Time series with Holt-Winters method in R

Question

I'm trying to implement the Holt-Winters method in R. I have a time series whose data contains measurements over 24 hours of the day. I have a total of 5 years of data, that is, 43824 observations. I divided them into 43656 training and 168 tests. When I apply the method, I see that the values such as RMSE and MAPE are not bad, but when I plot them, it is seen that the real data and the predictions are not compatible. I'm sharing the codes: do you think I'm doing something wrong? Also, I can set the parameters of the Holt-Winters method with a for loop or something like a grid, but is there anything I can set in a shorter time?

data

date                hour                  tem
  <dttm>              <dttm>              <dbl> 
1 2018-01-01 00:00:00 1899-12-31 00:00:00  7.68 
2 2018-01-01 00:00:00 1899-12-31 01:00:00  7.30 
3 2018-01-01 00:00:00 1899-12-31 02:00:00  7.21 
4 2018-01-01 00:00:00 1899-12-31 03:00:00  7.53 
5 2018-01-01 00:00:00 1899-12-31 04:00:00  7.78 
6 2018-01-01 00:00:00 1899-12-31 05:00:00  7.93

ts

df2<-msts(r$tem, seasonal.periods=c(24,365.25*24))

componendf2_df2 <- decompose(df2)
plot(componendf2_df2)     

decompose

code

HW5 <- HoltWinters(train, alpha=0.07, beta=0.05011, gamma=0.008011,seasonal = "multiplicative")
 HW5_for <- forecast(HW5, h=168, level=0.95)
accuracy(HW5_for$mean,test )

output

     ME     RMSE       MAE       MPE     MAPE      ACF1 Theil's U

Test set 0.1607322 1.272415 0.8948736 0.7688493 28.02144 0.9874498  5.969364

graph

test%>% 
  autoplot() +
  autolayer(test, series = "actual")+
  autolayer(HW5_for$mean, series = "fit")

Answer 1

You rather obviously have multiple-seasonalities: intra-daily, intra-weekly and intra-yearly (the latter is clearly visible in your first plot panel). Straight-up Holt-Winters can't deal with that, it can only model a single seasonality. And it will not do a good job if you try to model the yearly seasonality with it, if that is even technically possible, because it would try to initialize about $365\times 24 = 8760$ initial states and then update them over just five years. You could model the intra-daily seasonality using Holt-Winters - but that would completely lose the intra-yearly seasonality, which appears to be dominant based on your first plot.

So I would definitely recommend you move away from Holt-Winters here. Our tag wiki contains pointers to alternative methods. You already defined your time series as an msts type, which makes sense, so now you could just feed it to forecast::tbats(). Note, though, that this can take a long time. It may be quite competitive in terms of accuracy and much faster to model this using multiple regression, using one set of harmonics with cycles of 24/12/8 hours (do not use dummies), another set with 168/84/56 hours, another set with cycles of 8760/4380/2920 hours, and potentially interactions. I have also had good results, in terms of both runtime and accuracy, using the MSTL function as implemented in the forecast package.

That said, even these methods will only be able to achieve a certain accuracy. There is a limit to forecastability.

Finally, your series have quite high residual coefficients of variation. You may want to reconsider the MAPE as an accuracy measure in this case.