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How to calculate time varying coefficient linear regression?
We want to estimate the following model: yt = β1tX1t + β2tX2t + ut, t = 1, …, T, where the coefficients are functions of a rescaled time period τ = t / T with T = 1000. In particular, β1t = sin(2πτ) and β2t = 2τ. The regressors, X1t ∼ N(0, 1) and X2t ∼ χ2(4), are independent of the error term, ut ∼ t(10). ## Calculating regression bandwidth…
How to find the central value of a time varying coefficient?
The data generating process of the example below has time-varying coefficients and therefore its estimation with function lm will only find a central value of the time-varying coefficients.
Which is more accurate tvreg or time varying coefficient?
As we see in the plot, the estimation assuming a constant β1t lays in the middle of all the values of β1t, while the estimation assuming time-varying coefficients is more accurate and closer to the true values. Package tvReg calculates the confidence intervals the class attributes tvlm, tvar, tvsure and tvirf with the confint method.
Can you predict in a time varying setting?
Unlike the other regression models, prediction in a time-varying setting is not trivial. To predict, we would need to know the covariates values beyond the observed times, but if we knew that, we would also know if the subject was still alive or not!
How are confidence intervals calculated for tvvar and TVLM?
The variable coefficients estimates, as well as if confidence intervals if calculated, are plotted for the class attributes tvlm, tvar, tvsure and tvirf. The fitted values and the residuals are plotted for the class attribute tvvar because the interpretation of its coefficients is not relevant.
How to fit TV-LM to the data?
Function tvLM fits a TV-LM to the data using the tvOLS method in the estimation. The only mandatory argument is formula which should be a single formula for a single equation model. This formula follows the standard regression formula in R (see documentation of formula ).