# 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.

707 questions
Filter by
Sorted by
Tagged with
20 views

### how to fit ar(1) model with predetermined value of autocorrelation parameter in R? [migrated]

I have the following data: ar <- arima.sim(list(order=c(1,0,0), ar=0.9), n=M1) + 10 How to fit an AR(1) model to simulated data above with ar parameter=0.5? ...
35 views

### Time series prediction for a chaotic multivariate data

I am trying to forecast a chaotic multivariate time series, and any architecture I use ( LSTM, MLP or tried to implement Autoregression architectures from few papers like https://arxiv.org/pdf/1704....
21 views

### Why the lag number of an AR model doesn't indicate the number of lags in a plotted ACF?

In the below image, there are AR models with differing lags. As far as I know, each autocorrelation function plot has an x-axis that is "number of lags". Can someone help me understand how ...
35 views

### ar() in R and Matlab give different results for same dataset

I have a Matlab script that performs some autoregressions and am trying to replicate it in R, but can't get them to match. So as a MWE, I'm trying to get the same results in R as are obtained by this ...
15 views

23 views

### Conditional distribution of Ornstein-Uhlenbeck on two fixed points

The conditional distribution of a Ornstein-Uhlenbeck $X(t)$ conditional on $X(0)$ is given by $$X(t)|X(0) = X(0)e^{-t} + \mu(1 - e^{-t})$$ This process is usually only defined for $t>0$ (future ...
54 views

### Non-Sensible Estimates for MLE of AR Processes

I am taking a course on Time Series Econometrics and I am solving a problem set that requires students to explicitly write maximum likelihood functions for, as an example, AR processes and estimate ...
8 views

### Is there a point on performing time series analysis on data that are not gathered with a consistent frequency?

To be more specific, what I have in mind is data gathered from android games. These data wouldn't have any time consistency because a user is free to play as many games as he wants whenever he wants, ...
26 views

### Time series - best approach?

Good evening, newbie to the forum but I would appreciate some advice on a new problem I’m working on. We are collecting water samples and measuring a number of things simultaneously in the water, as ...
35 views

### Unbiased Estimator of AR(1) Models?

What are the options for unbiased estimators of AR(1) (or AR(p)) models? Bias reduction techniques may also be included (jack knife would be one). I found one paper called "Bias correction using ...
17 views

### Equivalence of trend stationary process and stationary process

I am new to Time Series, and I am having some trouble dealing with the constant of an AR(p) process, which of course 'reinforces' itself over time to become a deterministic trend. For simplicity sake, ...
22 views

### What does it mean “analyze sample time series data when only a single series is available”?

Since the book says, it will use time series to mean either realization of a process or a process, I have no idea how to interpret the following sentence. "This notion, called weak stationary(i.e....
15 views

Box-Jenkins approach to time series analyses uses a series of diagnostics, one of which calculating Partial autocorrelation function (PACF). The goal is to determine the order ...
70 views

41 views

### ARIMA Model Non-Stationary Time Series

Suppose that the data generated process is the following: Y(t) = 1.2*Y(t-1) + 0.2 The process is clearly non-stationary. My question is why we can't fit an AR(1) model and make predictions?
12 views

### AR(p) by iterated vs. lag method. Different results

Reading "Applied Econometrics Time Series" By Walter Enders I am trying to derive the stationary AR(p) model as he does on page 58, fourth edition. This is the AR(P) model \begin{equation} y_t=a_0+\...
25 views

### Why do AR(1) times series generated by two methods look similar but have different variance estimate in Python

I come across one question when I use two ways to generate AR(1) sequences. By definition, AR(1) sequence is $x_t = \phi_1 x_{t-1} + \varepsilon_t,\quad \varepsilon_t\sim N(0, \sigma^2)$ I found ...
15 views

### Is there a root of AR-polynomial which is the same for any $\phi$?

I am learning timeseries models and got some doubts. Consider an ARIMA(1,1,0) process $Xt$. Let $\phi(z)$ is AR-polynomial. $(1-\phi B )(1-B)=Z_t$. $(1-B)X_t=Y_t$. I read in my study material ...
11 views

### Can an AR(1) process with finite past be well-defined?

I am wondering if there is a true need for the infinite past of an AR(1) process to be defined. Usually, an AR(1) is a stationary process defined by the set of equations \begin{equation} X_t = \...
21 views

### How fast does a auto-regressive process converge?

Recently I have come across a time series data that happened to fit MA(1) process really well, and I would like to know how fast does this series to mean revert ? I did some google search there seems ...
14 views

### Does AR in the TAR model of time series still need to consider stationarity?

For example, first order difference operation? Because I had to implement the TAR algorithm with the MCP penalty function myself, I had to understand the calculation details
32 views

### Interpret AR(3) output from arima function in R

I have AR(3) like following. I'm not sure whether it is interpreted to $$Y_t = 5.6923 + 1.0519 Y_{t-1} -0.2292 Y_{t-2} -0.3931 Y_{t-3} + e$$ or other? Thank you. ...
26 views

### What is the best way to present the following predictive regression relationship?

If I have a predictive regression with a single regressor of the form \begin{equation} y_t=\beta x_{t-1}+\varepsilon_t \end{equation} where \begin{equation} x_t=\rho x_{t-1}+u_t \end{equation} Then I ...