One-sided HP filter

[Binh Pham]

Dear Statalisters,

I post the code for One-sided HP filter which is particularly easy to implement using the stock tsfilter command.
The main idea is that HP filter is the smoother which employs all information t=1..T, i.e. f(y | T) while one-sided HP filter is filtering up to time t, i.e. f(y | t). I replicate the matlab code by Alexander Meyer-Gohde and see there is an identical result.

We just need to loop from time t=3 to T since we would loss the first two obs due to its lags. Note that, Stock and Watson (1999) defined the one-sided HP filter as follows: y(t) = tau(t) + epsilon(t); (1 - L)^2*tau(t) = eta(t).

There is an equivalent Kalman version of one-sided HP filter in Stata elsewhere in the forum, but it seems that the snippet code below is easy to read and apply. To use it just replace "series..." by your actual series name.

capture drop series_1scycle
local start  3
local end   _N
forvalues time = `start'/`end' {
        qui tsfilter series_1scycle = series_original in 1/`time', smooth(`lambda')
        qui replace series_1scycle = series_original in `time'
}
generate series_1strend = series_original - series_1scycle

PS: I am not sure the code can produce the exact result of the one-sided HP filter as suggested in Stock and Watson (1999). But you can test with matlab code (serial version) by Alexander Meyer-Gohde and compare two results.

[Mark Davis]

I had a student trying to do this with panel data and I wrote a kludge. I'm pretty sure there is a better way but I wanted to put this out there incase anyone in the future is looking to do this

*one sided filter
    sum id
    local max_id= `r(max)'
    
    *loop through countries
    forvalues i=1/`max_id'{
        disp in red "id = `i'"
        
        preserve
            *keep individual country
            keep if id==`i'
            qui describe
            *if country has observations
            if `r(N)'>0{
                
                *code from stata list
                local start  8
                local end  = _N
                *add lambdas here
                local lambdas 400000 1600
                
                foreach lambda in `lambdas'{
                            
                    forvalues time = `start'/`end' {
                        capture tsfilter hp sp_index_1scycle = sp_index in 1/`time', smooth(`lambda')
                        capture replace sp_index_1scycle = sp_index in `time'
                    }
                    generate sp_index_1strend_`lambda' = sp_index - sp_index_1scycle        
                }
                keep id date sp_index_1strend*
                if i!=1 append using data/temp_tstresnd.dta
                save data/temp_tstresnd.dta, replace
            }
        
        restore
    
    }

[Nick Cox]

 
 if i!=1 append using data/temp_tstresnd.dta

should be

 
 if `i' != 1 append using data/temp_tstresnd.dta

If this code worked before, there was a fortunate accident with a variable named (or abbreviating to)

 i

in the original dataset. Or you had the code right in the original, but it's reported differently here.

[Mark Davis]

Thank you. I’m not sure how that happened.

[Nick Cox]

Trivial, but rather than

sum id
local max_id = `r(max)'      

forvalues i = 1/`max_id' {

this is a simpler way to start

sum id, meanonly    

forvalues i = 1/`r(max)' {