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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Is a random walk + white noise modal an ARIMA(0,1,1)? [on hold]

Let $Y_t=Y_{t-1}+\epsilon_t$ be a random walk and $Y_0=0$ Why is it true that the process $X_t=Y_t+\eta_t$, where $\eta_t$ is a white noise, so that $cov(\epsilon_t,\eta_s)=0$ for all $t,s$?
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Simulating a dynamical system

Basically I need to replicate Hartley's 'A User's Guide to Solving Real Business Cycle Models' . Specifically (to make question relevant to stats.stackexchange), I want to simulate the dynamical ...
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autoregressive coefficient and white noise

I have one variable of Monthly rainfall data. I have developed a forecasting model using Back-propagation Neural Network Model (using Matlab), with 3 input units and one output unit, the three inputs ...
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What is the difference between autoregressive, auto-regression and multiple linear regression?

I have developed three neural network models for monthly rainfall forecasting the first has three input, which is the values of the previous three months. the second has six inputs and the third has ...
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59 views

Regressor vs. AR/MA terms

I'm running a regression to model Hong Kong's office rentals series: Source:Private Office - Average Rents by Grade by District (from 1982) Source:All HK Property Market Statistics ...
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Autocorrelation and Partial Correlation plots in ARMA models

Consider the following input and its Autocorrelation and Partial Autocorrelation plots (source). What are the shaded blue areas in these plots? I often see them when studying ARMA models. What do ...
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52 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 ...
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33 views

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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30 views

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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34 views

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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86 views

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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63 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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45 views

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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40 views

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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47 views

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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33 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
112 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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26 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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1answer
25 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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81 views

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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66 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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83 views

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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76 views

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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1answer
68 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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49 views

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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26 views

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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48 views

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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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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186 views

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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1answer
33 views

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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99 views

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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71 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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167 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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55 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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218 views

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 ...