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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Breusch-Pagan Test for ARIMA Model in R [closed]

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: ...
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how to fit ar(1) model with predetermined value of autocorrelation parameter in R? [migrated]

I have the following data: ar <- arima.sim(list(order=c(1,0,0), ar=0.9), n=M1) + 10 How to fit an AR(1) model to simulated data above with ar parameter=0.5? ...
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35 views

Time series prediction for a chaotic multivariate data

I am trying to forecast a chaotic multivariate time series, and any architecture I use ( LSTM, MLP or tried to implement Autoregression architectures from few papers like https://arxiv.org/pdf/1704....
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324 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 ...
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Why the lag number of an AR model doesn't indicate the number of lags in a plotted ACF?

In the below image, there are AR models with differing lags. As far as I know, each autocorrelation function plot has an x-axis that is "number of lags". Can someone help me understand how ...
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1answer
171 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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How does autoregression work in R?

I don't understand results of ar() function in R. I made up a very simple case, Fibonacci sequence: ...
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35 views

ar() in R and Matlab give different results for same dataset

I have a Matlab script that performs some autoregressions and am trying to replicate it in R, but can't get them to match. So as a MWE, I'm trying to get the same results in R as are obtained by this ...
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How to learn 'end of sequence' for continuous sequence?

Consider Autoregressive model (i.e. RNN Language model) which try to output next token given all previous tokens. When generating sequence with this model, model need to learn when should be end of ...
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Negatively correlated estimators for the AR-1 process

I have the following question. Assume we have a stochastic process \begin{equation} y_t = \gamma + \phi y_{t-1} + \epsilon_t, \ \epsilon_t \sim \mathcal{N}(0, \sigma^2), \end{equation} where $|\phi| &...
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1answer
158 views

The relationship between autoregressive model and distributed-lag model

The autoregressive models (koyck model, adaptive expectation model, potential adjustment model) I have learned so far are all derived from distributed lag models. And intuitively it makes sense since ...
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variance of an autoregressive process

Let $\{x_t\}_{t\in\mathbb{N}}$ be a zero mean strictly stationary sequence of random variables and $c:\mathbb{N}\to\mathbb{R}$ the (auto)covariance function. If the process follows the AR(1) model $$...
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How to estimate a spatial weight matrix empirically?

Let $y$ be an n-vector of observations on the dependent variable and $X$ be the $n \times k$ design matrix with observations for $n$ units on $k$ variables. I aim to estimate a time-series cross-...
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1answer
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Does the Transformer decoder query based on the previous token?

Consider the decoder part of the popular Transformer architecture; briefly put, the decoder module consists of a composition of self-attention layers and performs auto-regressive prediction. Because ...
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How would you convert an ARIMA(0,0,1)(0,1,0)12 model to equation form? [duplicate]

How would you convert an ARIMA(0,1,1)(0,1,1)12 model to equation form?
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Why ACF is used in MA and PACF is used AR models?

I'm reading Analysis of Financial Time Series(Third Edition) RUEY S. TSAY. The author summarizes the model selection of AR(p) and MA(q) as follows: For MA models, ACF is useful in specifying the ...
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1answer
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Why are AR(p) processes always invertible?

My question is the following: If we have an AR(p) process, then we have the following $$ \Phi(B)X_{t}=Z_{t} $$. I understand that to check for causal/non-causal stationarity, we consider the roots of $...
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1answer
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Proof of contemporaneous exogeneity, and its implications for an AR(1) model

It can be shown by contradiction that exogeneity fails to hold for an AR(1) model. Is there any proof that contemporaneous exogeneity does not fail to hold? All I've come across is assuming it does ...
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Conditional distribution of Ornstein-Uhlenbeck on two fixed points

The conditional distribution of a Ornstein-Uhlenbeck $X(t)$ conditional on $X(0)$ is given by $$ X(t)|X(0) = X(0)e^{-t} + \mu(1 - e^{-t}) $$ This process is usually only defined for $t>0$ (future ...
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1answer
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Non-Sensible Estimates for MLE of AR Processes

I am taking a course on Time Series Econometrics and I am solving a problem set that requires students to explicitly write maximum likelihood functions for, as an example, AR processes and estimate ...
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Is there a point on performing time series analysis on data that are not gathered with a consistent frequency?

To be more specific, what I have in mind is data gathered from android games. These data wouldn't have any time consistency because a user is free to play as many games as he wants whenever he wants, ...
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1answer
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Forecasting an index with google in R

I am trying to predict an index using Google Trend Data. I try to orientate myself by this paper. In this paper the authors use the three variables: Sales, Index and SearchFrequency to forecast the ...
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Time series - best approach?

Good evening, newbie to the forum but I would appreciate some advice on a new problem I’m working on. We are collecting water samples and measuring a number of things simultaneously in the water, as ...
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35 views

Unbiased Estimator of AR(1) Models?

What are the options for unbiased estimators of AR(1) (or AR(p)) models? Bias reduction techniques may also be included (jack knife would be one). I found one paper called "Bias correction using ...
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Equivalence of trend stationary process and stationary process

I am new to Time Series, and I am having some trouble dealing with the constant of an AR(p) process, which of course 'reinforces' itself over time to become a deterministic trend. For simplicity sake, ...
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Modelling auto-correlated binary time series

What are the usual approach to modelling binary time series? Is there a paper or a text book where this is treated? I think of a binary process with strong auto-correlation. Something like the sign of ...
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1answer
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What does it mean “analyze sample time series data when only a single series is available”?

Since the book says, it will use time series to mean either realization of a process or a process, I have no idea how to interpret the following sentence. "This notion, called weak stationary(i.e....
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Advantages of using PACF

Box-Jenkins approach to time series analyses uses a series of diagnostics, one of which calculating Partial autocorrelation function (PACF). The goal is to determine the order ...
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1answer
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ACF of differenced MA(p) process

I have an MA(4) process applied to the first order seasonal difference of $Y_t$ as follows: $(1-B^s) Y_t = (1+\theta_1B+\theta_2B^2+\theta_3B^3+\theta_4B^4) Z_t$ where $Z_t \sim N(0,\sigma^2)$ This ...
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Boosted AR for time series forecasting?

I have time series data recorded at multiple locations, stored in a matrix $Y$. I have fit a Vector Autoregressive Model to it which forecasts the data pretty well on a test set. However, if I plot ...
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Variance of an AR and ARMA process derived from lag notation

This question concerns the asymptotic variance of an $\text{ARMA}(p,q)$ process. Suppose that an $\text{ARMA}$ process can be rewritten as an $\text{MA}(\infty)$ process, and from this we can in ...
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What kind of statistical test do I need in testing the lag order in an Auto Regression model AR(4) against a restricted AR(3)?

Bit stumped on this one and none of my resources are helping to clarify this one for me. I've been given an estimated Autoregression Model AR(4) model of the sort: Yt = b0 + b1 x Yt-1 + b2 x Yt-2 + b3 ...
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1answer
657 views

Relation between AR(p) stationarity and causality

Let's take an AR(p) model $\phi(L)y_t=z_t$ where $\phi(L)=1-\phi_1-...-\phi_pL^p$ and L is the lag operator. I have just studied that if there are no roots of the polynomial on the unit circle, $1/\...
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What's a stationary VAR?

What is a stationary VAR (vector autoregression)? Can a VAR with non-stationary variables be stationary? How do you test whether a VAR is stationary or non-stationary? (Example in ...
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1answer
160 views

Interpreting effect sizes in cross-lagged -auto-regressive models

I am running an auto-regressive, cross-lagged panel model between three variables (individual survey responses) to understand the over-time dynamics between them. But I am trying to make sure I ...
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1answer
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Why doesn't PACF cut off for MA processes?

While studying for a time series paper I came across the terms 'partial autocorrelation function' (PACF) and 'autocorrelation function' (ACF) in conjugation to $AR$ and $MA$ processes, why is it such ...
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Causal AR Model?

This questions is about necessary conditions (in form of inequality on coefficients) for the causality of autoregressive models. For instance, $|\phi_1| < 1$ is a necessary condition for an AR(1) ...
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1answer
161 views

Linear Regression : Can I use both levels and changes in the same model?

I have a linear model with 1 predictor variable in the form of: $Y = a + b_{1}*X$ Both $X$ and $Y$ are stationary variables and the fit of the model is good. I have also created 2 other models based ...
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arima (0,1,0). How can I interpret it in this case? [duplicate]

I was predicting time series using auto.arima () in R and I found something I don't know how to interpret. For a certain number of time series, auto.arima () indicated that the best arima model was ...
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Mean of target values at different time points as predictor in multiple regression

I've received regression model that predicts crop yield based on data collected at 3 time points (years). Input data contains multiple attributes and crop yield in the given year for a given location....
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Why does my SARIMA model not capture the seasonality?

I have sales data over 100+ days. Every Saturday has 0 sales. For the other days there is also a clear seasonality. Tuesday always has the highest sales, and the order in which the other days follow ...
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1answer
222 views

When to use AR and when to use MA model?

When to use an AR model and when to use an MA model to model time-series data. What aspects of data are modelled by the AR process which can't be done by MA and vice-versa?
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1answer
78 views

ARIMA doesn't include the trend

I have a problem with my ARIMA(1,1,1) predictions. I have a time series with no seasonal component but with an obvious trend. To get rid of it I take the first difference by setting d=1. The model ...
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Component contributions in Additive Model Time Series

I have trained a model for forecasting time series in a greedy procedure: Fit the Trend component T(t) of the series on the original signal y(t) Fit a Cyclical/Seasonal S(t) component of the series ...
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How to interpret Autocorrelation plots?

I have sales data per day. To create an ARIMA model, they suggest to first look at an autocorrelation plot. How I interpret this is that they look how my sales are correlated to eachother for ...
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1answer
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What can we predict from the follow ACF and PACF plots?

This is a time series of a wind speed data collected every hour for a month. What can you interpret from the ACF and PACF plots about the trends and seasonal components? Are there any? And which model ...
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Smoothing autoregressive coefficients

I fit an autoregressive model to a time series with 1837 observations using the R ar() function setting the maximum number of lags to 20. The function selected an AR(19) model using the AIC criterion, ...
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Cumulative Effect

Let $X_t$ be a causal AR($p$) model. If we have $n$ observations of this time series and fit an AR($m$) model with $m\gt p$ to the data; that is $$X_t = \phi_1 X_{t-1} + \cdots + \phi_m X_{t-m} + W_t,...
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1answer
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ARIMA Model Non-Stationary Time Series

Suppose that the data generated process is the following: Y(t) = 1.2*Y(t-1) + 0.2 The process is clearly non-stationary. My question is why we can't fit an AR(1) model and make predictions?
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AR(p) by iterated vs. lag method. Different results

Reading "Applied Econometrics Time Series" By Walter Enders I am trying to derive the stationary AR(p) model as he does on page 58, fourth edition. This is the AR(P) model \begin{equation} y_t=a_0+\...

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