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)

Julia together with few packages needs to be installed

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

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;

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

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

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

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.