yth_glm

The yth_glm function wraps glm and primarily exists to model the output for the yth_filter. On that note, the function API allows one to use the ... to pass any additional arguments to glm.

The yth_filter returns an object of class glm, so one can use all generic methods associated with glm objects. Here is an example of passing the results of a yth_glm model to the plot function, which outputs the standard plot diagnostics associated with the method.

```{r, warning=FALSE, message=FALSE} library(neverhpfilter)

data(GDPC1)

log_RGDP <- 100*log(GDPC1)

gdp_model <- yth_glm(log_RGDP$$"1960/"$$, h = 8, p = 4)

plot(gdp_model)

## yth_filtered

This is the main function of the package. It both accepts and outputs `xts` 
objects. The resulting output contains various series discussed in Hamilton (2017). 
These are a user defined combination of the original, trend, cycle, and random 
walk series. See documentation and the original paper for further details.

```{r, warning=FALSE, message=FALSE}
gdp_filtered <- yth_filter(log_RGDP, h = 8, p = 4)

tail(gdp_filtered, 16)

class(gdp_filtered)

As the output is an xts object, it inherits all generic methods associated with xts. For example, one can conveniently produce clean time series graphics with plot.xts.

Not the use of xts::addPanel function, which is used to panel plot the cycle component of the yth_filter.

{r, warning = FALSE} plot(log_RGDP, grid.col = "white", col = "blue", legend.loc = "topleft", main = "100 x Log of Real GDP (GDPC1)") addPanel(yth_filter, output=c("cycle"), type="h", on=NA, col="darkred" )

Choices for h and p

In the original paper, Hamilton aggregates the PAYEMS monthly employment series into data of quarterly periodicity prior to apply his filter. That is a desirable approach when comparing with other economic series of quarterly periodicity. However, using the yth_filter function, one can choose to retain the monthly series and adjust the h and p parameters accordingly.

The default parameters of h = 8 and p = 4 assume times series data of a quarterly periodicity. For time series of monthly periodicity, one can retain the same look-ahead and lag periods with h = 24 and p = 12. See the yth_filter documentation for more details.

```{r, warning = FALSE} Employment_log <- 100*log(PAYEMS$$"1950/"$$)

employment_cycle <- yth_filter(Employment_log, h = 24, p = 12, output = “cycle”)

plot(employment_cycle, grid.col = “white”, type = “h”, up.col = “darkgreen”, dn.col = “darkred”, main = “Log of Employment cycle”)

In addition to adjusting parameters to accommodate other periodicities, one may 
wish to explore longer term cycles by extending `h`. Below are examples of moving 
the look-ahead period defined by `h` from 8 quarters (2 years), to 20 quarters 
(5 years), and then 40 quarters (10 years). 

```{r}
gdp_5yr <- yth_filter(log_RGDP, h = 20, p = 4, output = c("x", "trend", "cycle"))

plot(gdp_5yr["1980/"][,1:2], grid.col = "white", legend.loc = "topleft", 
     main = "Log of Real GDP and 5-year trend", 
     panels = 'lines(gdp_5yr["1980/"][,3], type="h", on=NA)')

gdp_10yr <- yth_filter(log_RGDP, h = 40, p = 4, output = c("x", "trend", "cycle"))

plot(gdp_10yr["1980/"][,1:2], grid.col = "white", legend.loc = "topleft", 
     main = "Log of Real GDP and 10-year trend",
     panels = 'lines(gdp_10yr["1980/"][,3], type="h", on=NA)')

Conclusion

These functions give you an avenue to filter econometric time series into trend and cycle components. They identify a more stable trend and cycle components that doesn’t have the estimation issues associated with the head and tail portions of those generated by the HP-filter.