# Questions tagged [dynamic-regression]

Dynamic regression is a type of regression, where one of the independent variables is a lagged dependent variable.

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### How to repoduce the fitted values from a forecast::Arima in R by hand?

We have fit an ARIMA (1,0,0) with exogenous reggressors using the forecast package in R and would like to write about this model. However when we write out the ...
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### Fixed Effects Problem when regressing GDP per capita growth on lagged GDP per capita

For my thesis I am studying the impact that economic sanctions can have on the GDP per capita growth rate of targeted countries. I am using panel data for 56 countries spanning a period of 23 years. I ...
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### Contribution of regressors in regression with ARMA error

I am trying to forecast 'Patients' by fitting linear regression with ARMA error (auto.arima, Xreg) with 5 regressors. 'patients' and all 5 regressors have seasonality. 1) Is there any way to quantify ...
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### Forecasting many stores sales with optimal reconciliation and regression

I am forecasting many stores sales via the optimal reconciliation approach. The problem is that forecasts are not as accurate as I would like. Edit: Part of the problem is that a small subset of ...
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### If I add a lagged dependent variable, do I need to add the lagged independent variables too?

If I have a normal regression model y_t = βx_t + ε_t and want to add a y_(t-1), would this be proper? ...
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### Do dynlm and dlm have same mathematical expressions?

I am currently using dynamic linear regression (dynlm) for my analysis. However, I do also find another model called dynamic linear model (dlm). I find that dlm has an official mathematical ...
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### [R]: DOLS - number of leads and lags

I have a model model_1=dynlm(y_log~x1_log+x2) where y_log, x1_log are I(1) and x2 is something between I(0) and I(1) (I rejected unit root with ADF test but KPSS ...
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### What does small N or small T really mean in panel data sets?

A common notion in literature on the comparison of various estimation techniques for dynamic panel models is that it's always stressed that each of these different estimation techniques perform best ...
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### Stationary of exogenous variables in Dynamic Regression with SARIMA errors

I want to create a dynamic regression model with ARIMA-errors. What I am trying to figure out is if the exogenous variable, x_t and the variable I want to predict, y_t need to have the exact same ...
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### auto.arima model with many regressors

I am trying to forecast a seasonal series with 30 regressors using auto.arima. I have several questions regarding the correct methodology that I need to pursue. 1) Should I fit auto.arima with all ...
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### Need help with a DOLS model

I am attempting to build a multivariate DOLS model. More specifically, it is model that is already being used where I work, but I am trying to replicate the model in R. Currently, the model is used ...
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### dynamic time warping (DTW): unexpected results

on the wave of the suggestions given to me on this topic I started (time series similarities: which techniques for each transformation?) I decided to give another try at Dynamic Time Warping but I ...
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### kalman filter multiple observations per time step

I'm trying to use a Kalman Filter to estimate an online dynamic regression coefficient between two variables (e.g. http://www.thealgoengineer.com/2014/online_linear_regression_kalman_filter/) In the ...
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### Test for the significance of the effect of an intervention in a time series

I am looking for the best approach to test for the significance of the effect of an intervention that occurred at a known time on a time series data. Using a toy dataset as an example, I have come up ...
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### What is the difference between VAR, Dynamic Regressive, and ARMAX models?

All of these models seem to be used in predicting an endogenous time series variable, using several lagged exogenous time series variables. If it is so, how do we decide when to use which?
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### Prewhitening Regressors in Lagged Time Series Regression

I'm trying to identify significant lags in a time series regression such that $Y = \beta_0X_t + \beta_1X_{t-1} + ... + \beta_iX_{t-i} + \alpha_0Z_t + \alpha_1Z_{t-1} + ... + \alpha_jZ_{t-j}$ I ...
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### Dynamic regression linear models in R

I have a question regarding Dynamic regression linear models. I wonder if it is possible to implement a MLR model (in R) using 'lm' and creating lagged values of predictors and dependent variables. ...
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### Difference between SUTSE (Seemingly Unrelated Time Series Equations) and SUR (Seemingly Unrelated Regressions)

I am studying time-series econometrics and in particular Dynamic Linear Models for multivariate time-series. Someone can help me in understanding which is the difference between SUTSE (Seemingly ...
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### What is the impact of management on tree mortality caused by insect pest?

I am monitoring tree death caused by insects and potential impact of human treatment on yearly amount of tree mortality in areas with and without human intervention. My data are recorded by remote ...
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### Textbook approach to modeling non-proportional hazards in the Cox model

In Cox models with time varying coefficients, the effect of covariates on the hazard is allowed to change through time. In cases where a coefficient has a linear relationship with time, I am aware of ...
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### Cox-Snell residuals for Cox model with time varying coefficient

I am using the time transform feature of the coxph function in the survival package to model the effect of a time varying ...
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### Schoenfeld residual test for model with time varying coefficients?

I'm working with the survival package in R. I fit a Cox proportional hazard model (coxph) and did a scaled Schoenfeld residual test (...
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### How to forecast with a regression model with ARIMA errors?

I have obtained the following coefficients after using the auto.arima function in R: $y_t = 0.87 x_t - 0.51x_{t-1} + n_t$ where $n_t = 0.83n_{t-1} + e_t$ My question is, how to obtain $\hat{n}_{t-1}$...
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### I can't correct the OLS model with heteroskedasticity by the lmtest means

i'm using a selvaggio model to explain the behavior of deposits in a bank's data, and i need to use the estimated parameters, the problem is the heteroskedasticity that i detectect with breusch-pagan ...
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### Including time-varying regional fixed effects in Arellano-Bond estimation (R plm package)

I want to estimate a dynamic panel model with firm level time invariant fixed effects and time-varying regional fixed effects. I'm trying to implement this with R package ...
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### What are the reservations of Dynamic Linear Models (DLMs)?

I am studying dynamic linear models (DLMs). I am not sure I understand all its intricacies. My novice take is that those models can work very well if: you have a lot of data (several hundreds of ...
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### Arellano Bond in Stata: very high p-values when using the robust twostep estimator

I am doing a panel regression with N=21, T= 28 with 8 regressors which is dynamic in structure (includes a lag of the dependent variable). Using the robust one step estimator by Arellano & Bond, ...
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### State Space Model Specification (KFAS) [closed]

I am using KFAS to fit a dynamic logistic model of the form; $\hat{y} = \bf \beta_t x + \epsilon$ $\beta_t = \beta_{t-1} + \eta$ So the regression parameters change over time, and act as latent ...
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### Time-dependent Poisson regression

I have a time series that count the number of "type 1" events in a city, for each day. The serie contains a lot of zeros because type 1 events are rare (about 80% of counts are zeros). I'm using a ...
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### What statistical methods are there to recommend a movie like on Netflix?

I am looking to implement a dynamic model to recommend a movie to a user. The recommendation should be updated every time the user watches a movie or rates it. To keep it simple I am thinking of ...
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### What's wrong if I fit the auto-regression with OLS?

I am doing auto-regress by usual linear regression package. e.g. $y_t=φx+ε_t$ with $x =y_{t-1}$ My reason is that, Auto-regression does assumes iid errors, same for linear regression. Linear ...
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### Dynamic regression and prewhitening

I'm working on a time series forecasting problem where sales needs to be predicted using weather variables. The weather variables are auto correlated and hence pre-whitening is needed to find the true ...
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### ARIMAX Forecasting in SPSS vs. R

I'm using time series data containing both trend and seasonality. I also have 2 endogenous predictor variables that I would like to include in my model. In R I've used the forecast package to develop ...
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### Lag length selection in a dynamic model, ARDL approach to cointegration in R

I want to programme an ARDL approach to cointegration in R. Below is the generic equation: \Delta y_t=\beta_0+\sum \beta_i \Delta y_{t-i}+\sum \gamma_k \Delta x_{1,t-k}+\sum \psi_j \Delta x_{2,t-j}+\...
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### Consistent estimate vs out-of-sample performance

When there is a cross-correlation structure in linear regression errors, the usual approach is to model the errors as an ARIMA process. It leads to a consistent estimate of the parameters of the model....
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### Dynamic panel data

Can anyone please recommend a good source (academic and basic) for understanding the concepts of dynamic panel data estimation methods and why its preferred over static data analysis?
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### Correct procedures to detect and correct outliers for aggregated/SKU time series

Background I am currently working with sets of product sales time series at SKU-level for a FMCG company. Data are available in a weekly format for multiple years and sales data for hundreds of ...
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### How to identify relationship between response time series(Yt) & input time series(Xt) only in terms of Yt-1 & Xt?

I have a response time series(Y) & Input time series Xt & Zt. My only objective is to identify functional form Yt=f(Yt-1,Xt,Zt) where f(Yt-1,Xt,Zt) contains only lags of Yt , Xt & Zt as ...
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### Estimating a dynamic spatial panel

I am analyzing a spatial panel dataset using the XSMLE package in Stata. My units are a subset of US states (11) and my panel is strongly balanced. The package returns estimations for Main, Spatial, ...
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### How to write ar & ma terms in dynamic regression/arimax in terms of actual predictors?

I have done Arimax with response series Y as sales/demand & a set of input series on time series data at monthly level. The estimates from the arimax model is as shown below. I want to now write ...
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### How to identify functional form of relationship between response & input series in dynamic regression/arimax?

Problem statement A US insurance company advertises on national television in an attempt to increase the number of insurance quotations provided (and consequently the number of new policies). ...
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### R: Dynamic Regression with ARIMA model using xreg, make use of step function?

This might fit better here than on stackoverflow, I guess. I was trying to build a dynamic regression model with the dynlm package, but it did not work out. After reading this by Hyndman, I now ...
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### Assumptions and terminology for dynamic regression with endogenous offset ($y_t=y_{t-1}+\beta X_{t-1}+\epsilon_t$)

I'm dealing with a fairly simple time series regression model with the following basic form: $y_t=y_{t-1}+\beta X_{t-1}+\epsilon_t$ I'm assuming that observations of $y$ are known without error. $X$ ...