# Computes Time-Varying Parameters Regression. This function computes Time-Varying Parameters Regression (TVP) with the updating procedure as in Raftery et. al (2010). ```r tvp(y,x,V,lambda,W=NULL,kappa=NULL,c=NULL) ``` ## Arguments - `y`: `numeric` or a column `matrix` of a dependent variable - `x`: `matrix` of independent variables, different columns should correspond to different variables - `V`: `numeric`, initial variance in the state space equation for the recursive moment estimator updating method, as in Raftery et al. (2010) - `lambda`: `numeric`, a forgetting factor between 0 and 1 used in variance approximations - `W`: optional, `numeric`, initial value of variance for the model equations, if not specified the method based on the linear regression, as in Raftery et al. (2010) is used - `kappa`: optional, `numeric`, a parameter in the exponentially weighted moving average in variance updating (see also `fDMA`), between 0 and 1, if not specified the method as in Raftery et al. (2010) is used - `c`: optional, `logical`, a parameter indicating whether constant is included, if not specified `c=TRUE` is used, i.e., constant is included ## Details It is not possible to set `c=FALSE` if `ncol(x)=0`. In such a case the function will automatically reset `c=TRUE` inside the code. ## Returns class `tvp` object, `list` of - **$y.hat**: fitted (forecasted) values - **$thetas**: estimated regression coefficients - **$pred.dens.**: predicitive densities from each period - **$y**: `y`, forecasted time-series ## Examples ```r wti <- crudeoil[-1,1] drivers <- (lag(crudeoil[,-1],k=1))[-1,] ld.wti <- (diff(log(wti)))[-1,] ld.drivers <- drivers[-1,] ld.drivers[,c(4,6)] <- (diff(drivers[,c(4,6)]))[-1,] ld.drivers[,c(1:2,5,7)] <- (diff(log(drivers[,c(1:2,5,7)])))[-1,] ld.drivers[,c(3,6)] <- ld.drivers[,c(3,6)]/100 t1 <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99) t2 <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99,W=1) t3 <- tvp(y=ld.wti,x=ld.drivers,V=1,lambda=0.99,W=1,kappa=0.75) # Model with constant only empty <- matrix(,nrow=nrow(ld.drivers),ncol=0) t4 <- tvp(y=ld.wti,x=empty,lambda=0.99,V=1) ``` ## References Raftery, A. E., Karny, M., Ettler, P., 2010. Online prediction under model uncertainty via Dynamic Model Averaging: Application to a cold rolling mill. **Technometrics** 52 , 52--66. Sanderson, C., Curtin, R., 2016. Armadillo: A template-based C++ library for linear algebra. **Journal of Open Source Software** 1 , [https://arma.sourceforge.net/armadillo_joss_2016.pdf](https://arma.sourceforge.net/armadillo_joss_2016.pdf). ## See Also `grid.tvp`, `print.tvp`, `summary.tvp`, `plot.tvp`.

tvp function