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 - 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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10 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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11 views

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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22 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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44 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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46 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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27 views

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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44 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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8 views

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
33 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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18 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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1answer
18 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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37 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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41 views

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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12 views

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
51 views

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
53 views

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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2answers
121 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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18 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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17 views

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
128 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
91 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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42 views

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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41 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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84 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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39 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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204 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
20 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
75 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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61 views

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
220 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
40 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
54 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 ...
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178 views

Mean reversion in AR(1) process

Mean reverting level in following AR(1) process is $b/(1-a)$. $$x(t) = a + bx(t-1).$$ I understand this. I read that the mean reverting level for AR(1) process given below with finite differencing ...
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1answer
108 views

Practical issues with dynamic panel data modeling

Unfortunately for me, I've got a situation where I need to control for the lag of a dependent variable as a robustness check against an alternative interpretation of my main regression. The baseline ...
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3answers
167 views

Under what circumstances is an MA process or AR process appropriate?

I have a very basic question. Please let me know if this has been asked before, but in my defence I haven't seen it on Cross Validated. I understand that if a process depends on previous values of ...
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Methods for measuring snowball effects in a “complete” longitudinal dataset

I'm looking for ways to test for "cumulative advantage" effects in a longitudinal dataset (see image) I guess the data set is principally similar to this: http://www.caldercenter.org/whatis.cfm , ...
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65 views

Is the Moving Average of ARMA the same of Moving Average of Stock Market?

I'm studying time series prediction and I have some questions. Is the Moving Averages movel studied the methods of the ARMA family has the same concept as the methods studied in Moving Averages ...
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28 views

How do you calculate standard error in a Dickey-Fuller test?

So in everything I've found, they tell you have to calculate $\rho$, or how to test for confidence interval for it. What I am trying to figure out is how to calculate the SE which would get us our ...
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45 views

Predicting time series with OpenBUGS

I have a number of fairly short time series (about 4–100 observations) which I need to forecast into the future. I decided to use Bayesian inference, because there is external information about each ...
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95 views

How can I correct for residual autocorrelation in a fixed effect panel model?

The residuals have an AR(2) structure. Is it appropriate to add AR terms to a fixed-effects panel model?
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1answer
104 views

calculating the expected value and variance of a log AR(1) process

I have an AR(1) process that looks like this: $$ \ln(g_t) = (1 - \rho_g)(\ln(\mu_g) - c) + \rho_g\ln(g_{t-1}) + \epsilon^g_t $$ where $|\rho_g| < 1$, $\epsilon^g_t \sim N(0, \sigma^2_g)$, and ...
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149 views

R fit restricted AR(p) model

I have a question about using R to fit an AR model. If we want fit a AR(p) model, the equation will be $Y_t = φ_1Y_{t-1} + φ_2Y_{t-2} + ... + φ_pY_{t-p} + Z_t$. What about I only want to fit the model ...
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165 views

Fit a moving average (MA) time series model to the data (R:stats::ar equivalent)

I am looking for some tools for automatic fitting of moving average (MA) time series model to my data in R. I know R:stats::ar ...
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Why must the solutions of the characteristic equation be greater than 1 for an Auto-regressive model to be stationary?

According to my notes, stationarity occurs if: All the solutions of the characteristic equation of the $AR(P)$, $1-\phi_1X-\phi_2X^2-...-\phi_PX^P=0$, are greater than 1 in modulus. No ...
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82 views

How to interpret the expression of MA(1) as AR($\infty$)

When AR(1) is expressed as MA($\infty$), I can interpret it as: let's say my wage this year depends only on last year's wage and a random shock (my boss' mood). But last year's wage also depends on ...
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1answer
128 views

Determining order of AR model

Suppose that we have the following model $$ y[t] = A_1\sin(\omega_1 t+\phi_1)+A_2\sin(\omega_2 t + \phi_2)+ \cdots + A_p \sin(\omega_pt + \phi_p) + z(t) . $$ Let us call this signal as B. Then in ...
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63 views

What does “AR(p) filtered series” mean?

I guess this means that omitting some variables in a certain interval, say, $(x_1, x_2, x_3, x_4, x_5) \to (x_1, x_5)$ in AR(4) model. Is it right? Or does this means eliminating autocorrelations ...