ForecastingCombinations.jl
Forecasting using a parallel combinatoric approach.
Installation
Pkg.clone("https://github.com/lucabrugnolini/ForecastingCombinations.jl")
Documentation
The procedure is described in Brugnolini L. (2018). The application in the paper is on predicting the probability of having inflation around the European Central Bank's target.
Introduction
Given a (balanced) dataset of K macroeconomic variables, the objective is to select the best model to predict future values of a target variable. The selection procedure consists in (i) select the best iBest variables according to several out-of-sample criteria and then use these variables in models that use their combination. More specifically:
-
the procedure selects the best
iBest
variables using two different criteria (mean absolute error (MAE) and root mean squared error (RMSE) included in the model as a vector fLoss of functions in the form f(Prediction,TrueValue)). This selection step is univariate, i.e. the variables are chosen by running a simple out-of-sample regression of the target variable on each variable of the dataset. -
the
iBest
variables are combined into set of 2, 3, ..., iBest variables. For each of these sets, the model is estimated and then avaluated out-of-sample. The best model is the one with the lowest out-of-sampleMSE
. We also augment each model with the first principal component of all variable in the dataset. Thus, there are a total of 2 (2^iBest) models.
The complexity is O((T-Ts)*2^iBest) where T is the sample size, Ts is the number of observation in the initial estimation window.
Example
Forecasting US non-farm-payroll one and two months ahead H = [1,2]
using a dataset containing 116 US variables taken from McCracken and Ng (2015). iBest
is set to 16. The code below is an example of parallelization on N_CORE
.
addprocs(N_CORE)
@everywhere using ForecastingCombinations
@everywhere using CSV, DataFrames, GLM
@everywhere mae(vX::Vector,vY::Vector) = mean(abs.(vX-vY)) ## MAE loss function
@everywhere rmse(vX::Vector,vY::Array) = sqrt(mean((vX-vY).^2)) ## RMSE loss function
@everywhere const fLoss = [mae rmse] ## Vector of loss functions
@everywhere const sStart_s = "01/01/15" ## This is the beginning of the out-of-sample window
@everywhere const iSymbol = :NFP ## Target variable
@everywhere const vSymbol = [:Date, :NFP, :NFP_bb_median] ## Variables to be removed from the dataset (non-numerical and dep. var.)
@everywhere const H = [1,2] ## Out-of-sample horizon
@everywhere const iBest = 16 ## iBest
@everywhere const ncomb_load = iBest ## TODO: remove this option
@everywhere const dfData = CSV.read(joinpath(Pkg.dir("NFP"),"test","data.csv"), header = true)
@everywhere const iStart = find(dfData[:Date] .== sStart_s)[1]
## computes the two steps variable selection
l_plot,r = sforecast(dfData,vSymbol,iSymbol,H,iStart,iBest,ncomb_load,fLoss)
## `fforecast` uses results previously stored with `sforecast`
l_plot,r = fforecast(dfData,vSymbol,iSymbol,H,iStart,iBest,ncomb_load,fLoss)
# Plot the forecasts
l_plot
## Remove process added
rmprocs(2:N_CORE)
In case one is interested in predicting probabilities, as the US probability of recession, simply include a link function in sforecast
or fforecast
, and use a binary variable as dependent variable.
@everywhere const l = ProbitLink() # link function for probability model
## computes the two steps variable selection
l_plot,r = sforecast(dfData,vSymbol,iSymbol,H,iStart,iBest,ncomb_load,l,fLoss)
## `fforecast` uses results previously stored with `sforecast`
l_plot,r = fforecast(dfData,vSymbol,iSymbol,H,iStart,iBest,ncomb_load,l,fLoss)
References
Brugnolini L. (2018) "Forecasting Deflation Probability in the EA: A Combinatoric Approach." Central Bank of Malta Working Paper, 01/2018.
McCracken, Michael W., and Serena Ng.(2016) "FRED-MD: A Monthly Database for Macroeconomic Research." Journal of Business & Economic Statistics 34.4:574-589.