Neural Networks to Model Energy Commodity Price Dynamics 1 Dpt. DIET - Dpt. of Information...

Neural Networks to Model Energy

Commodity Price Dynamics

1Dpt. DIET - Dpt. of Information Engineering, Electronics and Telecommunications

2Dpt. DAES – Dpt. of Economic and Social Analysis

M.Panella1, F.Barcellona2, V.Santucci1, R.L.D’Ecclesia2

Prof. M.Panella30th USAEE/IAEE

NORTH AMERICAN CONFERENCEOCT. 9-12 - 2011

[email protected]

[email protected]

[email protected]

Washington, Oct. 09‐12, 2011

Outline

Aim

Some literautre

Datasets

Experimental setup

Numerical results

Conclusions and future developments


Motivation

To provide a powerful tool to replicate economic and financial series dynamics

To apply a new methodology based on a neural network approach to build a forecast for specific standard price time series of energy commodities

To backtest the results and set up risk management strategies


Qualitative techniques: opinion based approaches testing based approaches

Available methodologies

Forecasting process like a black box.

Methodological approaches to analize time series: Standard approaches Modern approaches

Autoregressive models (AR) Moving average models (MA) ARMA models

Quantitative techniques: explanatory methods time series based methods

ARIMA models ARCH and GARCH

models


Some Recent Literature

A.G. Malliaris e Mary Malliaris ‘Time series and Neural Networks comparison on gold, oil and the euro’, International Joint Conference on Neural Networks, 2009.

Cristina Bencivenga, Rita D’Ecclesia, ‘Integration of Energy commodity markets: the case of Europe and US’, Journal of Risk Management in Financial Institutions, Henry Stewart Publications, 2011

Cristina Bencivenga, Rita D’Ecclesia, ‘Energy commodities price dynamics: understanding oil price volatility’, Journal of Energy Economics, 2011

R. Gencay and M. Qi. ‘Pricing and Hedging Derivative Securities with neural Networks: Bayesian Regularization, Early Stopping, and Bagging’. IEEE 2001.

R. Garcia, R. Gencay. ‘Pricing and hedging Derivative securities with neural networks and a homogeneity hint’. Journal of Econometrics 94 (2000).

F. Malik, M. Nasereddin. ‘Forecasting output using oil prices: A cascaded artificial neural network approch’. Journal of Econometrics and Business 58 (2006).


Forecasting and function approximation

• Problem: when dealing with real-world (often chaotic) data sequences, the previous AR predictor would hardly fail since it is based on a linear approximation model and on a trivial embedding technique.

• Given a sampled sequence S(n), the general approach to its prediction is based on the solution of a suitable function approximation problem y=f(x)

N

1ii

N

1iniiAR

nn

1)iS(nam)(nS xa)(f

1)NS(n ... 1)S(n S(n)x , m)S(n y

ˆ

Embedding technique


Embedding of chaotic time series

X(n+1) = F(X(n))

S(n) = G(X(n))

X(n) = State vector

S(n)Embedding theory

t1)T)(NS(n ... T)S(n S(n)x(n)X n

Predictor: Function approximation: (training set)

• The sampled sequence S(n) to be predicted originates from an unknown autonomous context:

T: time lag between samples (AMI)

N: embedding dimension (FNN)

Reconstructed state-space:

)xf(m)(nS n~

)f(

m)S(ny

x

n

n


Radial Basis Function Neural Network

...

x1

x2

x3

Dx

...

3w

Mw

1w

2w

=

=M

jjwy

1

Fj(x)

F1(x)

F2(x)

F3(x)

FM(x)

Fj(x): nonlinear (vector) function

A hidden layer of radial kernels:Performs a non-linear transformation of input space. The resulting hidden space is typically of higher dimensionality than the input spaceAn output layer of linear neurons:

The output layer performs linear regression to predict the desired targets


ANFIS (Adaptive Neuro-Fuzzy Inference System) Network Architecture

Fu

zzificatio

n

Rule 1 antecedent

Rule M antecedent

No

rma

lizatio

n X

Rule 1 consequent

Rule M consequent

X

+x y(x)

(1)(x)

(M)(x)

(1)(x)

(M)(x)

y(1)(x)

y(M)(x)

• Sugeno 1st-order type rules: (k)0

n

1jj

(k)j

(k)(k)nn

(k)11 axayB is xBisx

, ... , THENANDIF

• Approximate reasoning:

‒ Fuzzification of crisp inputs: x=[x1 x2 … xn];

‒ Membership functions: (k)(x) reliability of linguistic (fuzzy) rules

‒ Soft (fuzzy) decision:

M

1k

(k)(k) )x()yx()xy(


Data set

EUR Brent European Energy Exchange

(EEX) National Balancing Point (NBP)

US West Texas Intermediate (WTI) PJM Interconnection (Eastern

Interconnection) Henry Hub (HH)

Input-output series: Input series (training phase): 8 two-

year period from 2001-2002 to 2008-2009;

Output series (testing phase): 8 years from 2003 to 2010 (each follows the previous two years)

Unique time series for both phases (training and testing), described by data of three-year period (from 2001-2002-2003 to 2008-2009-2010).

We used logarithmic transformed prices of both European and American energy commodities (oil, electricity and gas):a


Test 1/3

The considered models are:

GARCH/ARIMA111 models using different numbers of forecasting factors and starting sample size

LSE (Least Squares Estimation)

RBF (Radial Basis Function)

MOG: developed by the Dept. DIET (gaussian model)

ANFIS2: matlab plug-in


For each price series the robustness of the used model has been tested by setting different values of the parameters:

RBF:

alfa (maximum percentage of neurons in the network);

MOG:

alfa (maximum number of clusters)

lambda (model weights)

ANFIS2:

T_OPT[1] (number of epochs in the training phase)

The training process should be implemeted by firstly using an embedding technique in order to choose T and N (delay and embedding dimension)

Set as default T=1 and N=5

Test 2/3


As qualitative results we consider: Plots of the two series, real and predicted Values that reflect the prediction reliability

The prediction accuracy is measured by: Mean Squared Error - MSE Normalised Mean Square Error - NMSE Signal-to-noise ratio or SNR (dB) Mean absolute percentage error - MAPE (%)

Tests 3/3


In the testing phase of theoretical models, it is essential to define some criteria to assess the efficacy of the chosen model.

Three different criteria, based on a comparison of some series characteristics, are used:

Reproduce the same characteristics of trend, seasonality, volatility and jumps

Easy calculation and numerical implementation Match of statistical properties of the two series

Results analysis 1/5

Summarized in the four moments:MeanStd DvSkewnessKurtosis

Features of the series probability

distribution

RELIABLE FORECAST



Here are graph and table resulting from the 2003 forecast for European oil (Brent) using MOG predictor (alpha = 0.9, lambda = 0.5)



Here are graph and table resulting from the 2003 forecast for American oil (WTI) using

MOG predictor (alfa=0.9, lambda=0.5)



Here are graph and table resulting from the 2003 forecast for Brent using linear model (LSE)

whose statistical analysis returned a perfect coincidence of all 4 moments.

Perfect match



Here are graph and table resulting from the 2003 forecast for Brent using RBF model (alfa=0.5), whose statistical analysis return a good match only for first and second moments.


Conclusions and Future developments

Structuring data:Different energy assets

• reference to current (actuality)Extend forecast time range

Modeling:Different forecasting methods:

• embedding techniques • subband (spectral)

decompositionOther financial tools

Correlation between NN and moments up to fourth order. This introduces new forecasting assumptions for energy commodities

Reduction of computational cost

The accurate prediction of energy priceseries will allow to estimate the existing relationships between the variousCommodities and to price derivative instruments in order to set up risk management strategies

Neural Networks to Model Energy Commodity Price Dynamics 1 Dpt. DIET - Dpt. of Information...

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