# [R] fitting a sinus curve

David Winsemius dwinsemius at comcast.net
Thu Jul 28 19:58:38 CEST 2011

```On Jul 28, 2011, at 1:07 PM, Hans W Borchers wrote:

> maaariiianne <marianne.zeyringer <at> ec.europa.eu> writes:
>
>> Dear R community!
>> I am new to R and would be very grateful for any kind of help. I am
>> a PhD
>> student and need to fit a model to an electricity load profile of a
>> household (curve with two peaks). I was thinking of looking if a
>> polynomial
>> of 4th order,  a sinus/cosinus combination or a combination of 3
>> parabels
>> fits the data best. I have problems with the sinus/cosinus
>> regression:
>
> time <- c(
> 0.00, 0.15,  0.30,  0.45, 1.00, 1.15, 1.30, 1.45, 2.00, 2.15, 2.30,
> 2.45,
> 3.00, 3.15, 3.30, 3.45, 4.00, 4.15, 4.30, 4.45, 5.00, 5.15, 5.30,
> 5.45, 6.00,
> 6.15, 6.30, 6.45, 7.00, 7.15, 7.30, 7.45, 8.00, 8.15, 8.30, 8.45,
> 9.00, 9.15,
> 9.30, 9.45, 10.00, 10.15, 10.30, 10.45, 11.00, 11.15, 11.30, 11.45,
> 12.00,
> 12.15, 12.30, 12.45, 13.00, 13.15, 13.30, 13.45, 14.00, 14.15,
> 14.30, 14.45,
> 15.00, 15.15, 15.30, 15.45, 16.00, 16.15, 16.30, 16.45, 17.00,
> 17.15, 17.30,
> 17.45, 18.00, 18.15, 18.30, 18.45, 19.00, 19.15, 19.30, 19.45,
> 20.00, 20.15,
> 20.30, 20.45, 21.00, 21.15, 21.30, 21.45, 22.00, 22.15, 22.30,
> 22.45, 23.00,
> 23.15, 23.30, 23.45)
> watt <- c(
> 94.1, 70.8, 68.2, 65.9, 63.3, 59.5, 55, 50.5, 46.6, 43.9, 42.3,
> 41.4, 40.8,
> 40.3, 39.9, 39.5, 39.1, 38.8, 38.5, 38.3, 38.3, 38.5, 39.1, 40.3,
> 42.4, 45.6,
> 49.9, 55.3, 61.6, 68.9, 77.1, 86.1, 95.7, 105.8, 115.8, 124.9,
> 132.3, 137.6,
> 141.1, 143.3, 144.8, 146, 147.2, 148.4, 149.8, 151.5, 153.5, 156,
> 159, 162.4,
> 165.8, 168.4, 169.8, 169.4, 167.6, 164.8, 161.5, 158.1, 154.9,
> 151.8, 149,
> 146.5, 144.4, 142.7, 141.5, 140.9, 141.7, 144.9, 151.5, 161.9,
> 174.6, 187.4,
> 198.1, 205.2, 209.1, 211.1, 212.2, 213.2, 213, 210.4, 203.9, 192.9,
> 179,
> 164.4, 151.5, 141.9, 135.3, 131, 128.2, 126.1, 124.1, 121.6, 118.2,
> 113.4,
> 107.4, 100.8)
>
>> df<-data.frame(time,  watt)
>> lmfit <- lm(time ~ watt + cos(time) + sin(time),  data = df)
>
> Your regression formula does not make sense to me.
> You seem to expect a periodic function within 24 hours, and if not
> it would
> still be possible to subtract the trend and then look at a periodic
> solution.
> Applying a trigonometric regression results in the following
> approximations:
>
>    library(pracma)
>    plot(2*pi*time/24, watt, col="red")
>    ts  <- seq(0, 2*pi, len = 100)
>    xs6 <- trigApprox(ts, watt, 6)
>    xs8 <- trigApprox(ts, watt, 8)
>    lines(ts, xs6, col="blue", lwd=2)
>    lines(ts, xs8, col="green", lwd=2)
>    grid()
>
> where as examples the trigonometric fits of degree 6 and 8 are used.
> I would not advise to use higher orders, even if the fit is not
> perfect.

Thank you ! That is a real gem of a worked example. Not only did it
introduce me to a useful package I was not familiar with, but there
was even a worked example in one of the help pages that might have
specifically answered the question about getting a 2nd(?) order trig
regression. If I understood the commentary on that page, this method
might also be appropriate for an irregular time series, whereas
trigApprox and trigPoly would not?

This is adapted from the trigPoly help page in Hans Werner's pracma
package:

A <- cbind(1, cos(pi*time/24), sin(pi*time/24), cos(2*pi*time/24),
sin(2*pi*time/24))
ab <- qr.solve(A, watt)
ab
# [1] 127.29131 -26.88824 -10.06134 -36.22793 -38.56219
ts <- seq(0, pi, length.out = 100)
xs <- ab[1] + ab[2]*cos(ts) +
ab[3]*sin(ts) + ab[4]*cos(2*ts) +ab[5]*sin(2*ts)
plot(pi*time/24, watt, col = "red", xlim=c(0, pi), ylim=range(watt),
main = "Trigonometric Regression")
lines(ts, xs, col="blue")

Hans:  I corrected the spelling of "Trigonometric", but other than
that I may well have introduced other errors for which I would be
happy to be corrected. For instance, I'm unsure of the terminology
regarding the ordinality of this model. I'm also not sure if my pi/24
and 2*pi/24 factors were correct in normalizing the time scale,
although the prediction seemed sensible.

>
> Hans Werner
>
>> Thanks a lot,
>> Marianne

--
David Winsemius, MD
West Hartford, CT

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