Using the “forecastHybrid” package
David Shaub
2016-06-04
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 immediatly with sane default settings to forecast the AirPassengers timeseries, run the following:
quickModel <- hybridModel(AirPassengers)
forecast(quickModel)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1961 449.2345 420.9284 474.4528 409.9071 486.2105
## Feb 1961 430.6313 402.5180 463.4376 392.8622 477.7219
## Mar 1961 476.7830 427.8241 541.2952 416.7423 560.7848
## Apr 1961 489.7697 445.6985 533.1953 425.6737 554.8180
## May 1961 499.5002 443.0128 546.2434 420.7317 570.5889
## Jun 1961 565.0479 498.8558 624.6220 471.1949 654.7751
## Jul 1961 642.0951 550.5136 710.4620 517.2336 747.2133
## Aug 1961 634.3779 543.3613 713.0508 507.8542 752.2024
## Sep 1961 544.6736 468.8133 632.2052 435.9204 668.8588
## Oct 1961 487.0592 405.1625 557.1301 374.8081 591.0168
## Nov 1961 424.2973 349.4447 494.6448 321.6167 526.0871
## Dec 1961 467.7083 388.8923 560.4230 356.0996 597.5240
## Jan 1962 485.2039 392.2920 586.0717 357.3798 626.2887
## Feb 1962 468.2825 381.4061 580.0403 345.6841 621.2372
## Mar 1962 516.9659 424.9010 673.9258 391.0899 723.3987
## Apr 1962 530.3586 418.8586 661.0549 375.7208 711.1125
## May 1962 540.9867 416.8132 674.9179 371.9359 727.5080
## Jun 1962 610.7640 469.7070 769.4987 416.9301 831.1089
## Jul 1962 691.3629 518.5862 873.0125 457.8729 944.7378
## Aug 1962 683.0417 511.9731 874.2538 449.6093 947.8275
## Sep 1962 588.7815 441.7638 773.5659 385.8483 840.2075
## Oct 1962 527.7480 381.7623 680.4912 331.6121 740.4049
## Nov 1962 461.9285 329.2070 603.1846 284.3727 657.4195
## Dec 1962 506.8868 366.2764 682.3729 314.6143 744.9800plot(forecast(quickModel))
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 of the component models: auto.arima(), ets(), 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 the gas dataset with auto.arima(), ets(), and tbats() components, run
# Build a hybrid forecast on the gas dataset using auto.arima, ets, and tbats models.
# Each model is given equal weight
hm1 <- hybridModel(y = gas, 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## Series: structure(c(1709, 1646, 1794, 1878, 2173, 2321, 2468, 2416, 2184, 2121, 1962, 1825, 1751, 1688, 1920, 1941, 2311, 2279, 2638, 2448, 2279, 2163, 1941, 1878, 1773, 1688, 1783, 1984, 2290, 2511, 2712, 2522, 2342, 2195, 1931, 1910, 1730, 1688, 1899, 1994, 2342, 2553, 2712, 2627, 2363, 2311, 2026, 1910, 1762, 1815, 2005, 2089, 2617, 2828, 2965, 2891, 2532, 2363, 2216, 2026, 1804, 1773, 2015, 2089, 2627, 2712, 3007, 2880, 2490, 2237, 2205, 1984, 1868, 1815, 2047, 2142, 2743, 2775, 3028, 2965, 2501, 2501, 2131, 2015, 1910, 1868, 2121, 2268, 2690, 2933, 3218, 3028, 2659, 2406, 2258, 2057, 1889, 1984, 2110, 2311, 2785, 3039, 3229, 3070, 2659, 2543, 2237, 2142, 1962, 1910, 2216, 2437, 2817, 3123, 3345, 3112, 2659, 2469, 2332, 2110, 1910, 1941, 2216, 2342, 2923, 3229, 3513, 3355, 2849, 2680, 2395, 2205, 1994, 1952, 2290, 2395, 2965, 3239, 3608, 3524, 3018, 2648, 2363, 2247, 1994, 1941, 2258, 2332, 3323, 3608, 3957, 3672, 3155, 2933, 2585, 2384, 2057, 2100, 2458, 2638, 3292, 3724, 4652, 4379, 4231, 3756, 3429, 3461, 3345, 4220, 4874, 5064, 5951, 6774, 7997, 7523, 7438, 6879, 6489, 6288, 5919, 6183, 6594, 6489, 8040, 9715, 9714, 9756, 8595, 7861, 7753, 8154, 7778, 7402, 8903, 9742, 11372, 12741, 13733, 13691, 12239, 12502, 11241, 10829, 11569, 10397, 12493, 11962, 13974, 14945, 16805, 16587, 14225, 14157, 13016, 12253, 11704, 12275, 13695, 14082, 16555, 17339, 17777, 17592, 16194, 15336, 14208, 13116, 12354, 12682, 14141, 14989, 16159, 18276, 19157, 18737, 17109, 17094, 15418, 14312, 13260, 14990, 15975, 16770, 19819, 20983, 22001, 22337, 20750, 19969, 17293, 16498, 15117, 16058, 18137, 18471, 21398, 23854, 26025, 25479, 22804, 19619, 19627, 18488, 17243, 18284, 20226, 20903, 23768, 26323, 28038, 26776, 22886, 22813, 22404, 19795, 18839, 18892, 20823, 22212, 25076, 26884, 30611, 30228, 26762, 25885, 23328, 21930, 21433, 22369, 24503, 25905, 30605, 34984, 37060, 34502, 31793, 29275, 28305, 25248, 27730, 27424, 32684, 31366, 37459, 41060, 43558, 42398, 33827, 34962, 33480, 32445, 30715, 30400, 31451, 31306, 40592, 44133, 47387, 41310, 37913, 34355, 34607, 28729, 26138, 30745, 35018, 34549, 40980, 42869, 45022, 40387, 38180, 38608, 35308, 30234, 28801, 33034, 35294, 33181, 40797, 42355, 46098, 42430, 41851, 39331, 37328, 34514, 32494, 33308, 36805, 34221, 41020, 44350, 46173, 44435, 40943, 39269, 35901, 32142, 31239, 32261, 34951, 38109, 43168, 45547, 49568, 45387, 41805, 41281, 36068, 34879, 32791, 34206, 39128, 40249, 43519, 46137, 56709, 52306, 49397, 45500, 39857, 37958, 35567, 37696, 42319, 39137, 47062, 50610, 54457, 54435, 48516, 43225, 42155, 39995, 37541, 37277, 41778, 41666, 49616, 57793, 61884, 62400, 50820, 51116, 45731, 42528, 40459, 40295, 44147, 42697, 52561, 56572, 56858, 58363, 45627, 45622, 41304, 36016, 35592, 35677, 39864, 41761, 50380, 49129, 55066, 55671, 49058, 44503, 42145, 38698, 38963, 38690, 39792, 42545, 50145, 58164, 59035, 59408, 55988, 47321, 42269, 39606, 37059, 37963, 31043, 41712, 50366, 56977, 56807, 54634, 51367, 48073, 46251, 43736, 39975, 40478, 46895, 46147, 55011, 57799, 62450, 63896, 57784, 53231, 50354, 38410, 41600, 41471, 46287, 49013, 56624, 61739, 66600, 60054), .Tsp = c(1956, 1995.58333333333, 12), class = "ts")
## ARIMA(2,1,1)(1,0,0)[12]
##
## Coefficients:
## ar1 ar2 ma1 sar1
## 0.5117 0.1824 -0.9638 0.8478
## s.e. 0.0502 0.0498 0.0134 0.0277
##
## sigma^2 estimated as 3201509: log likelihood=-4236.9
## AIC=8483.81 AICc=8483.94 BIC=8504.63# 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 0.3333333
## ############
## ets with weight 0.3333333
## ############
## tbats with weight 0.3333333summary(hm1)## Length Class Mode
## auto.arima 16 ARIMA list
## ets 18 ets list
## tbats 23 tbats list
## weights 3 -none- numeric
## frequency 1 -none- numeric
## x 476 ts numeric
## models 3 -none- character
## fitted 476 ts numeric
## residuals 476 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(hm1, type = "fit")
plot(hm1, type = "models")
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" (currently unimplemented) to the weights argument.
hm2 <- hybridModel(wineind, weights = "insample.errors", errorMethod = "MASE")
hm2## Hybrid forecast model comprised of the following models: auto.arima, ets, nnetar, stlm, tbats
## ############
## auto.arima with weight 0.06343296
## ############
## ets with weight 0.06591713
## ############
## nnetar with weight 0.6433027
## ############
## stlm with weight 0.08305598
## ############
## tbats with weight 0.1442912After 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, indiviudal components may also be replaced
hm2$weights## auto.arima ets nnetar stlm tbats
## 0.06343296 0.06591713 0.64330272 0.08305598 0.14429121newWeights <- c(0.1, 0.2, 0.3, 0.1, 0.3)
names(newWeights) <- c("auto.arima", "ets", "nnetar", "stlm", "tbats")
hm2$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] 1885.009 1782.309 1826.064 1853.645 2148.805 2305.098head(residuals(hm1))## [1] 1885.009 1782.309 1826.064 1853.645 2148.805 2305.098In-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 74.07929 1445.469 785.3591 0.4536887 3.476193 -0.1110871
## Theil's U
## Test set 0.4776571Rather that 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
## Training set 151.1913 1779.854 1005.769 0.8861332 4.446548 0.5391395
## ACF1
## Training set -0.002784589
##
## $ets
## ME RMSE MAE MPE MAPE MASE
## Training set 41.67757 1451.139 788.3641 0.2856501 3.54687 0.4226001
## ACF1
## Training set -0.1370769
##
## $tbats
## ME RMSE MAE MPE MAPE MASE
## Training set 29.36895 1468.979 799.4452 0.1892828 3.600394 0.4629775
## ACF1
## Training set -0.1295208Forecasting
Now’s let’s forecast future values. The forecast() function produce an S3 class forecast object for the next 48 periods from the ensemble model.
hForecast <- forecast(hm1, h = 48)Now plot the forecast for the next 48 periods. The prediction intervals are preserved from the individual component models and currently use the most extreme value from an individual model, producing a conservative estimate for the ensemble’s performance.
plot(hForecast)
Advanced usage
The package aims to make fitting ensembles easy and quick, but it still allows advanced tuning of all the parameters available in the “forecast” package. This is possible through usage of the a.args, e.args, n.args, s.args, and t.args lists. These optional list arguments may be applied to one, none, all, or any combination of the included individual component models. Consult the documentation in the “forecast” package for acceptable arguments to pass in the auto.arima, ets, nnetar, stlm, and tbats functions.
hm2 <- hybridModel(y = gas, models = "aenst",
a.args = list(max.p = 12, max.q = 12, approximation = FALSE),
n.args = list(repeats = 50),
s.args = list(robust = TRUE),
t.args = list(use.arma.errors = FALSE))Since the lambda argument is shared between all the models in the “forecast” framework, it is included as a special paramemeter that can be used to set the Box-Cox transform in all models instead of settings this individually. For example,
hm3 <- hybridModel(y = wineind, models = "ae", lambda = 0.15)
hm3$auto.arima$lambda## [1] 0.15hm3$ets$lambda## [1] 0.15Users can still apply the lambda argument through the tuning lists, but in this case the list-supplied argument overwrites the default used across all models. Compare the following two results.
hm4 <- hybridModel(y = wineind, models = "aens", lambda = 0.2,
a.args = list(lambda = 0.5),
n.args = list(lambda = 0.6))
hm4$auto.arima$lambda## [1] 0.5hm4$ets$lambda## [1] 0.2hm4$nnetar$lambda## [1] 0.6hm4$stlm$lambda## [1] 0.2Covariates can also be supplied to auto.arima and nnetar models as is done in the “forecast” package. To do this, utilize the a.args and n.args lists. Unlike the usage in the “forecast” package, the xreg argument should be passed as a dataframe, not a matrix. If a xreg is used in training, it must also be supplied to the forecast() fucntion in the xreg argument. Note that if the number of rows in the xreg to be used for the forecast does not match the supplied h forecast horizon, the function will overwrite h with the number of rows in xreg and issue a warning.
# Use the beaver1 dataset with the variable "activ" as a covariate and "temp" as the timeseries
# Divice this into a train and test set
trainSet <- beaver1[1:100, ]
testSet <- beaver1[-(1:100), ]
trainXreg <- data.frame(trainSet$activ)
testXreg <- data.frame(testSet$activ)
# Create the model
beaverhm <- hybridModel(trainSet$temp,
models = "aent",
a.args = list(xreg = trainXreg),
n.args = list(xreg = trainXreg))
# Forecast future values
beaverfc <- forecast(beaverhm, xreg = testXreg)## Warning in forecast.hybridModel(beaverhm, xreg = testXreg): The number of
## rows in xreg should match h. Setting h to nrow(xreg).# View the accuracy of the model
accuracy(beaverfc, testSet$temp)## ME RMSE MAE MPE MAPE
## Training set 0.003383503 0.08734354 0.05924452 0.008866405 0.1605821
## Test set 0.076655153 0.10618603 0.08527091 0.207386207 0.2308624
## MASE ACF1
## Training set 0.8981941 0.01770916
## Test set 1.2927748 NA