing difficulty in understanding some ...
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### Doubts in linear regression

If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1)$, then what does this constant term imply? Will it hamper the estimates if ...
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### Do the assumptions for linear regression apply to AR(p) models?

If we have a stationary time series and we want to model it as an AR(p) process, what conditions must hold besides the stationarity itself? Are they the same a the assumptions for linear regression: ...
134 views

### Dealing with autocorrelation using Generalized Least Squares

I have a time series data set where the auto correlation of the residuals follow an exponential decay. I was wondering how I should deal with this? I would like to fit a linear model and have tried ...