Using the "forecastHybrid" package
David Shaub
2020-08-27
The "forecastHybrid" package provides functions to build composite models using multiple individual component models from the "forecast" package. These hybridModel objects can then be manipulated with many of the familiar functions from the "forecast" and "stats" packages including forecast(), plot(), accuracy(), residuals(), and fitted().
Installation
The stable release of the package is hosted on CRAN and can be installed as usual.
install.packages("forecastHybrid")The latest development version can be installed using the "devtools" package.
devtools::install_github("ellisp/forecastHybrid/pkg")Version updates to CRAN will be published frequently after new features are implemented, so the development version is not recommended unless you plan to modify the code.
Basic usage
First load the package.
library(forecastHybrid)Quick start
If you don't have time to read the whole guide and want to get started immediately with sane default settings to forecast the USAccDeaths timeseries, run the following:
quickModel <- hybridModel(USAccDeaths)## Fitting the auto.arima model## Fitting the ets model## Fitting the thetam model## Fitting the nnetar model## Fitting the stlm model## Fitting the tbats modelforecast(quickModel)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1979 8354.580 7924.712 8968.899 7706.957 9272.235
## Feb 1979 7543.318 6864.957 8184.977 6542.338 8468.428
## Mar 1979 8241.755 7223.731 8886.679 6888.559 9146.115
## Apr 1979 8531.595 7606.103 9194.629 7249.674 9500.477
## May 1979 9336.334 8105.778 10112.349 7734.506 10442.376
## Jun 1979 9776.752 8519.977 10525.745 8226.434 10878.297
## Jul 1979 10683.548 9158.635 11613.448 8784.188 11987.171
## Aug 1979 9986.536 8979.890 10830.331 8697.308 11224.086
## Sep 1979 9001.395 8281.314 9944.791 7892.801 10357.609
## Oct 1979 9256.502 8309.414 10198.510 8056.898 10629.548
## Nov 1979 8781.928 8033.333 9732.246 7589.183 10180.765
## Dec 1979 9112.847 8255.912 10255.628 7816.759 10720.971
## Jan 1980 8382.947 7485.300 9496.297 7033.420 10011.749
## Feb 1980 7600.342 6687.306 8749.398 6141.503 9295.201
## Mar 1980 8249.630 7033.489 9586.522 6637.427 10161.075
## Apr 1980 8542.046 7338.446 9940.466 7010.225 10542.396
## May 1980 9333.203 7749.995 10861.976 7355.042 11490.092
## Jun 1980 9762.515 8118.797 11280.306 7714.097 11933.559
## Jul 1980 10654.632 8600.469 12373.743 8150.610 13051.201
## Aug 1980 9963.104 8598.231 11596.927 8248.308 12297.755
## Sep 1980 8988.101 7949.455 10718.099 7261.423 11441.542
## Oct 1980 9250.330 8063.717 10978.824 7417.369 11724.196
## Nov 1980 8788.215 7623.215 10519.779 6856.540 11286.453
## Dec 1980 9106.311 7938.375 11050.531 7288.262 11837.932plot(forecast(quickModel), main = "Forecast from auto.arima, ets, thetam, nnetar, stlm, and tbats model")
Fitting a model
The workhorse function of the package is hybridModel(), a function that combines several component models from the "forecast" package. At a minimum, the user must supply a ts or numeric vector for y. In this case, the ensemble will include all six component models: auto.arima(), ets(), thetam(), nnetar(), stlm(), and tbats(). To instead use only a subset of these models, pass a character string to the models argument with the first letter of each model to include. For example, to build an ensemble model on a simulated dataset with auto.arima(), ets(), and tbats() components, run
# Build a hybrid forecast on a simulated dataset using auto.arima, ets, and tbats models.
# Each model is given equal weight
set.seed(12345)
series <- ts(rnorm(18), f = 2)
hm1 <- hybridModel(y = series, models = "aet", weights = "equal")## Fitting the auto.arima model## Fitting the ets model## Fitting the tbats modelThe individual component models are stored inside the hybridModel objects and can viewed in their respective slots, and all the regular methods from the "forecast" package could be applied to these individual component models.
# View the individual models
hm1$auto.arima## Series: y
## ARIMA(0,0,0) with zero mean
##
## sigma^2 estimated as 0.6659: log likelihood=-21.88
## AIC=45.76 AICc=46.01 BIC=46.65# See forecasts from the auto.arima model
plot(forecast(hm1$auto.arima))
Model diagnostics
The hybridModel() function produces an S3 object of class forecastHybrid.
class(hm1) ## [1] "hybridModel"is.hybridModel(hm1)## [1] TRUEThe print() and summary() methods print information about the ensemble model including the weights assigned to each individual component model.
print(hm1) ## Hybrid forecast model comprised of the following models: auto.arima, ets, tbats
## ############
## auto.arima with weight 0.333
## ############
## ets with weight 0.333
## ############
## tbats with weight 0.333summary(hm1)## Length Class Mode
## auto.arima 18 forecast_ARIMA list
## ets 19 ets list
## tbats 21 bats list
## weights 3 -none- numeric
## frequency 1 -none- numeric
## x 18 ts numeric
## xreg 1 -none- list
## models 3 -none- character
## fitted 18 -none- numeric
## residuals 18 ts numericTwo types of plots can be created for the created ensemble model: either a plot showing the actual and fitted value of each component model on the data or individual plots of the component models as created by their regular S3 plot() methods. Note that a plot() method does not exist in the "forecast" package for objects generated with stlm(), so this component model will be ignored when type = "models", but the other component models will be plotted regardless.
plot(quickModel, type = "fit")
plot(quickModel, type = "models")
Since version 0.4.0, ggplot graphs are available. Note, however, that the nnetar, and tbats models do not have ggplot::autoplot() methods, so these are not plotted.
plot(quickModel, type = "fit", ggplot = TRUE)## Warning: Removed 12 row(s) containing missing values (geom_path).
plot(quickModel, type = "models", ggplot = TRUE)## Warning in is.na(xlab): is.na() applied to non-(list or vector) of type 'NULL'## Warning in is.na(xlab): is.na() applied to non-(list or vector) of type 'NULL'By default each component model is given equal weight in the final ensemble. Empirically this has been shown to give good performance in ensembles [see @Armstrong2001], but alternative combination methods are available: the inverse root mean square error (RMSE), inverse mean absolute error (MAE), and inverse mean absolute scaled error (MASE). To apply one of these weighting schemes of the component models, pass this value to the errorMethod argument and pass either "insample.errors" or "cv.errors" to the weights argument.
hm2 <- hybridModel(series, weights = "insample.errors", errorMethod = "MASE", models = "aenst")## Warning in hybridModel(series, weights = "insample.errors", errorMethod =
## "MASE", : Using insample.error weights is not recommended for accuracy and may
## be deprecated in the future.## Fitting the auto.arima model## Fitting the ets model## Fitting the nnetar model## Fitting the stlm model## Fitting the tbats modelhm2 ## Hybrid forecast model comprised of the following models: auto.arima, ets, nnetar, stlm, tbats
## ############
## auto.arima with weight 0.164
## ############
## ets with weight 0.164
## ############
## nnetar with weight 0.306
## ############
## stlm with weight 0.173
## ############
## tbats with weight 0.194After the model is fit, these weights are stored in the weights attribute of the model. The user can view and manipulated these weights after the fit is complete. Note that the hybridModel() function automatically scales weights to sum to one, so a user should similar scale the weights to ensure the forecasts remain unbiased. Furthermore, the vector that replaces weights must retain names specifying the component model it corresponds to since weights are not assigned by position but rather by component name. Similarly, individual components may also be replaced
hm2$weights ## auto.arima ets nnetar stlm tbats
## 0.1637556 0.1635812 0.3058342 0.1732488 0.1935802newWeights <- c(0.1, 0.2, 0.3, 0.1, 0.3)
names(newWeights) <- c("auto.arima", "ets", "nnetar", "stlm", "tbats")
hm2$weights <- newWeights
hm2## Hybrid forecast model comprised of the following models: auto.arima, ets, nnetar, stlm, tbats
## ############
## auto.arima with weight 0.1
## ############
## ets with weight 0.2
## ############
## nnetar with weight 0.3
## ############
## stlm with weight 0.1
## ############
## tbats with weight 0.3hm2$weights[1] <- 0.2
hm2$weights[2] <- 0.1
hm2## Hybrid forecast model comprised of the following models: auto.arima, ets, nnetar, stlm, tbats
## ############
## auto.arima with weight 0.2
## ############
## ets with weight 0.1
## ############
## nnetar with weight 0.3
## ############
## stlm with weight 0.1
## ############
## tbats with weight 0.3This hybridModel S3 object can be manipulated with the same familiar interface from the "forecast" package, including S3 generic functions such as accuracy, forecast, fitted, and residuals.
# View the first 10 fitted values and residuals
head(fitted(hm1))## [1] 0.012621269 0.010804126 0.008561907 0.008984650 0.010541407 0.008636514head(residuals(hm1))## Time Series:
## Start = c(1, 1)
## End = c(3, 2)
## Frequency = 2
## [1] 0.5729075 0.6986619 -0.1178652 -0.4624818 0.5953460 -1.8265925In-sample errors and various accuracy measure can be extracted with the accuracy method. The "forecastHybrid" package creates an S3 generic from the accuracy method in the "forecast" package, so accuracy will continue to function as normal with objects from the "forecast" package, but now special functionality is created for hybridModel objects. To view the in-sample accuracy for the entire ensemble, a simple call can be made.
accuracy(hm1) ## ME RMSE MAE MPE MAPE ACF1
## Test set -0.006167957 0.8146777 0.6675259 101.5092 101.5092 -0.2202369
## Theil's U
## Test set 0.9281098In addition to retrieving the ensemble's accuracy, the individual component models' accuracies can be easily viewed by using the individual = TRUE argument.
accuracy(hm1, individual = TRUE) ## $auto.arima
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.006161102 0.8159991 0.6667319 100 100 0.7381739 -0.2202409
##
## $ets
## ME RMSE MAE MPE MAPE MASE
## Training set -6.878921e-05 0.8160167 0.6674428 100.7412 100.7412 0.7389609
## ACF1
## Training set -0.2202415
##
## $tbats
## ME RMSE MAE MPE MAPE MASE
## Training set -0.02459618 0.812366 0.6684029 103.7863 103.7863 0.6244447
## ACF1
## Training set -0.2201724Forecasting
Now's let's forecast future values. The forecast() function produce an S3 class forecast object for the next 48 periods from the ensemble model.
hForecast <- forecast(hm1, h = 48) Now plot the forecast for the next 48 periods. The prediction intervals are preserved from the individual component models and currently use the most extreme value from an individual model, producing a conservative estimate for the ensemble's performance.
plot(hForecast) 
Advanced usage
The package aims to make fitting ensembles easy and quick, but it still allows advanced tuning of all the parameters available in the "forecast" package. This is possible through usage of the a.args, e.args, n.args, s.args, and t.args lists. These optional list arguments may be applied to one, none, all, or any combination of the included individual component models. Consult the documentation in the "forecast" package for acceptable arguments to pass in the auto.arima, ets, nnetar, stlm, and tbats functions.
hm3 <- hybridModel(y = series, models = "aefnst",
a.args = list(max.p = 12, max.q = 12, approximation = FALSE),
n.args = list(repeats = 50),
s.args = list(robust = TRUE),
t.args = list(use.arma.errors = FALSE)) ## Fitting the auto.arima model## Fitting the ets model## Fitting the thetam model## Fitting the nnetar model## Fitting the stlm model## Fitting the tbats modelSince the lambda argument is shared between most of the models in the "forecast" framework, it is included as a special parameter that can be used to set the Box-Cox transform in all models instead of settings this individually. For example,
hm4 <- hybridModel(y = wineind, models = "ae", lambda = 0.15)## Fitting the auto.arima model## Fitting the ets modelhm4$auto.arima$lambda ## [1] 0.15
## attr(,"biasadj")
## [1] FALSEhm4$ets$lambda## [1] 0.15
## attr(,"biasadj")
## [1] FALSEUsers can still apply the lambda argument through the tuning lists, but in this case the list-supplied argument overwrites the default used across all models. Compare the following two results.
hm5 <- hybridModel(y = USAccDeaths, models = "aens", lambda = 0.2,
a.args = list(lambda = 0.5),
n.args = list(lambda = 0.6)) ## Fitting the auto.arima model## Fitting the ets model## Fitting the nnetar model## Fitting the stlm modelhm5$auto.arima$lambda## [1] 0.5
## attr(,"biasadj")
## [1] FALSEhm5$ets$lambda## [1] 0.2
## attr(,"biasadj")
## [1] FALSEhm5$nnetar$lambda## [1] 0.6hm5$stlm$lambda## [1] 0.2
## attr(,"biasadj")
## [1] FALSENote that lambda has no impact on thetam models, and that there is no f.args argument to provide parameters to thetam. Following forecast::thetaf on which thetam is based, there are no such arguments; it always runs with the defaults.
Covariates can also be supplied to auto.arima and nnetar models as is done in the "forecast" package. To do this, utilize the a.args and n.args lists. Note that the xreg may also be passed to a stlm model, but only when method = "arima" instead of the default method = "ets". Unlike the usage in the "forecast" package, the xreg argument should be passed as a matrix, not a dataframe. The stlm models require that the input series will be seasonal, so in the example below we will convert the input data to a ts object. If a xreg is used in training, it must also be supplied to the forecast() function in the xreg argument. Note that if the number of rows in the xreg to be used for the forecast does not match the supplied h forecast horizon, the function will overwrite h with the number of rows in xreg and issue a warning.
# Use the beaver1 dataset with the variable "activ" as a covariate and "temp" as the time series
# Divide this into a train and test set
trainSet <- beaver1[1:100, ]
testSet <- beaver1[101:110, ]
trainXreg <- matrix(trainSet$activ)
testXreg <- matrix(testSet$activ)
# Create the model
beaverhm <- hybridModel(ts(trainSet$temp, f = 6),
models = "aenst",
a.args = list(xreg = trainXreg),
n.args = list(xreg = trainXreg),
s.args = list(xreg = trainXreg, method = "arima"))## Fitting the auto.arima model## Fitting the ets model## Fitting the nnetar model## Fitting the stlm model## Fitting the tbats model# Forecast future values
beaverfc <- forecast(beaverhm, xreg = testXreg, PI=FALSE)
# View the accuracy of the model
accuracy(beaverfc, testSet$temp)## ME RMSE MAE MPE MAPE MASE
## Training set 0.0008460645 0.08323059 0.05587866 0.001903305 0.1513580 0.8471650
## Test set 0.0366499469 0.06776142 0.05258665 0.099283334 0.1426878 0.7972555
## ACF1
## Training set -0.01249166
## Test set NACross Validation
It can be useful to perform cross validation on a forecasting model to estimate a model's out-of-sample forecasting performance. The cvts() function allows us to do this on arbitrary functions. We could do this as part of a model selection procedure to determine which models to include in our call to hybridModel() or merely to understand how well we expect to forecast the series during unobserved windows.
For example, let's perform cross validation for a stlm() model and a naive() model on the woolyrnq time series. The most important cvts() arguments that commonly need adjusting are rolling (if TRUE, the model will always be fit on a fixed windowSize instead of growing by one new observation for each new model fit during cross validation), windowSize (starting length of time series to fit a model), and maxHorizon (the forecast horizon for predictions from each model). Since a naive forecast is a good baseline that any decent model should surpass, let's see how the stlm() model compares.
stlmMod <- cvts(woolyrnq, FUN = stlm, windowSize = 100, maxHorizon = 8)
naiveMod <- cvts(woolyrnq, FUN = naive, windowSize = 100, maxHorizon = 8)
accuracy(stlmMod)## ME RMSE MAE
## Forecast Horizon 1 143.26726 276.46300 236.44509
## Forecast Horizon 2 -185.31041 305.09020 242.36353
## Forecast Horizon 3 -269.48582 284.78038 269.48582
## Forecast Horizon 4 -82.66850 121.21761 88.65454
## Forecast Horizon 5 -128.73274 128.89398 128.73274
## Forecast Horizon 6 -66.81041 250.92150 241.86353
## Forecast Horizon 7 -44.48582 58.45955 44.48582
## Forecast Horizon 8 -62.66850 143.10601 128.65454accuracy(naiveMod)## ME RMSE MAE
## Forecast Horizon 1 -768.5 802.0365 768.5
## Forecast Horizon 2 -229.0 324.5628 230.0
## Forecast Horizon 3 142.5 184.0611 142.5
## Forecast Horizon 4 -88.0 124.4508 88.0
## Forecast Horizon 5 -1040.5 1040.5001 1040.5
## Forecast Horizon 6 -110.5 254.7165 229.5
## Forecast Horizon 7 367.5 367.7479 367.5
## Forecast Horizon 8 -68.0 144.9414 128.0We see from looking at the accuracy measure--in particular the smaller RMSE and MAE--the stlm() model unsurprisingly performs better and will likely give us better future forecasts. We also notice that the apparent edge over the naive forecast tends to diminish or even disappear for longer forecast horizons, and a look at the original time series makes this result obvious: this time series lacks an obvious trend and is a relatively difficult time series to forecast past a fewer seasonal periods, so the naive model will not perform relatively poorly.
plot(woolyrnq)
We can also use custom functions, for example fcast() from the "GMDH" package. We must be very careful that our custom forecast function still produces an expected "forecast" S3 class object and that the ts object start, end, and frequency properties are preserved.
library(GMDH)
GMDHForecast <- function(x, h){
fc <- GMDH::fcast(x, f.number = h)
# GMDH doesn't produce a ts object with correct attributes, so we build it
end <- tsp(x)[2]
freq <- frequency(x)
# Set the correct start, end, and frequency for the ts forecast object
tsProperties <- c(end + 1 / freq, end + h / freq, freq)
tsp(fc$mean) <- tsProperties
tsp(fc$upper) <- tsProperties
tsp(fc$lower) <- tsProperties
class(fc) <- "forecast"
return(fc)
}
series <- subset(woolyrnq, end = 12)
gmdhcv <- cvts(series, FCFUN = GMDHForecast, windowSize = 10, maxHorizon = 1)As a final example, suppose we foolish want to implement our own version of naive() for performing cross validation. The FUN and FCFUN could then look like
customMod <- function(x){
result <- list()
result$series <- x
result$last <- tail(x, n = 1)
class(result) <- "customMod"
return(result)
}
forecast.customMod <- function(x, h = 12){
result <- list()
result$model <- x
result$mean <- rep(x$last, h)
class(result) <- "forecast"
return(result)
}
series <- subset(AirPassengers, end = 94)
cvobj <- cvts(series, FUN = customMod, FCFUN = forecast.customMod)Cross Validation Weights
Previously we explored fitting hybridModel() objects with weights = "equal" or weights = "insample.errors, but we can now leverage the process conducted in cvts() to select the appropriate weights intelligently based on the expected out-of-sample forecast accuracy of each component model. While this is the methodologically-sound weight procedure, it also comes at significant computational cost since the cross validation procedure necessitates fitting each model several times for each cross validation fold in addition to the final fit on the whole dataset. Fortunately this process can be conducted in parallel if multiple cores are available. Some of the arguments explained above in cvts() such as windowSize and the cvHorizon can also be controlled here.
cvMod <- hybridModel(woolyrnq, models = "ns",
weights = "cv.errors", windowSize = 100,
cvHorizon = 8, num.cores = 4)
cvMod