# 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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123 views

### Proof of errors being serially uncorrelated in an AR(1)?

I am preparing for an econometrics exam and I have reached a lecture on serial correlation which I do not seem to understand the proof. The text I am about to cite is in Wooldridge 6th edition "...
156 views

### How to formulate equation for ARIMA models? [duplicate]

I have tried to generate/write equation for forecasting using ARIMA models. But I think my equations were wrong and I am stuck with it. Kindly please help me to obtain equations for 1.(ARIMA (0,1,2) ...
240 views

### How to maximize the log likelihood of an AR(p) model?

How would I maximize this log likelihood function? And with respect to what? I think I should maximize it with respect to the coefficients $\phi$, is that correct?
65 views

### How predict time series B given A; predict time series transform?

Assume a unidirectional circuit that transforms information. If one records the activity from the middle and end of the circuit they will end up with two times series. My goal is to predict the ...
191 views

### Likelihood Ratio test AR(1) model

Question: Consider the normal random variables $X_1,\dots,X_n$, where $X_{i} = \theta X_{i-1} + \epsilon_{i-1}$ for $i=1,2,\dots,n$ and $X_0 = 0$ and $\epsilon_i \stackrel{iid}{\sim} N(0,\sigma^2)$...
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### Comparing AR Models in R when AIC isn't available

I need to compare between an AR(4) and AR(5) model, but when I try to estimate the AR(4) model, I received the following result: Error in optim(init[mask], armafn, method = optim.method, hessian = ...
278 views

### How to model auto-correlation with a sinusoidal decay pattern in time series data?

I have ambient temperature data recorded at 90-minute intervals (16 readings per day) over approximately one year. I’m using GAMs to characterise the daily temperature profile in different seasons but ...
34 views

### First order autoregression

Hi, I don't get that how to use the variable T in this question. And how do we use these numbers we know to estimat $\beta_0$ and variables? Is there any formula for it? Thanks!
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### Prove that the moment condition fails for AR(1) process with autocorrelated error

Consider the simple time series model: $y_t=\rho y_{t-1} + \varepsilon_t$ where $\varepsilon_t$ is autocorrelated. This results in that the moment condition, $E[y_{t-1}\varepsilon_t]=0$, does not hold,...
436 views

### How to fit a model to my binary time series data using R?

Problem I have a binary time series with a binary dependent variable and several independent variables. What are some appropriate and easy to understand approaches using R that I haven't thought of? ...
267 views

### Check if time series has drift or drift and trend

Let's say you have some time series data that you think exhibits a drift, but you are unsure. Is it better to test first a regression with a drift and a trend to see if that is stationary? Secondly, ...
74 views

### Autoregressive coefficients and heteroscedasticity

The estimated parameter in an AR (1) with just one dependent variable is 0.92. I have checked the residuals for heteroscedasticity and both the Breusch-Pagan test and the White test confirm the ...
138 views

### model two spatial auto correlation in spdep package in r

I hope to fit the spatial autoregressive model : $$y= \gamma_1 Wy + \gamma_2 By + X\beta +\epsilon. \quad (1)$$ where $W, B$ are different weight matrices. However, every references I've found only ...
126 views

### Stata: Predicted values in autoregressive system

I'm trying to replicate the results from Yagan (2016, pp 8-11). There, the following autoregressive system is run: The author then runs this system based on data until 2007. Then, he computes ...
84 views

### Incorporating autocorrelation into forecasts

I have a time series $x_{t}$ which is an AR(1) process with a constant term, e.g. $x_{t} = c + \phi x_{t-1} + \epsilon_{t}$ How can I incorporate information about the autocorrelation of $x_{t}$ ...
171 views

### How to implement a multiple regression for AR models (time series)?

Let's say I have the following model: So I have an AR model of order 3, and I want to estimate A1, A2, and A3. I understand how regression normally works for two variables x and y. Also, after doing ...
112 views

### In the midasr package in r, how is the AR* model different than the AR model?

At the end of the ?midas_r documention example what is the fourth parameter option in the mls() of the lagged dependent variable "*" doing that is different that the "regular" AR(1) model above? I've ...
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### Solving for a difference equation for $s_{t}$

Given $f_{t}=u_{t} - \bar{P}$ and the law of motion for $u_{t} = \rho u_{t-1} + \epsilon_{t}$, where $0<\rho<1$, $\epsilon_{t}$ is mean-zero iid and can be interpreted as a domestic price level ...
223 views

### How can I test for seasonality when the trend is not supposed to be monotonic but sinusoidal?

My knowledge of time-series analysis is limited. So far I have only assessed whether there was a seasonality in my time series data with the assumption of monotonic trend. To test that I would have ...
36 views

### Does Auto-correlation cause AR(p) model?

This is the autocorrelation case. $y_{t}=X_{t}B+u_{t}$ where $u_{t}=\rho u_{t-1}+e_{t},$ $e_{t}$ is iid From this autocorrelated disturbances, I might be able to say $y_{t}=\gamma y_{t-1}+w_{t}$,...
563 views

### Can ARIMA be used to forecast trend in time series data?

I am new to ARIMA. I have a time series data that has a negative trend.I need to predict its value for the upcoming time period. I know that one of the steps in ARIMA is to de-trend data through ...
135 views

### Autocorrelated Returns?

I'm trying to compute some VAR models for the Amgen Pharmaceutical company (NasdaqGS: AMGN), however I've noticed that the daily returns seem to be significantly autocorrelated at a number of lags (...
560 views

### Autocorrelation function decay for AR(p), how to proof

How can I demonstrate that the Autocorrelation function (ACF) for an AR(p) decay exponentially? It seems so simple but neither Enders' book nor Greene's has such proof.
192 views

### Conditional covariance of AR(1)

I am trying to derive the conditional covariance of an AR(1) process, $\text{Cov}(y_t,y_{t+h})$. I have been trying to solve it taking in account the law of iterated expectations (LIE). However, I ...
294 views

### Stable VAR($p$) procress: Is there an easy way to do this?

Assume a $K$-dimensional VAR($p$) process given by $$y_t=\nu+A_1y_{t-1}+\ldots+A_py_{t-p}+u_t$$ This process is called stable if the roots of the reverse characteristic polynomial are bigger than 1 in ...
714 views

### Extract shock size from impulse response function in a VAR system

I have the results from a standard VAR model with Monte Carlo simulated confidence bands. I have the graphs for the impulse responses as well and I know that the shock size is one standard deviation. ...
3k views

### Why different output eviews 8 vs. eviews 9; how to interpret?

Currently, I am working on forecasting. I try various models. One of the models I tried is an AR model. As I have monthly data, I use the 12th period back in time. So the model is like ...
110 views

### What mean coefficients in autoregressive model and how calculate them?

What mean coefficients in autoregressive model and how calculate them ? yt=c+ϕ1yt−1+ϕ2yt−2+⋯+ϕpyt−p+et, ϕ1, ϕ2 ... This coefficients are "fourier transform"? Can ...
270 views

### Ljung Box test for residuals of constrained ARIMAX(2,1,0) model

I have this ARIMA(2,1,0) model with one exogenous variable: $$\Delta y_t=c+\phi_2 \Delta y_{t-2}+\beta_x x_t+\varepsilon_t$$ I want to run Ljung Box test of residual autocorrelation with test ...
317 views

### How to include seasonality in the data ARMAX model that has multiple periodicities?

I am doing regression with ARIMA errors. The residuals are as shown in the figure below. Clearly, the scatter plot shows that this time series has some sort of periodicity or seasonality, but its very ...
248 views

### Modeling Non-Stationary Time Series Data

Data set: response and predictors are all non-stationary, time series variables After performing Box-Cox transformations and testing a variety of power transformations on each variable, the non-...
517 views

### Autoregressive model in R

Citation: As the data represent repeated measurements from individual plots, within-plot correlation may result in inefficient estimates and underestimation of standard error. Therefore the ...
261 views

### What is geometric autoregressive process?

Can anyone give a definition for Geometric Autoregressive Process? Any specific properties? And, in what fields is this mostly applied? To add some context to the question, here is a section of the ...
2k views

### Is non-stationary AR(p) process constant in mean?

A non-stationary $AR(1)$ process, which is a random walk, is constant in mean, but not constant in variance. How about the other $AR(p)$ processes with the order $p>1$? Are they constant in mean?
4k views

### How to perform Prais-Winsten autoregression in SPSS 16? [closed]

When performing a linear regression on my dataset, Durbin-Watson was very low (0.276). I found a tutorial online that suggested performing an Prais-Winston autocorrelation. The tutoral came with ...