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()`

.

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.

First load the package.

```
library(forecastHybrid)
```

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) forecast(quickModel) plot(forecast(quickModel), main = "Forecast from auto.arima, ets, thetam, nnetar, stlm, and tbats 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")

The 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$auto.arima # See forecasts from the auto.arima model plot(forecast(hm1$auto.arima))

The `hybridModel()`

function produces an S3 object of class `forecastHybrid`

.

class(hm1) is.hybridModel(hm1)

The `print()`

and `summary()`

methods print information about the ensemble model including the weights assigned to each individual component model.

print(hm1) summary(hm1)

Two 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) plot(quickModel, type = "models", ggplot = TRUE)

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") hm2

After 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$weights newWeights <- c(0.1, 0.2, 0.3, 0.1, 0.3) names(newWeights) <- c("auto.arima", "ets", "nnetar", "stlm", "tbats") hm2$weights <- newWeights hm2 hm2$weights[1] <- 0.2 hm2$weights[2] <- 0.1 hm2

This `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)) head(residuals(hm1))

In-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)
```

In 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)

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)
```

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))

Since 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) hm4$auto.arima$lambda hm4$ets$lambda

Users 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)) hm5$auto.arima$lambda hm5$ets$lambda hm5$nnetar$lambda hm5$stlm$lambda

Note 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 # Divice this into a train and test set trainSet <- beaver1[1:100, ] testSet <- beaver1[-(1:100), ] trainXreg <- matrix(trainSet$activ) testXreg <- matrix(testSet$activ) # Create the model beaverhm <- hybridModel(ts(trainSet$temp, f = 6), models = "aenst", a.args = list(xreg = trainXreg), n.args = list(xreg = trainXreg), s.args = list(xreg = trainXreg, method = "arima")) # Forecast future values beaverfc <- forecast(beaverhm, xreg = testXreg) # View the accuracy of the model accuracy(beaverfc, testSet$temp)

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) accuracy(naiveMod)

We 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)

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

```

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