An Artificial Intelligence Approach Peter Tiňo CERCIA, University of Birmingham, UK a collaboration with J. Binner Aston Business School, Aston University, UK B. Jones State University of New York, USA G. Kendall Nottingham University, UK J. Tepper Nottigham Trent University, UK
Motivations What is money? Traditional interpretation of what money is capturing: Store of value Unit of account Medium of exchange Changing environment New monetary assets Banks blend with Building Societies, etc. Need to adequately measure money...... in order to construct money supply (monetary policy), but... how to combine and measure different objectives in a changing environment? P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 1
Our framework How do we know if we have been successful or not? Inflation targeting - one of the main monetary policy tools. Macroeconomists: having robust measures of money will help us in predicting inflation. In the past... We used to know how much money there was in the economy. Stable relationship between the quantity of money and prices. Macroeconomic control through targeting money supply.... but then... the case of missing money Financial innovation distorted formerly stable relationships. Major economies abandoned monetary targeting in the late 1980s. P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 2
Divisia Money - Bank of England Aggregate m certain Assets where we know the value (rate of return) Personal sector monetary aggregate containing: 1. Notes and coins 2. Non-interest bearing time deposits 3. Interest bearing savings (short term) 4. Interest bearing time deposits (long term) 5. Building society deposits (long term) Interest rate captures liquidity: L = IR P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 3
Money Stock Mismeasurement? Traditional simple sum index M = m i (Fisher, 1922) i Aggregate m i - the amount of asset i Weighted average index (such as Divisia) weighted by interest rate s i takes the degree of liquidity into account DM = i Aggregate s i m i P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 4
Divisia Monetary Index Capture services provided by monetary assets consumer price index for money Compare with a high yielding non-monetary asset - what else we could have done with the money... more liquid monetary asset = more services R t - max. rate of return on non-monetary asset at time t r i,t - rate of return on monetary asset i at time t price/value: p i,t = R t r i,t R t + 1 = 1 r i,t + 1 R t + 1 P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 5
Normalize across monetary assets j in the whole economy m i,t - quantity of monetary asset i at time t ν i,t = p i,t m i,t j p j,t m j,t Capture the flow of values of money - share weight s i,t = 1 2 (ν i,t ν i,t 1 ) Discrete-time approximation of the continuous flow (in log-scale) ln M t ln M t 1 = i s i,t (ln m i,t ln m i,t 1 ) P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 6
Predicting Inflation Rates - Data Monthly data 4 Levels of aggregation: M1, M2, MZM, M3 aggregation levels currently monitored in USA narrow broad At each aggregation level: Simple sum Weighting non-monetary benchmarks - BAA (a long bond in USA) - upper envelope St Louis Fed Reserve Bank style P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 7
Data - Cont d Interest rates short term long term Important? Short term IR are currently used in UK to control inflation. Training: Jan 61 - Feb 97 Validation: Mar 97 - Apr 01 Test: May 01 - Jun 05 P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 8
US Inflation Rates 0.16 0.14 inflation rate train validate test 0.12 0.1 0.08 0.06 0.04 0.02 0 0 50 100 150 200 250 300 350 400 450 500 P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 9
Predicting Inflation Rates - Models Evolutionary (FF) Neural Networks ES - crossover + Gaussian mutation evolve a population of neural networks finite length input window (finite input memory) Recurrent Neural Networks self-recurrent internal state units dynamically construct internal representations of temporal dependencies trained via BPTT P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 10
Kernel regression linear in parameters linear techniques in feature space finite length input window (finite input memory) Kernel width, input lag and other model hyperparameters are set on the validation set Kernel Recursive Least Squares - Kernelized version of the classical Recursive Least Squares (RLS) technique Other kernel-based regression techniques used: Kernel Partial Least Squares Relevance Vector Machine Gaussian Process P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 11
Kernel Recursive Least Squares R F(x) = w K(x,x) Σ i i i F K(x 1,x) K(x 2,x) K(x 3,x) K(x 4,x) X P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 12
Baseline - Random Walk y(t) - the actual observed inflation rate at time t. ŷ(t) - inflation rate predicted to occur at time t by our model. Predict that in T months (prediction horizon) we will observe the current inflation rate: ŷ(t + T ) = y(t) Corresponds to random walk hypothesis with moves governed by a symmetrical zero-mean density function. It measures the degree to which the efficient market hypothesis applies. P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 13
Root Mean Square Error Evaluation Methods RMSE = 1 N N (y(t) ŷ(t)) 2 t=1 Improvement in RMSE over baseline (RW) IORW (M) = = RMSE(RW ) RMSE(M) 100% RMSE(RW ( 1 RMSE(M) ) 100% RMSE(RW ) P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 14
Our Hypothesis USA MSI (divisia) - superior indicators of monetary conditions. Such evidence could reinstate monetary targeting. Most empirical studies based on cointegration techniques (Stracca 2003). We use artificial intelligence techniques to model regularities in past inflation rates and monetary indexes. P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 15
Results RMSE(RW) = 0.008827 All models implicitly included past inflation rates as input variable. Does inclusion of measures of money (or interest rates) improve predictive performance? P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 16
Evolved Neural Networks Evol NN M TB BAA Recurrent IORW M 1 - No No Yes :-( M 2 - No No No :-( M 3 M3 No No No :-( M 4 DM3 BAA Yes No Yes :-( :-( means worse than baseline P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 17
Recurrent Neural Networks RNN M TB BAA # Hidden IORW M 1 Envelop M1 Yes No 25 11.28 M 2 - No No 5 10.81 M 3 SS M3 Yes No 10 13.61 M 4 - Yes Yes 10 14.13 P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 18
Kernel Recursive Least Squares KRLS In Lag KW ν λ IORW M 1 10 1.5 0.21 0.1 7.09 M 2 10 1.2 0.27 0.1 39.62 M 3 10 1.2 0.28 0.1 35.77 M 4 12 1.2 0.27 0.1 43.42 P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 19
0.15 KRLS - Predicted Inflation Rates 0.1 0.05 0 0 100 200 300 400 500 600 Val 0.04 0.03 0.02 0.01 0 10 20 30 40 50 60 Tst 0.04 0.03 0.02 0.01 0 5 10 15 20 25 30 35 40 45 50 P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 20
Lessons Learnt 1. When controlling model complexity appropriately, it is possible to beat baseline RW model quite considerably. 2. It seems that enough information is present in the inflation rates alone, no standard additional measures of money are helpful. 3. Need to deal with model complexity issues in a more profound way. 4. Other compound measures of money may be useful, but they may be model/task dependent non-linear in nature P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 21
Conclusions and Future Work All approaches are valid, and all try to solve the same task prediction of inflation rate. The assumptions the models make about the structure of the data are different - this is the first shot. Further work required to develop the construction of Divisia. Hybrid approaches & apply to different datasets (e.g. Risk adjusted Divisia). P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 22
Conclusions and Future Work policy implementation Bank of England need to be transparent and accountable with their funding. Rule Extraction Need to understand better how each technique influences the results. We may able to influence Bank of England to pursue new avenues of research and adopt new ways of constructing money, still transparent (e.g. non-linearities). Philipp s Curve... P. Tiňo, J. Binner, B. Jones, G. Kendall, J. Tepper 23