yth_glm {neverhpfilter} | R Documentation |
Fits Hamilton's alternative model
Description
yth_glm
fits a generalized linear model suggested by James D. Hamilton as a better alternative to the Hodrick-Prescott Filter.
Usage
yth_glm(x, h = 8, p = 4, ...)
Arguments
x |
A univariate |
h |
An |
p |
An |
... |
all arguments passed to the function |
Details
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}
Value
yth_glm
returns a generalized linear model object of class glm
,
which inherits from lm
.
References
James D. Hamilton. Why You Should Never Use the Hodrick-Prescott Filter. NBER Working Paper No. 23429, Issued in May 2017.
See Also
Examples
data(GDPC1)
gdp_model <- yth_glm(GDPC1, h = 8, p = 4, family = gaussian)
summary(gdp_model)
plot(gdp_model)