Dynamic Sparsity Modelling

Transcription

1 Dynamic Sparsity Modelling Mike West Duke University Workshop on Multivariate Bayesian Time Series February 29 th 2016

2 Multivariate time series - eg: Global financial networks Models ~ Statistical networks Dynamics Volatility Structure Sparsity

3 Today Dynamic latent thresholding in time-varying parameter statistical models - impact on model/ network structure elucidation - impact on predictions & decisions

4 Sparsity modelling to date: Globally sparse models Sparse parameters and parameter processes & precision/volatility Bayesian variable selection methods Sparsity/data-informed parsimony - key as dimension increases - noise control, robust inferences - improved model fit, predictions & decisions (finance/portfolios) - lagged y: feed-forward network structure graphical models - zeros in off-diagonals ofmm - contemporaneous network structure. [ Carvalho, Wang, Reeson, Quintana etc 2003-now ]

5 Financial forecasting and portfolio decisions Sequential model learning & forecasting Bayesian decision theory: Sequential portfolio reallocations Key role of precision matrix You & Me investors: Individual retirement portfolios 30 Vanguard Mutual Funds 78 monthly returns example

6 Sparse mutual fund models in 4 metrics Where are the zeros in? Full graph %Edges

7 Sparsity for structure in dynamic portfolio decisions FX rates Large-scale global equities Mutual funds Data likes sparse models : Parsimony Improves forecasts Higher realized cumulative returns Lower risk portfolios Lower costs, more stability Risk Portfolio weight Pure prediction: $$$ returns Sparse model versus Standard model

8 Time-varying SPARSITY PATTERNS? BUT

9 Basic example: Dynamic regression via LT-AR(1)

10 Trajectories of LT AR parameters Posterior mean of Posterior probability of zero

11 Latent thresholding models - components Example dynamic auto-regression TV-VAR dynamic regression dynamic volatility model LTM?

12 Markov models for dynamic (sparse) volatility matrices AR(1) Univariate stochastic volatility LT-AR(1) Dynamic sparse Cholesky-style + diag Dynamic graphical model induced [ Lopes et al 2012-now: non-thresholded ]

13 Macroeconomic example: LT TV-VAR Decoupling: univariate models Recoupling: LT-MSV

14 Macro-economic forecasting Forecast RMSE Improved model fit, and forecasting accuracy & precision - shrinkage/parsimony

15 Macro-economic forecasting & interpretation - smoothed projections - less uncertainty about projections Non-threshold Impulse response: Of inflation 3 years ahead to current interest rate shock Latent threshold

16 LTM engenders smoother & rational projections Non-threshold Impulse response: Of inflation 2 years ahead to current interest rate shock Latent threshold

17 LTM engenders smoother & rational projections Non-threshold Impulse response: Of inflation 1 years ahead to current interest rate shock Latent threshold

18 Trajectories of LT Cholesky parameters Posterior mean of 2,1 3,1 3,2 Posterior probability of

19 Trajectories of LT TV-VAR dynamic parameters Posterior probability of

20 LTM in FX & volatility modelling Daily $ US FX and commodities: Jan-Jun 2009

21 LTM in FX & volatility modelling Dynamic regression, latent factors & volatility local level dynamic regression Oil, Gold diagonal: univariate SV models VAR(1) dynamic latent factor - independent components - Scalar entries of LT-AR(1)

22 LTM in FX: Dynamic factors

23 LTM in FX: Predictor and factor coefficients Posterior mean/intervals: Posterior probability on thresholded to zero

24 LTM parsimony improves: - forecasts & characterisation of multivariate volatility - portfolio decisions fed by forecasts : realized returns & risk profiles FX portfolio decisions-returns

25 Higher dimensional FX example

26 Dynamic sparsity Prob(non-zero) over time

27 Higher-dimensional LT factor model Bayesian forecasting and portfolio decisions using dynamic dependent factor models (with J. Nakajima & X. Zhou), Intl J Forecasting 2014

28 LT dependent dynamic factor models (Dynamic) dependence can matter statistically $cumulative portfolio And in other metrics

29 EEG network dynamics Multichannel EEG time series time-varying connectivities sparse connectivities? Models - dynamic lag/lead structure - multivariate volatility

30 Example: EEG LT TV-VAR Contemporaneous network Volatile precision matrix: Lagged network LT TV-VAR

31 EEG: Contemporaneous network snapshot: t=1501

32 EEG: Contemporaneous & lagged network dynamics lagged LT-TVVAR connectivities contemporaneous connectivities: LT-SV

33 Scale-up & sequential processing Scale-up dimensions Large economic series Multi-market financial data IT/network flows Scale-up and sequential analysis Cholesky: model decoupling Sequential: model emulation Implement: GPU? For: Events, anomaly detection Interventions Momentum building

34 More on LTMs Jouchi Nakajima Duke PhD 2012 Deputy Director of Global Economic Research Bank of Japan Latent threshold models: theory & methods LTMs + dynamic factor models LTMs + finance and portfolios LTMS + dynamic networks. & more recent J. Business & Economic Statistics, 2013 J. Financial Econometrics, 2013 International J. Forecasting, 2014 Digital Signal Processing,