# 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.

741 questions
Filter by
Sorted by
Tagged with
193 views

### Time Series AR1, coefficient accuracy different from linear regression

I am interested to know why running the R arima function's result has a different accuracy from my "manual" way of linear regression. ...
800 views

### Autoregression vs Sliding Window method

I'm a beginner at machine learning and have a question regarding time series. I have a data set dependent over time, with a single feature and I am trying to predict the future value of this. This far ...
508 views

### Autoregressive model for time series with structural breaks

I'm using a structural break model (threshold model or regime switching model) to examine the dynamics of a time series. The ADF test shows that the series has a unit root. Right now I'm regressing $y$...
276 views

### What is the distribution of the difference between two AR(1) processes?

I am reading a paper published in a good economics journal. An econometric model is presented in the paper. A part of the described model is not very clear to me. Please let me state a couple of ...
38 views

111 views

### What is the difference between GARCH, ARGARCH, and DCC-GARCH?

What is the difference between GARCH(1,1), AR(1)GARCH(1,1), and DCC-GARCH?
168 views

### Why is auto.arima modeling an AR(1) process as an MA(1)?

Playing around with auto.arima to see how effective it is at model selection. I first simulated an $AR(1)$ process with $X_{t+1} = 0.9 X_t + \epsilon_t$ ...
176 views

### Is this an Autoregression or OLS?

Say I have a time series $y_t = \frac{1}{n} \sum_{i=1}^n x_t^{(i)}$. For example, $y_t$ can be the returns of the S&P 500 index at time $t$ and the $x^{(i)}_t$ is return of the $i^{th}$ company in ...
878 views

### An autoregressive process has to be always gaussian?

It is well known that if a generic autoregressive process of $n$ order, $AR(n)$, has a gaussian white noise error term ("innovations"), then it is gaussian too. So I presume that if the error term is ...
249 views

### How to learn 'end of sequence' for continuous sequence?

Consider Autoregressive model (i.e. RNN Language model) which try to output next token given all previous tokens. When generating sequence with this model, model need to learn when should be end of ...
11k views

### Fitting model AR(1) with R

I've sampled 100 variables from a Gauss distribution with mean 0 and standard deviation 1. > set.seed(1) > wn=rnorm(100) Then I've fitted an AR(1) model ...
182 views

### How do I quantify the decay in the initial condition of an AR process?

I'm working on basic code that generates data from AR and VAR processes; the code generates enough observations to dampen the effect of the initial conditions. For example, if I want to generate 30 ...
180 views

### How to identify relationship between response time series(Yt) & input time series(Xt) only in terms of Yt-1 & Xt?

I have a response time series(Y) & Input time series Xt & Zt. My only objective is to identify functional form Yt=f(Yt-1,Xt,Zt) where f(Yt-1,Xt,Zt) contains only lags of Yt , Xt & Zt as ...
4k views

### Meaning of output of function “ar” in R

How should I read the output of the function ar in R. For example, take this VAR model: ...
489 views

### Evaluation of Autocorr/Part Autocorr values

I am practicing MA and AR modelling by using autocorrelation and partial autocorrelation values. My data is in the image below; I can see that only at lag 12 there is a value that might be considered ...
222 views

### Autoregressive model with exponential lags

I have a very highly sampled time series that I would like to fit an autoregressive model (AM) to (~3 million samples). From knowing what they represent, I have believe there should be unique ...
3k views

### Different results of Engle's Lagrange multiplier test for conditional heteroscedasticity from SAS and FinTS

To fit a simple AR(5) model, I use SAS PROC AUTOREG. I called the option ARCHTEST=(QLM) which provides Engle’s Lagrange ...
9k views

### Stationary ARMA model as infinite AR or MA process

How can a stationary, invertible ARMA(1,1) process be represented as either an infinite order AR or infinite order MA process?
29 views

### Burg's method for estimation of AR-models

I am trying to get an intuitive understanding of Burg's method for estimation the coefficients of an AR-model. Say we have an AR(1)-process with \begin{equation*} X_t = a X_{t-1} + \varepsilon_t \...
88 views

### Day-of-week effects on regression coefficients in autoregressive model?

I have a timeseries (sampled daily, weekdays only) whose volatility clearly shows dependency on day of week. In particular the standard deviation of the differenced series $\Delta y_t$ is smallest on ...
79 views

### Standard errors with delta method

Trying to recreate other author's results. E.g. this paper. Introduction to the model is on page 10, while table with results is presented on page 13. Under the table there's a small note that SE were ...
56 views

### 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: ...
417 views

### What's the variance of an AR(1)/ARCH(1)

The main question is: an AR(1)/ARCH(1) process has the variance of the ARCH(1)? I've tried to compute the unconditional variance of an AR(1)/ARCH(1) model, so an AR(1) in which the noise is modelled ...
233 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 ...
84 views

### Thomas Sargent's intuition as to why every covariance stationary series has an infinite-order Wold representation

In his classic book "Time Series Analysis", James Hamilton references Thomas Sargent (["Dynamic Macroeconomic Theory"], 1987, pp. 286-290) as a "nice sketch of the intuition behind this result [Wold ...
341 views

### How to relate roots of AR and MA to unit circle

I'm working on these problems and think I figured out most of the steps, but am stuck near the end as I don't understand how to relate my roots back to the unit circle in order to determine ...
80 views

### simulate autoregressive data that is also multivariate normal

I am trying to simulate data that is correlated to varying degrees. However, the data itself will have a degree of autocorrelation as well. I can get the first part of the problem with mvrnorm ...
69 views

### Result of an ADF-Test compared with an estimated AR (p) model

I am currently investigating the inflation persistence for different countries by using R. I took data from the OECD for Sweden (1993-2017) and checked first if the series is stationary with the ur....
81 views

### Stationary density of $\{X_t\}$ as a solution of integral equation

For the model, $X_t = \alpha X_{t-1} + \epsilon_t$, we find the integral equation related to stationary distribution in the following way: Let $X_{t-1}\thicksim f$ and $X_t|X_{t-1}=x \thicksim q(y|x)$...
80 views

### Fit ARMA model to ACF

If I have the autocovariance function $\gamma_\tau$ (numerically over a given set of lags $\tau = 0 \ldots n - 1$) of a stationary linear stochastic process, is there an efficient way to determine the ...
374 views

### Assumptions on Neural Networks (NNETAR)

Are there any assumptions that must be covered when fitting an NNETAR model? non-correlation, normality, or something? I've already saw Rob Hyndman post where he says NNETAR doesn´t need stationarity, ...
69 views

### Nonparametric Quantile Regression for AR(1)-ARCH(1) process

I would like to estimate the conditional scale function $(\sigma_\tau(X_t))$ in a QAR-QARCH model represented by: \begin{equation} Y_t = \mu_\tau(X_t) + \sigma_\tau(X_t)\epsilon_t,\, t = 1,2,\ldots \...
1k views