Smoothing by kernel regression

The function perform the smoothing of a time-series by non-parametric kernel regression.

Usage

kern_smooth(
  x,
  t = seq_along(x),
  h,
  t.for.pred = t,
  kernel = c("epanechnikov", "box", "normal"),
  param_smoother = list(),
  output = c("dataframe", "list")
)

Arguments

x: a numeric vector of the series to be smoothed.
t: a (numeric or Date) vector of time points. If missing, observations are considered to correspond to sequential time steps (i.e., 1, 2 ...).
h: a scalar indicating the bandwidth used by the smoothing function.
t.for.pred: a (numeric or Date) vector of time points at which to evaluate the smoothed fit. If missing, t is used.
kernel: a character string indicating which kernel to use: "epanechnikov" (the default), "box", or "normal" (abbreviations also work).
param_smoother: a list of additional parameters to provide to the internal smoothing function (see Details).
output: a character string indicating if the output should be a "dataframe" (default) or a list (for faster computation when the function is called repeatedly).

Value

a dataframe of time points (t.for.pred) and corresponding fitted values.

Details

The function is essentially a wrapper that calls different underlying functions depending on the kernel that is selected:

lpridge::lpepa() for "epanechnikov".
stats::ksmooth() for "normal" and "box". The argument param_smoother can be used to pass additional arguments to these functions.

References

A short post we found useful: http://users.stat.umn.edu/~helwig/notes/smooth-notes.html

Examples


## Smooth 10 first values of a vector

kern_smooth(stockprice$DAX[1:20], h = 5)
#>     t             x
#> 1   1 -0.0142344629
#> 2   2 -0.0080248366
#> 3   3 -0.0043075061
#> 4   4 -0.0025564727
#> 5   5 -0.0013302414
#> 6   6 -0.0020000346
#> 7   7 -0.0037240350
#> 8   8 -0.0038831231
#> 9   9 -0.0052112887
#> 10 10 -0.0055894783
#> 11 11 -0.0051979756
#> 12 12 -0.0040618781
#> 13 13 -0.0007538746
#> 14 14  0.0021554236
#> 15 15  0.0022715116
#> 16 16  0.0037383564
#> 17 17  0.0048464190
#> 18 18  0.0063879240
#> 19 19  0.0073951470
#> 20 20  0.0089770700


## Prediction at time step 2 and 3

kern_smooth(stockprice$DAX, h = 1, t.for.pred = c(2, 3))
#>   t           x
#> 1 2  0.01490435
#> 2 3 -0.02550618


## Smoothing using a vector of dates for time

kern_smooth(x = stockprice$DAX[1:10], t = stockprice$DateID[1:10], h = 5)
#>             t             x
#> 1  2000-04-03 -0.0142344629
#> 2  2000-04-04 -0.0083542527
#> 3  2000-04-05 -0.0027355458
#> 4  2000-04-06 -0.0003472332
#> 5  2000-04-07 -0.0005866131
#> 6  2000-04-10 -0.0006515250
#> 7  2000-04-11 -0.0039680278
#> 8  2000-04-12 -0.0072967854
#> 9  2000-04-13 -0.0125126832
#> 10 2000-04-14 -0.0190363342


## Smoothing conserves original order

kern_smooth(x = stockprice$DAX[10:1], t = stockprice$DateID[10:1], h = 5)
#>             t             x
#> 1  2000-04-14 -0.0190363342
#> 2  2000-04-13 -0.0125126832
#> 3  2000-04-12 -0.0072967854
#> 4  2000-04-11 -0.0039680278
#> 5  2000-04-10 -0.0006515250
#> 6  2000-04-07 -0.0005866131
#> 7  2000-04-06 -0.0003472332
#> 8  2000-04-05 -0.0027355458
#> 9  2000-04-04 -0.0083542527
#> 10 2000-04-03 -0.0142344629


## Effect of the bandwidth

plot(stockprice$DAX[1:100] ~ stockprice$DateID[1:100],
     las = 1, ylab = "DAX index", xlab = "Date")
points(kern_smooth(stockprice$DAX[1:100], stockprice$DateID[1:100], h = 1),
       type = "l", col = "grey")
points(kern_smooth(stockprice$DAX[1:100], stockprice$DateID[1:100], h = 3),
       type = "l", col = "blue")
points(kern_smooth(stockprice$DAX[1:100], stockprice$DateID[1:100], h = 10),
       type = "l", col = "red")
legend("topright", fill = c("grey", "blue", "red"),
       legend = c("1", "3", "10"), bty = "n", title = "Bandwidth (h)")



## Effect of the kernel

plot(stockprice$DAX[1:100] ~ stockprice$DateID[1:100],
     las = 1, ylab = "DAX index", xlab = "Date")
points(kern_smooth(stockprice$DAX[1:100], stockprice$DateID[1:100], h = 10),
       type = "l", col = "orange")
points(kern_smooth(stockprice$DAX[1:100], stockprice$DateID[1:100], h = 10, kernel = "box"),
       type = "l", col = "blue")
points(kern_smooth(stockprice$DAX[1:100], stockprice$DateID[1:100], h = 10, kernel = "norm"),
       type = "l", col = "red")
legend("topright", fill = c("orange", "blue", "red"),
       legend = c("epanechnikov", "box", "normal"), bty = "n", title = "Kernel method")