A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.

# 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.

635 questions
Filter by
Sorted by
Tagged with
14k views

### How to understand SARIMAX intuitively?

I'm trying to understand a paper about electric load forecasting but I'm struggling with the concepts inside, specially the SARIMAX model. This model is used to the predict the load and uses many ...
30k views

### Under what circumstances is an MA process or AR process appropriate?

I understand that if a process depends on previous values of itself, then it is an AR process. If it depends on previous errors, then it is an MA process. When would one of either of these two ...
1k views

### If an auto-regressive time series model is non-linear, does it still require stationarity?

Thinking about using recurrent neural networks for time series forecasting. They basically implement a sort of generalized non-linear auto-regression, compared to ARMA and ARIMA models which use ...
944 views

### Confused about Autoregressive AR(1) process

I create an autoregressive process "from scratch" and I set the stochastic part (noise) equal to 0. In R: ...
2k views

### Why do we care if an MA process is invertible?

I am having trouble understanding why we care if an MA process is invertible or not. Please correct me if I'm wrong, but I can understand why we care whether or not an AR process is causal, ie if we ...
1k views

### AR(1) process with heteroscedastic measurement errors

1. The problem I have some measurements of a variable $y_t$, where $t=1,2,..,n$, for which I have a distribution $f_{y_t}(y_t)$ obtained via MCMC, which for simplicity I'll assume is a gaussian of ...
10k views

### What is the difference between deterministic and stochastic model?

Simple Linear Model: $x=\alpha t + \epsilon_t$ where $\epsilon_t$ ~iid $N(0,\sigma^2)$ with $E(x) = \alpha t$ and $Var(x)=\sigma^2$ AR(1): $X_t =\alpha X_{t-1} + \epsilon_t$ where $\epsilon_t$ ~...
9k views

2k views

### Variance of a smoothed AR(1) process

The query I have relates to calculating the variance of AR(1) processes that are smoothed with a simple moving average. So: In an AR(1) process of the form: $$X_t=c+\varphi X_{t-1}+\varepsilon_t,$$...
692 views

### What is the expected value of the sample variance under a linear regression with omitted variables of an AR(2) process?

Lately, I have been interested in phenomenons related to omission of variables. For example, it can be shown that the expected value of the sample variance under the inclusion of one variable $x_1$ ...
710 views

325 views

### The distribution of the initial point of an AR process

Consider a stochastic process $\{X_t, t = 1, 2, \ldots\}$ following the model $$X_t = \alpha X_{t-1} + e_t,$$ where $e_t \thicksim f$. Can I say that the distribution of the initial point, $X_1$, ...
119 views

22k views

### Step-by-step example of predicting time series with ARIMAX or ARMAX model?

Could someone give me a step-by-step example of time series prediction using ARIMAX or ARMAX model? The example doesn't need to be long or complicated. It could be for example forecasting temperature ...
349 views

### Memoryless Property of a Markov Chain of Order 1. Is AR(1) memoryless or of infinite memory?

A stochastic process constitutes a discrete Markov Chain of order 1 if it has the memoryless property, in the sense that the probability that the chain will be in a particular state i, of a finite set ...
907 views

### Explanation of the 'free bits' technique for variational autoencoders

I have been reading through a couple of papers on the variational autoencoder model: 'Variational Lossy Autoencoder' and 'Improving Variational Inference With Inverse Autoregressive Flow'. There is ...