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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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 ...
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Stationarity of AR(1) process whose autoregressive parameter could change over time

Imagine an AR(1) has an autoregressive parameter which could change in time. $y_t-\mu=\phi_t (y_{t-1}-\mu)+\varepsilon_t\,$, where $\phi_t$ is not always constant but still lies inside the usual ...
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Autoregressive Model

I am currently attempting to build a regression model explaining Current Inflation as measure by monthly CPI. I am considering the following model; CPI = B0 + B1(LAG_CPI) + B2(Lag_Oil_Price) + ...
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Autocorrelation *across* random effects in nlme:lme?

I have response data measured at the site and month level. I wish to fit a year trend to the data and month to remove the seasonal trend. However, to avoid pseudoreplication, I have fitted year also ...
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Time series causation and probability

I have a series for an individual that looks like this: There are observations of the individual at random times. At each time they may experience an event and the outcome fo that event is binary ...
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Is is possible to determine conditional conjugacy in this case?

I'm working on a problem where I have to extract sufficient statistics for parameter estimation in a state-space model. Usually these come from the quantities used for conjugate updates. I'm OK with a ...
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Nonlinear Autoregressive model parameter estimation from time series

I'm working on a nonlinear multivariate autoregressive model of order 1 (markovian). It is a discrete-time dynamical system which models exchange of mass between compartments in a compartmental model ...
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1answer
57 views

Residual based bootstrap autoregressive series in MATLAB

I have defined the model as follows. Let $$y_1 = 0$$ and $$ y_i = \alpha + \beta y_{i-1} + \epsilon_i $$ for $i_2\ldots i_T$, where $\alpha$ and $\beta$ are the estimated coefficients and ...
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What is the auto-covarriance of a stationary AR1 process?

Say a stationary AR(1) process is given by: $$ X_t = c + \phi X_{t-1} + \epsilon_t $$ where $ \epsilon_t $ is a white noise process with zero mean and constant variance $ \sigma^2 $. Wikipedia ...
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Calculate prediction interval for SAR model (errorsarlm function in R)

I would like to predict prediction interval for a SAR model (function errorsarlm in R - package spdep). While the function predict.lm allows to set interval='prediction' parameter to predict the upper ...
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Stationarity of an AR(1) process

I have problems with answering problem (b) and (c) in the following exercise. Can any of you people help me out? Let N={0,1,2,...} denote the set of natural numbers, $\{\epsilon_t \}_{t \in N} \sim ...
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Least squares method for parameter estimation in AR(1) model

In order to estimate parameters $ \mu $ and $ \alpha$ least squares method can be used.This is what I did to find the least squares. $S=\sum_{t=2}^n(X_t-\mu-\alpha X_{t-1}+\alpha\mu)^2$. And ...
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what R function fits a smoothing spline regression model with correlated errors?

I want to fit a smoothing spline regression model with correlated errors (it's a time series) using R. All I could find is function ssr, from library ...
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1answer
29 views

simulating two correlated lognormal AR(1) time series

I'd like to simulate 2 correlated lognormal AR1 time series. I have already found this post which is the answer for 2 Normal AR1 time series How to simulate two correlated AR(1) time series? I've ...
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4answers
110 views

Time Series for each customer

Is it possible to create Time Series Analysis for each customer? Say if have 100 customers and I wanted to predict how much amount they are going to spend next. I have done the Time Series for the ...
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21 views

Autoregressive model - predictive power

I have estimated a VAR (vector autoregressive) model on credit growth in STATA. I want to test its predictive power by comparing its estimated credit growth to observed credit growth (correlation ...
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19 views

autoregressive distributed lag model

my study only on bivariate because i have 1 dependent(water consumption) and 1 independent(rainfall) by using EViews 8 siftware the water consumption variable is non-stationary, so i made differencing ...
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Standardization and autoregressive process

If I have an autoregression with an exogenous variable and standardized the exogenous variable to better interpret the coefficients, can I standardize the dependent autoregressive component also so ...
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1answer
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Time series regression with lagged dependent and independent variables

I have monthly data for air passengers, oil price and unemployment. I'm trying to create a model to forecast air travel demand using oil price and unemployment as explanatory variables but are facing ...
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62 views

Unable to calculate the density function for AR

The model is an AR(p) process excited by a white Gaussian noise $\epsilon_t$, \begin{align} Y_t = &c+ \phi_1Y_{t-1} + \phi_2 Y_{t-2}+ \ldots+ \phi_p Y_{t-p} + \epsilon_t\\ \epsilon_t = ...
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Conceptual Question: Autocorrelation of autoregressive process

An AR(1) process: $X_t = c+\theta X_{t-1} + \epsilon_t$ where $\epsilon_t$ is a zero mean white Gaussian noise. The Autocorrelation matrix is expressed by the formula mentioned in the Wikipedia ...
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Forecast of spot electricity prices

I recently started a job in power trading. But due to a sudden change in employment I am required to work on econometric models to gauge the supply and demand side of national power markets. So ...
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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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Non-linear auto-regressive model - preselection of relevant columns

Let us consider a dynamic system with nonlinear auto-regressive evolution such as $$ x_{t} = f(x_{t-1},x_{t-2},\dots,x_{t-d})+\epsilon_t $$ where $x_t\in\mathbb{R}^n$ is vector and $\epsilon_t$ is a ...
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58 views

Auto correlation function of AR(p) process

I am doing a time series course and in the theory part there are few things I don't understand.In obtaining auto correlation function for AR(p) process it is done as: AR(p)=$X_t = α_1X_{t−1} + ...
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Autoregressive distributed lag (ADL) models and Dummy variables

Is it okay to use an Autoregressive Distributed Lag (ADL) model with a dummy variable as the dependent variable? Or should I use a combination of logit/probit with an ADL model? I realize it might ...
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How to construct appropriately reverting geometric AR(1) process?

Suppose I have a mean-reverting AR(1) type process, $X_{t+1} = X_t + \theta(\mu - X_t) + \epsilon_t$ where $\theta > 0 $ and $\mathrm{Var}(\epsilon_t) = \sigma^2$. This process is clearly ...
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1answer
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Stochastic Volatility Model

In Kim et al. (1998) stochastic volatility model is specified as: $y_t=\beta\exp({\frac{h_t}{2}})\varepsilon_t,\quad t\geqslant1$ $h_{t+1}=\mu+\phi(h_t-\mu)+\sigma_\eta\eta_t$ $h_1\sim ...
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The inverse of AR correlation matrix

I want to find the inverse of the following matrix: $$ R_{k-1}=\begin{pmatrix} 1 &\rho &\rho^2 &\cdots &\rho^{k-2} \\ \rho &1 &\rho &\cdots ...
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On the derivation of the closed form Yule-Walker moment estimator of a GARCH(1,1). (exercise)

The exercise states: (Yule-Walker estimator) GARCH models are typically estimated by a numerical implementation of maximum likelihood methods. This procedure has the disadvantage that it does ...
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1answer
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Proving for an AR(2) process that $E[X_t | F_{t-1}]=E[X_t | F_{t-2}]=E[X_t | F_{t-3}]$

An exercise states: Using the law of iterated expectations applied to an AR(2) process, verify that $E_{t−k} . . . E_{t−1} (X_t ) = E(X_t |F_{t−k} ) $ for $ k = 1, 2, 3 $ where $ E_{t−k} (X_t ) = ...
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1answer
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How to build a function with the result of auto.arima in R?

I use: fit = auto.arima(Y, xreg=X) in R to get ARIMA(1,0,0), result as follows: ...
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How to write an AR(2) stationary process in the Wold representation

I managed to write an AR(1) process in the Wold representation with help from the geometric series. I am having trouble with a stationary AR(2). How could I do?
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Predicting dropout in an ordered process: Cox regression, autoregressive model, multilevel modeling?

I am working on a project in which I collected data about 100 people’s steps in an ordered process. All took at least one step, with some continuing up to a fourth step. Each person either drops out ...
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What is the “scale” parameter in “continuous autoregressive model” in cts package?

I am trying to use the "car" command in "cts package" in R program and I see the "scale" parameter there. I wonder whether this can be assumed to be equivalent to time intervals for time series ...
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AR models on non stationary data

i am currently reading Diebold and Li's 2006 paper: Forecasting the term structure of government yields where the authors fit, albeit simple, AR(1) models on clearly non stationary data. Why is this ...
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1answer
132 views

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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1answer
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Are Auto-Associative Regression Trees Distinct from Auto-Regressive Trees?

After some reading in the field I was confused as to whether these two models are distinct or really the same. I'm just looking for a simple yes/no with a brief explanation. Note that ...
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Handling overflow warnings in pymc

Abstract I am getting numerical overflow warnings in pymc that are stalling the sampler. I'll first specify what the context is then ask more directed questions about the solution. The context ...
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63 views

Autoregressive model with input variables in proc arima procedure

I am currently working on the time series analysis for series Y but I have to use other two variable A and B as an input variable in SAS proc arima procedure. But I am unable to interpret the cross ...
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138 views

Problem simulating AR and MA models using filters

I do not know how to use filter to simulate AR and MA models. To me it looks the same way for both MA and AR Estimate AR so then how do I know that the model is AR or MA ? For example, Problem1: For ...
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1answer
50 views

Whitening a regression with an AR process

I was reading a research paper: $Y_{t}\text{=}\beta_{0}+\beta_{1}X_{1t}+\beta_{2}X_{2t}$ (where $Y_{t}$ is stock returns and not the change in stock returns) ($X{}_{1t}$ is the return of a stock ...
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1answer
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Is there a convenient form for this large covariance matrix?

Consider the following bivariate vector autoregression: $$X_t=\mu +X_{t-1}A+\varepsilon_t,\ \varepsilon_t \overset{iid}{\sim} MVN(0, V),\ X_t=(X_{1,t},X_{2,t})',$$ where the assumptions on the ...
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1answer
21 views

Reference requested for Moving Average model

I am not from econometrics background and hence not familiar with text books which may contain a large moving average and an auto regressive model. I have found AR model from Simon Haykin's Adaptive ...
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1answer
82 views

Multivariate model and large regression

I am not familiar with the concept of multivariate model and just learning about regression model. I am familiar with Autoregressive model and Moving Average. Multivariate regression model provided ...
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Do AR models with GARCH errors have a positive spectral density?

Can someone please help me to verify that AR models with GARCH errors have a positive spectral density and are bounded?
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Determining parameters in AR model for non-stationary time series

I am currently trying to fit an AR model to some financial data. The time series $Y_t$ in levels is clearly non-stationary; however it appears the first differences $dY_t$ are stationary (and this is ...
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2answers
299 views

Steps to perform time series analysis

I'm trying estimate an autoregressive model with an exogenous variable. It's about the impact of changes in oil prices on the economy. I'm planning on regressing gdp growth rate on its own lagged ...
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1answer
41 views

Geographic regression

I'm working on a project to estimate real estate and started with some classique techniques, such as linear regression etc. The obtained results are already going in the good direction, but to get ...
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1answer
64 views

Spatially auto-regressive two-stage model

I'm working on a project in which I use a 'Generalized Spatial Two-Stage Least Squares' model, mostly known as $y= X \beta + \lambda W y + u$ and $u = \rho M u + \epsilon_n$ where $y$ and $u$ are ...