3,594 research outputs found
Time series forecasting with the WARIMAX-GARCH method
It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (WARIMAX-GARCH) method, is proposed to improve predictive performance and accuracy but also to address, at least in part, the problem of unavailable EVs. Basically, the WARIMAX-GARCH method obtains Wavelet âEVsâ (WEVs) from Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (ARIMAX-GARCH) models applied to Wavelet Components (WCs) that are initially determined from the underlying time series. The WEVs are, in fact, treated by the WARIMAX-GARCH method as if they were conventional EVs. Similarly to GARCH and ARIMA-GARCH models, the WARIMAX-GARCH method is suitable for time series exhibiting non-linear characteristics such as conditional variance that depends on past values of observed data. However, unlike those, it can explicitly model frequency domain patterns in the series to help improve predictive performance. An application to a daily time series of dam displacement in Brazil shows the WARIMAX-GARCH method to remarkably outperform the ARIMA-GARCH method, as well as the (multi-layer perceptron) Artificial Neural Network (ANN) and its wavelet version referred to as Wavelet Artificial Neural Network (WANN) as in [1], on statistical measures for both in-sample and out-of-sample forecasting
Regime Switching and Artificial Neural Network Forecasting
This paper provides an analysis of regime switching in volatility and out-of-sample forecasting of the Cyprus Stock Exchange using daily data for the period 1996-2002. We first model volatility regime switching within a univariate Markov-Switching framework. Modelling stock returns within this context can be motivated by the fact that the change in regime should be considered as a random event and not predictable. The results show that linearity is rejected in favour of a MS specification, which forms statistically an adequate representation of the data. Two regimes are implied by the model; the high volatility regime and the low volatility one and they provide quite accurately the state of volatility associated with the presence of a rational bubble in the capital market of Cyprus. Another implication is that there is evidence of regime clustering. We then provide out-of-sample forecasts of the CSE daily returns using two competing non-linear models, the univariate Markov Switching model and the Artificial Neural Network Model. The comparison of the out-of-sample forecasts is done on the basis of forecast accuracy, using the Diebold and Mariano (1995) test and forecast encompassing, using the Clements and Hendry (1998) test. The results suggest that both non-linear models equivalent in forecasting accuracy and forecasting encompassing and therefore on forecasting performance.Regime switching, artificial neural networks, stock returns, forecast
Forecasting and Forecast Combination in Airline Revenue Management Applications
Predicting a variable for a future point in time helps planning for unknown
future situations and is common practice in many areas such as economics, finance,
manufacturing, weather and natural sciences. This paper investigates and compares
approaches to forecasting and forecast combination that can be applied to service
industry in general and to airline industry in particular. Furthermore, possibilities to
include additionally available data like passenger-based information are discussed
Working Paper 113 - Monetary Policy Conduct Based on Nonlinear Taylor Rule: Evidence from South Africa
This paper analyses the applicability of a nonlinear Taylor rule in characterizing the monetary policy behavior of the South African Reserve Bank, using a logistic smooth transition regression approach. Using quarterly data from 1976 to 2008 to analyze the movement of the nominal short term interest rate for the South African Reserve Bank, we find that a nonlinear Taylor rule holds. On the contrary, some studies find that the South African Reserve Bank behavior can be described by a linear Taylor rule, but only because these studies removed the structural break which coincided with the Asian crises and estimated two different Taylor rules. Our study does not remove the structural break as it is an anomaly path, thus it uses the entire sampling period. Our results go counter to the above mentioned findings. In fact, our results are consistent with the international findings on the European Central Bank and the Bank of England that the nonlinear Taylor rule holds.
Efficient transfer entropy analysis of non-stationary neural time series
Information theory allows us to investigate information processing in neural
systems in terms of information transfer, storage and modification. Especially
the measure of information transfer, transfer entropy, has seen a dramatic
surge of interest in neuroscience. Estimating transfer entropy from two
processes requires the observation of multiple realizations of these processes
to estimate associated probability density functions. To obtain these
observations, available estimators assume stationarity of processes to allow
pooling of observations over time. This assumption however, is a major obstacle
to the application of these estimators in neuroscience as observed processes
are often non-stationary. As a solution, Gomez-Herrero and colleagues
theoretically showed that the stationarity assumption may be avoided by
estimating transfer entropy from an ensemble of realizations. Such an ensemble
is often readily available in neuroscience experiments in the form of
experimental trials. Thus, in this work we combine the ensemble method with a
recently proposed transfer entropy estimator to make transfer entropy
estimation applicable to non-stationary time series. We present an efficient
implementation of the approach that deals with the increased computational
demand of the ensemble method's practical application. In particular, we use a
massively parallel implementation for a graphics processing unit to handle the
computationally most heavy aspects of the ensemble method. We test the
performance and robustness of our implementation on data from simulated
stochastic processes and demonstrate the method's applicability to
magnetoencephalographic data. While we mainly evaluate the proposed method for
neuroscientific data, we expect it to be applicable in a variety of fields that
are concerned with the analysis of information transfer in complex biological,
social, and artificial systems.Comment: 27 pages, 7 figures, submitted to PLOS ON
Deep learning as closure for irreversible processes: A data-driven generalized Langevin equation
The ultimate goal of physics is finding a unique equation capable of
describing the evolution of any observable quantity in a self-consistent way.
Within the field of statistical physics, such an equation is known as the
generalized Langevin equation (GLE). Nevertheless, the formal and exact GLE is
not particularly useful, since it depends on the complete history of the
observable at hand, and on hidden degrees of freedom typically inaccessible
from a theoretical point of view. In this work, we propose the use of deep
neural networks as a new avenue for learning the intricacies of the unknowns
mentioned above. By using machine learning to eliminate the unknowns from GLEs,
our methodology outperforms previous approaches (in terms of efficiency and
robustness) where general fitting functions were postulated. Finally, our work
is tested against several prototypical examples, from a colloidal systems and
particle chains immersed in a thermal bath, to climatology and financial
models. In all cases, our methodology exhibits an excellent agreement with the
actual dynamics of the observables under consideration
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