Fits Hamilton's alternative model

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, ...)

Arguments

x

A univariate xts object of any zoo index class, such as Date, yearmon, or yearqtr. For converting objects of type timeSeries, ts, irts, fts, matrix, data.frame, or zoo to xts, please see as.xts.

h

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.

p

An integer, indicating the number of lags. A default of p = 4, suggested by Hamilton, assumes data is of quarterly periodicity. If data is monthly, one may choose p = 12 or aggregate the series to quarterly and maintain the default. Econometricians should use this parameter to accommodate the seasonality of their data.

...

Additional arguments passed to glm.

Value

yth_glm returns a generalized linear model object of class glm, which inherits from lm.

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.

References

James D. Hamilton. Why You Should Never Use the Hodrick-Prescott Filter. NBER Working Paper No. 23429, Issued in May 2017.

See also

glm, lm

Examples

data(GDPC1)

gdp_model <- yth_glm(GDPC1, h = 8, p = 4, family = gaussian)

summary(gdp_model)
#> 
#> Call:
#> stats::glm(formula = formula, family = ..1, data = data)
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) 195.9049    38.3005   5.115 5.63e-07 ***
#> xt_0          0.7590     0.1321   5.746 2.26e-08 ***
#> xt_1          0.1344     0.1729   0.778    0.437    
#> xt_2          0.0431     0.1729   0.249    0.803    
#> xt_3          0.1030     0.1327   0.777    0.438    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Dispersion parameter for gaussian family taken to be 115351.3)
#> 
#>     Null deviance: 1.1636e+10  on 302  degrees of freedom
#> Residual deviance: 3.4375e+07  on 298  degrees of freedom
#>   (11 observations deleted due to missingness)
#> AIC: 4398.5
#> 
#> Number of Fisher Scoring iterations: 2
#> 

plot(gdp_model)