Can someone explain me how to implement a dynamic linear regression on R? The concept is similar to a transfer function, which mathematically is defined in this way $ y_t=c+w(B)x_t + N_t$, where $y_t$ is the variable to forecast, $x_t$ is the exogenous variable, $w(B)$ is the backshift operator related to the exogenous variable and $N_t$ is the error term following an ARMA model. To implement a transfer function model on R, the function auto.arima with the xreg specification is used. Ex: assume the goal is to forecast the energy price (p) using a transfer function model where the exogenous variable is the demand for energy, then I write:

p <- auto.arima(p.train, xreg=demand.train, stationary=TRUE, seasonal=TRUE)
fcast.p <- forecast(p, h=90, xreg=demand.test)
error <- MAPE(fcast.p$mean, p.test)

But how about a dynamic linear regression model? This is mathematically defined as $y_t=c + u(B)y_t + v(B) x_t + \epsilon_t$. I know the function dynlm, but I don't understand how to choose the optimal coefficients for lagged values of my variables.

Can someone explain me how to implement a dynamic linear model in R?

The concept is similar to a transfer function, which mathematically is defined as: $$ y_t=c+w(B)x_t + N_t $$ Where $y_t$ is the variable to forecast, $x_t$ is the exogenous variable, $w(B)$ is the backshift operator related to the exogenous variable, and $N_t$ is the error term following an ARMA model.

To implement a transfer function model in R, the function auto.arima with the xreg specification is used. For example, suppose that the goal is to forecast the energy price p using a transfer function model where the exogenous variable is the demand for energy, I can then write:

p <- auto.arima(p.train, xreg=demand.train, stationary=TRUE, seasonal=TRUE)
fcast.p <- forecast(p, h=90, xreg=demand.test)
error <- MAPE(fcast.p$mean, p.test)

But how about a dynamic linear regression model? This is mathematically defined as: $$ y_t=c + u(B)y_t + v(B) x_t + \epsilon_t $$ I know about the function dynlm, but I don't understand how to choose the optimal coefficients for lagged values of my variables.

Can someone explain me how to implement both models on R? I saw that to implement a tranfer function, you just need to use the auto.arima function and specify xreg, but how about a dynamic linear model? I only know the function dynlm, but I don't understand how to choose the optimal coefficients for lagged values of my variables. Namely, given the formula for dynamic linear model $y_t=c + u(B)y_t + v(B) x_t + \epsilon_t$, how am I supposed to find the optimal backshift polynomial $u(B)$ and $v(B)$ ?

Can someone explain me how to implement a dynamic linear regression on R? The concept is similar to a transfer function, which mathematically is defined in this way $ y_t=c+w(B)x_t + N_t$, where $y_t$ is the variable to forecast, $x_t$ is the exogenous variable, $w(B)$ is the backshift operator related to the exogenous variable and $N_t$ is the error term following an ARMA model. To implement a transfer function model on R, the function auto.arima with the xreg specification is used. Ex: assume the goal is to forecast the energy price (p) using a transfer function model where the exogenous variable is the demand for energy, then I write:

p <- auto.arima(p.train, xreg=demand.train, stationary=TRUE, seasonal=TRUE)
fcast.p <- forecast(p, h=90, xreg=demand.test)
error <- MAPE(fcast.p$mean, p.test)

But how about a dynamic linear regression model? This is mathematically defined as $y_t=c + u(B)y_t + v(B) x_t + \epsilon_t$. I know the function dynlm, but I don't understand how to choose the optimal coefficients for lagged values of my variables.