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:

1. 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.

2. 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-sample MSE. 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.