DistributionalForecasts.jl

The code has been developed in Julia 0.6.4. version, as a code accompanying the Anatolyev and Barunik (2019) paper, and provides an estimation and inference for a model forecasting conditional probability distributions of asset returns (henceforth AB model). For further details, see

Anatolyev, S. and Baruník, J., (2019): Forecasting dynamic return distributions based on ordered binary choice, International Journal of Forecasting, 35(3), pp.823-835. DOI, manuscript available here for download (Jan 2019)

Software requirements

Julia together with few packages needs to be installed

Pkg.add("DataFrames")
Pkg.add("CSV")
Pkg.add("GLM")
Pkg.add("Optim")

Example: Forecasting dynamic return distributions

Note the full example is available as an interactive IJulia notebook here

Load required packages

using DataFrames, CSV, GLM, Optim 

# load main functions
include("DistributionalForecasts.jl");

Load example data (returns of XOM)

data = CSV.read("data_30stocks_returns.txt");
tdim, rdim = size(data)

Choose number of cutoff levels and order of polynomials

# no. of quantiles
js = 37;

# choice of polynomial order
p1=2;
p2=3;

Parameter Estimation

Obtain fast parameter estimates of AB without inference. A vector of $js+p1+p2+2$ parameters is returned:

$$\delta_{0,1},\delta_{0,2},...,\delta_{0,js},\kappa_{0,1},...\kappa_{p1+1,1},\kappa_{0,2},...\kappa_{p2+1,2}$$

par=OrderedLogitparameters(data[:,30].*1.0,js,p1,p2)
par'

1×44 RowVector{Float64,Array{Float64,1}}:
 -2.87124  -2.48832  -2.2352  -2.0323  …  -17.5198  -16.8475  25.976

Inference

Estimate the AB model and obtain full inference and evaluation of fit

est=OrderedLogit(data[:,30].*1.0, js,p1,p2);

Estimates of intercepts $\delta_{0,1},\delta_{0,2},...,\delta_{0,js}$

est[1][1:js]'

1×37 RowVector{Float64,Array{Float64,1}}:
 -2.87124  -2.48832  -2.2352  -2.0323  …  2.10511  2.47381  2.57944  3.04193

Estimates of $\kappa_{0,1},...\kappa_{p1+1,1},\kappa_{0,2},...\kappa_{p2+1,2}$

est[1][(js+1):(js+p1+p2+2)]'

1×7 RowVector{Float64,Array{Float64,1}}:
 -0.0528382  -0.116755  0.0523652  0.108634  -17.5198  -16.8475  25.976

standard errors for all coefficients

est[2]'

1×44 RowVector{Float64,Array{Float64,1}}:
 0.117504  0.101611  0.0915005  …  8.10445  5.70739  7.8312  9.23371

T-stats

est[3]'

1×44 RowVector{Float64,Array{Float64,1}}:
 -24.4352  -24.4886  -24.4283  -23.1584  …  -3.06967  -2.15133  2.81317

Log Likelihood

est[4]

10285.797921780777

Information criteria (AIC/BIC)

est[5:6]

2-element Array{Any,1}:
 -20482.2
 -20222.0

Recover Probabilities Predicted by the AB model

Obtain forecast of return distribution for time $t+1$ based on the in-sample window

window=500
INS=data[1:window,30].*1
OOS=data[window:(window+1),30].*1

probs=forecastProbs(INS,OOS,js,p1,p2)

1×37 Array{Float64,2}:
 0.0670917  0.0868857  0.108024  0.124577  …  0.928052  0.928632  0.951298

Statistical Evaluation

A number of statistical tests from Gneiting and Raftery (2007), and Gonzalez-Rivera and Sun (2015) are implemented in the DistributionalForecasts.jl file.

TBD

Gonzalez-Rivera, G. and Y. Sun (2015). Generalized autocontours: Evaluation of multivari- ate density models. International Journal of Forecasting 31(3), 799–814.

Gneiting, T. and A. Raftery (2007). Strictly proper scoring rules, prediction, and estimation. Journal of American Statistical Association 102 (477), 359–378.