yth_glm fits a generalized linear model suggested by James D. Hamilton as a better alternative to the Hodrick-Prescott Filter.
yth_glm(x, h = 8, p = 4, ...)An integer, defining the lookahead period.
Defaults to h = 8, suggested by Hamilton. The default assumes
economic data of quarterly periodicity with a lookahead period of 2 years.
This function is not limited by the default parameter, and Econometricians may
change it as required.
An integer, indicating the number of lags. A Default of
p = 4, suggested by Hamilton, assumes data is of quarterly periodicity.
If data is of monthly periodicity, one may choose p = 12 or aggregate
the series to quarterly periodicity and maintain the default. Econometricians
should use this parameter to accommodate the Seasonality of their data.
all arguments passed to the function glm
yth_glm returns a generalized linear model object of class glm,
which inherits from lm.
For time series of quarterly periodicity, Hamilton suggests parameters of h = 8 and p = 4, or an \(AR(4)\) process, additionally lagged by \(8\) lookahead periods. Econometricians may explore variations of h. However, p is designed to correspond with the seasonality of a given periodicity and should be matched accordingly. $$y_{t+h} = \beta_0 + \beta_1 y_t + \beta_2 y_{t-1} + \beta_3 y_{t-2} + \beta_4 y_{t-3} + v_{t+h}$$ $$\hat{v}_{t+h} = y_{t+h} - \hat{\beta}_0 + \hat{\beta}_1 y_t + \hat{\beta}_2 y_{t-1} + \hat{\beta}_3 y_{t-2} + \hat{\beta}_4 y_{t-3}$$ Which can be rewritten as: $$y_{t} = \beta_0 + \beta_1 y_{t-8} + \beta_2 y_{t-9} + \beta_3 y_{t-10} + \beta_4 y_{t-11} + v_{t}$$ $$\hat{v}_{t} = y_{t} - \hat{\beta}_0 + \hat{\beta}_1 y_{t-8} + \hat{\beta}_2 y_{t-9} + \hat{\beta}_3 y_{t-10} + \hat{\beta}_4 y_{t-11}$$
James D. Hamilton. Why You Should Never Use the Hodrick-Prescott Filter. NBER Working Paper No. 23429, Issued in May 2017.
# NOT RUN {
data(GDPC1)
gdp_model <- yth_glm(GDPC1, h = 8, p = 4, family = gaussian)
summary(gdp_model)
plot(gdp_model)
# }
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