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.

learn more… | top users | synonyms

1
vote
0answers
37 views

Using ARIMA to Create a Model in R

I'm trying to get understand why the values for my model are different when using two different functions. The first one is from Example 9.2 (International Visitors to Australia), using the ...
2
votes
1answer
47 views

Breusch-Pagan Test for ARIMA Model in R

I am testing my model using the Breusch-Pagan Test, but have not been able to find anything online regarding how to calculate it for an ARIMA Model. My AR1 Model is: ...
3
votes
0answers
37 views

Analysis of Multiple Time Series Data with Exogenous Shocks

Real Life ProblemThis one is a tough one and some crowd sourcing seems like a good way to get some feedback. I am trying to determine the effect of Non-Farm Payroll surprises on a subsector of the ...
0
votes
0answers
37 views

AR(2) model interpretation

If I have a negative sign in my AR(2) model equation, (for example, $y = 100 - 50x_{t-1} + 25x_{t-2}$) and if my AR(1) and AR(2) has same r-square value, is it okay to interpret it as model overfit? ...
1
vote
0answers
24 views

How do I interpret weak exogeneity in an ADL model?

First year econ graduate student here; looking at an ADL (Autoregressive Distributed Lag) model for the first time. Consider $Y_t = \omega Z_t + \alpha Y_{t-1} + \beta Z_{t-1} + \mu + \epsilon_t$, ...
1
vote
0answers
21 views

How do I interpret lagsarlm output from R's spdep?

I've run lagsarlm on my dataset, using a mixed model and using a row-standardized adjacency matrix. I have results that I think are good, but would am not sure how ...
0
votes
0answers
17 views

How do I choose the correct model for a regression? [migrated]

So the central question of my project is to what extent does a country's level of export contibution towards GDP (i.e. exports as a % of total GDP) affect its GDP growth. I'm comparing this ...
3
votes
0answers
65 views

Longitudinal data analysis where meaning and metric of response variable varies over time

Determining what factors predict change over time is a topic of investigation in many fields and there are a variety of readily implemented methods for analysing repeated measures in the same metric. ...
0
votes
0answers
12 views

How to fit an logistical autoregression in R?

I modeled the relationship of $X$ and $Y$ by the logistic function. The residual plot displays autocorrelation which I'd like to rid. I want to try adding trend component to $X$, thus the model ...
2
votes
0answers
15 views

How can I compute cross-correlation and auto-correlation in R using pooled data?

I'm trying to perform a lagged linear regression on time series data sourced from ~10,000 hospital patients, for the purpose of estimating causal relationships between administration of a drug and a ...
2
votes
0answers
42 views

ARX model selection

I have an autoregressive model with exogenous variables: $S_{t} = \sum_{i=1}^{p} a_i S_{t-i} + \sum_q \sum_{i=1}^{r} b^q_i X^{q}_{t-i}$ where $S_t$ is the signal I want to predict and $X^q_t$ the ...
0
votes
1answer
54 views

How to interpret the Durbin-Watson test output in R [closed]

Just for "train" with linear regression in R I'm doing a Durbin-Watson test over the residuals of a regression (over stock ...
3
votes
1answer
77 views

Difference between different autoregressive models

I am trying to understand the difference between these three different specifications of an autoregressive model for variable var in Stata: ...
0
votes
0answers
26 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 ...
2
votes
3answers
110 views

Estimation of unit-root AR(1) model with OLS

Given a random walk $x_t$, $$x_t=x_{t-1}+\varepsilon_t,$$ consider estimating the slope coefficient $\beta$ in $$x_t=\beta x_{t-1}+\varepsilon_t$$ by OLS. This question and the following answer ...
7
votes
2answers
308 views

Random walk estimation with AR(1)

When I estimate a random walk with an AR(1), the coefficient is very close to 1 but always less. What is the math reason that the coefficient is not greater than one?
1
vote
0answers
47 views

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

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 $t,s$?
0
votes
1answer
33 views

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 ...
0
votes
0answers
58 views

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 ...
0
votes
0answers
29 views

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 ...
1
vote
0answers
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 ...
2
votes
2answers
179 views

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 ...
0
votes
0answers
58 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 ...
2
votes
1answer
38 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 ...
0
votes
0answers
25 views

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) + ...
0
votes
1answer
64 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 ...
0
votes
0answers
15 views

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 ...
0
votes
0answers
37 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 ...
1
vote
1answer
107 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 ...
3
votes
1answer
78 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 ...
0
votes
1answer
51 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 ...
1
vote
0answers
57 views

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 ...
0
votes
0answers
41 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 ...
0
votes
0answers
83 views

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 ...
1
vote
1answer
64 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 ...
1
vote
1answer
45 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 ...
1
vote
4answers
125 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 ...
0
votes
0answers
35 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 ...
0
votes
1answer
40 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 ...
0
votes
0answers
15 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 ...
1
vote
1answer
156 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 ...
2
votes
1answer
68 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 = ...
1
vote
1answer
101 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 ...
1
vote
0answers
65 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 ...
1
vote
1answer
80 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 ...
0
votes
0answers
10 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 ...
0
votes
1answer
84 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} + ...
2
votes
0answers
66 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 ...
1
vote
1answer
32 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 ...
2
votes
1answer
55 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 ...