DynamicFactorModeling.jl (Incomplete)

Currently not open to contributions!

Overview

This is Julia package allows the user to easily construct, simulate, and estimate linear multi-level/hierarchical dynamic factor models (HDFMs) using a variety of Bayesian approaches. A wonderful explanation of HDFMs is provided in [5]. For an example, check out [4].

The following three HDFM estimation approaches are offered:

1. Principal component analysis (PCA) (overviewed in [1]);
2. Kim-Nelson (KM) state-space approach (introduced in [2] and [3]);
3. Otrok-Whiteman (OW) approach (introduced in [5] and [3]).

Installation

DynamicFactorModeling.jl is still in development and not available through the Julia registry. Thereofore, you may install and load the package using the GitHub repo url in the following manner:

using Pkg
Pkg.add(url = "https://github.com/gionikola/DynamicFactorModeling.jl")
using DynamicFactorModeling

Walkthrough

1. Specify HDFM

#
nlevels = 2

#
nvar = 9

#
nfactors = [1, 2]

#
fassign = [1 1
    1 1
    1 1
    1 1
    1 2
    1 2
    1 2
    1 2
    1 2]

#
flags = [2, 2]

#
varlags = [2, 2, 2, 2, 2, 2, 2, 2, 2]

#
varcoefs = [0.0 1.0 1.0
    0.0 0.5 0.2
    0.0 0.7 0.4
    0.0 0.3 0.5
    0.0 0.5 1.0
    0.0 0.5 0.7
    0.0 0.4 0.5
    0.0 0.5 0.2
    0.0 0.5 0.2]

#
varlagcoefs = [0.5 0.25
    0.5 0.25
    0.5 0.25
    0.5 0.25
    0.5 0.25
    0.5 0.25
    0.5 0.25
    0.5 0.25
    0.5 0.25]

#
fcoefs = Any[]
fmat = [0.85 -0.3][:, :]
push!(fcoefs, fmat)
fmat = [0.5 0.05
    0.2 -0.1]
push!(fcoefs, fmat)

#
fvars = Any[]
fmat = [1.0]
push!(fvars, fmat)
fmat = [1.0, 1.0]
push!(fvars, fmat)

#
varvars = 0.5 * ones(nvar);

#
hdfm = HDFM(nlevels = nlevels,
    nvar = nvar,
    nfactors = nfactors,
    fassign = fassign,
    flags = flags,
    varlags = varlags,
    varcoefs = varcoefs,
    varlagcoefs = varlagcoefs,
    fcoefs = fcoefs,
    fvars = fvars,
    varvars = varvars)

2. Simulate HDFM

#
ssmodel = convertHDFMtoSS(hdfm)

#
num_obs = 100
data_y, data_z, data_β = simulateSSModel(num_obs, ssmodel::SSModel)

3. Estimate HDFM

#
hdfmpriors = HDFMStruct(nlevels = nlevels,
    nfactors = nfactors,
    factorassign = fassign,
    factorlags = flags,
    errorlags = varlags,
    ndraws = 1000,
    burnin = 50)

#
results = PCA2LevelEstimator(data_y, hdfmpriors)

4. Variance decomposition

#
vardecomp = vardecomp2level(datamat, results.means.F, reshape(results.means.B, 3, 50)', fassign)

References

[1] Jackson, L.E., Kose, M.A., Otrok, C. and Owyang, M.T. (2016), "Specification and Estimation of Bayesian Dynamic Factor Models: A Monte Carlo Analysis with an Application to Global House Price Comovement", Dynamic Factor Models (Advances in Econometrics, Vol. 35), Emerald Group Publishing Limited, Bingley, pp. 361-400.

[2] Kim, Chang-Jin and Nelson, Charles, (1998), Business Cycle Turning Points, A New Coincident Index, And Tests Of Duration Dependence Based On A Dynamic Factor Model With Regime Switching, The Review of Economics and Statistics, 80, issue 2, p. 188-201.

[3] Kim, Chang-Jin and Nelson, Charles, (1999), State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications, vol. 1, 1 ed., The MIT Press.

[4] Kose, M. Ayhan, Christopher Otrok, and Charles H. Whiteman. 2003. "International Business Cycles: World, Region, and Country-Specific Factors." American Economic Review, 93 (4): 1216-1239.

[5] Moench, Emanuel, Serena Ng, Simon Potter. 2013. Dynamic Hierarchical Factor Models. The Review of Economics and Statistics, 95 (5): 1811–1817.

[6] Otrok, Christopher and Whiteman, Charles, (1998), Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa, International Economic Review, 39, issue 4, p. 997-1014.