Neural network and regression methods for optimizations between two meteorological factors
Introduction
Research on the cross-correlations of collective modes has been ubiquitous in physics, atmospheric geophysics, seismology, finance, physiology, and genomics over last three decades [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. In the field of physics, the correlation method has been particularly described by correlation functions in the Boltzmann–Langevin equation with the fluctuation effect [18], and the correlation functions of the fluctuating pressure tensor and the heat-flow vector have been evaluated by using the Chapman–Enskog approximation. If two systems interact mutually, such an interaction gives rise to the phenomenon of collective modes. This phenomenon can be analyzed using the cross-correlation of traditional methods, random matrix theory, and the detrended cross-correlation analysis (DCCA) method [19], [20]. The DCCA method was useful to analyze several models such as autoregressive fractionally integrated moving average processes, electroencephalography, stock prices and their trading volumes, and taxi accidents, and recently several investigations have been introduced and analyzed the multiscale multifractal DCCA [21].
Furthermore, climate change is a cause for concern for many scientists around the world. Changes in the components of climate have resulted in considerable climate variations for this complex system [22], [23]. With the numerical weather prediction of the World Meteorological Organization, the statistical quantities of heat transfer, solar radiation, wind, humidity, and surface hydrology have been calculated within each grid cell of our earth, and these interactions are presently proceeding to be calculated to shed light on the atmospheric properties. ENSO forecast models have been categorized into three types: coupled physical models, statistical models, and hybrid models [24], [25], [26]. Among these models, the statistical models introduced for ENSO forecasts have been the neural network (NN) model, linear regression model, and canonical correlation analysis [27], [28]. Barnston et al. [29] have found that the statistical models have reasonable accuracies in forecasting sea surface temperature anomalies.
Until now, many models have been proposed for human memory as a collective property of neural networks. Neural network (NN) models introduced by Little [30] and Hopfield [31] have been based on an Ising Hamiltonian extended by equilibrium statistical mechanics. A detailed discussion of the equilibrium properties of the Hopfield model was discussed in Amit et al. [32].
As synaptic connections are taken to be symmetric and each neuron is connected to an infinite number of other neurons, the exact solutions of the equilibrium properties have been obtained in the NN. In the past viewpoint on the NN, many researchers tried to train layered NNs such as speech recognition, generation, handwriting recognition, protein structure, and neurobiological systems [33], [34], [35], [36], [37], [38]. Learning in feedforward NNs has been studied with a statistical–mechanical framework. The training algorithm has been used to find a class of network weights that optimizes a suitable cost function that quantifies the error on the training set [39]. As error is minimized and approaches a very small value, we can find and analyze a novel forecasting model that is not simple or easy. In particular, among the many statistical models used in meteorological forecasts, the artificial neural network (ANN) and the multiple regression method (MRM) have been developed in many published papers to predict meteorological factors (temperature, humidity, rainfall, wind speed, and so on).
The artificially developed NN is called the ANN and is different from the biological NN. The investigation of the ANN in meteorological forecasting is not new and is applied to useful fields. Several researchers have successfully applied it to the task of identifying patterns in meteorological time series. As some estimate price time series or technical trading rules in economics and econometrics, three NN architectures, i.e., the ANN, the recurrent NN and the psi-sigma NN, are applied to the task of forecasting [40], [41]. Readers are referred to the published papers of Zhang et al. [42] and Ghazali et al. [43].
In the financial performance of the NN, Tsaih et al. [44] have attempted to forecast stock index futures, and they have suggested that NNs perform better than the ANN. Tenti [45] and Dunis and Huang [46] have achieved encouraging results by using recurrent NNs to forecast exchange rates. Hussain et al. [47] have particularly presented the forecasting results of psi-sigma NN for some exchange rates using univariate series as inputs in their networks. Dunis et al. [48] have studied exchange rates series with psi-sigma NN, but failed to outperform the multi-layer perceptron, the recurrent NN and the high-order NN in a simple trading application. Furthermore, the ANN has been extended to NN-genetic and NN-fuzzy methods in mathematical and financial models. As the integrated NN models (the NN-GARCH, NN-EGARCH, and NN-EWMA models, and so on) enhance predictive power by comparing the volatilities of single models, these have been proposed in the framework of precision and direction accuracy [49], [50], [51], [52]. Furthermore, if we apply the meteorological factors to the integrated NN models, such an investigation will play a crucial role in the development and contribution of the MRM in meteorological fields.
Until now, the MRM has been used to treat statistical forecasting for the data of time series, the hypothetical experiment of some influences, the modeling of casual relationship, and so on. The MRM was used to train the relation between two or more independent variables [53], [54], [55], while simple regression analysis trained one independent variable. Multiple regression analysis is considered to be an optimal model to predict the future, and this analysis is accepted as a forecast for time, assuming that the prediction is the most recent time change.
To our knowledge, DCCA, ANN, and MRM are primarily valuable for more deeply extending and investigating statistical forecasting from the relationships between meteorological factors. The purpose of this paper is to discuss the temporal variation characteristics of two meteorological factors (temperature and humidity) in four metropolitan cities (Seoul, Busan, Daegu, Daejeon) in South Korea. Three methods are introduced as follows: Firstly, we employ the DCCA method to extract the correlated tendency between temperature and humidity. Secondly, we use the ANN approach, and lastly analyze the MRM. Data for calculations are given in Section 2. Basic formulas for the DCCA method, the ANN, and the MRM are provided in Section 3. In Section 4, corresponding calculations and the results for these models are presented. The results of error in the ANN and MRM are also presented and discussed. Concluding remarks are given in Section 5.
Section snippets
Data
We extracted the time series data of meteorological factors from the data network of the Korea Meteorological Administration (KMA). We will discuss meteorological factors measured at global standard weather observatories located in South Korea.
We used the data of the manned regional meteorological offices of the KMA to ensure the reliability of data, and it is hourly data for seven years from 2008 to 2014. In this study, we examined the DCCA analysis of two meteorological factors (temperature
DCCA
In this subsection, we are simply concerned with one difference set and another different difference set () of meteorological factors, selected from hourly time series of two meteorological factors (temperature and humidity). First of all, for time series , the mean and the variance are defined by and respectively. It is assumed from the mean and the variance that the cross-correlation function is defined by
DCCA
In this study, we examined the DCCA analysis of two meteorological factors (temperature and humidity) during five years from 2010 to 2014. We decided on daily time lags of one day to 28 days and on window sizes from to 100. Fig. 2 shows the DCCA coefficient versus a function of window size s between temperature and humidity at different time lags of 1, 7, 14, 21, and 28 days in spring, summer, autumn, and winter in Seoul. In particular, the DCCA coefficient as a function of window
Summary
The temporal variation features of two meteorological factors (temperature and humidity) in four metropolitan cities (Seoul, Busan, Daegu, Daejeon) in South Korea were studied. In this analysis, the time series data of the two meteorological factors were used. Data were extracted from seven years (2008 to 2014) of hourly time series data in meteorological offices of the Korea Meteorological Administration (KMA). Three methods for this study were discussed as follows. We employed the DCCA method
Acknowledgment
This is supported by a Research Grant of Pukyong National University (2017 year).
References (58)
- et al.
Firing patterns transition and desynchronization induced by time delay in neural networks
Physica A
(2018) - et al.
Dynamical behavior of the correlation between meteorological factors
J. Korean Phys. Soc.
(2017) - et al.
Progress during toga in understanding and modeling global teleconnections associated with tropical sea surface temperatures
J. Geophys. Res.
(1998) - et al.
Long-lead seasonal forecasts - where do we stand
Bull. Am. Meteor. Soc.
(1994) - et al.
Spin-glass models of neural networks
Phys. Rev. A
(1985)Phys. Rev. Lett.
(1985) Modeling Brain Function: The World of Attractor Neural Networks
(1989)- et al.
Forecasting with artificial neural networks: the state of the art
Int. J. Forecast.
(1998) - R. Ghazali, A. Hussain, M. Merabti, Higher order neural networks for financial time series prediction, in: The 10th...
- et al.
Forecasting s & 500 stock index futures with a hybrid ai system
Decis. Supp. Syst.
(1998) - et al.
Forecasting and trading currency volatility: an application of recurrent neural regression and model combination
J. Forecast.
(2002)
Conditional heterosdasticity in asset returns: a new approach
Econometrica
Neural Networks for Pattern Recognition
Novel constructive and destructive parsimonious extreme learning machines
IEEE Trans. Neural Netw. Learn. Syst.
Long-range correlations in the diffuse seismic coda
Science
Climate networks around the globe are significantly affected by el niño
Phys. Rev. Lett.
Cross-correlations between volume change and price change
Proc. Natl. Acad. Sci.
A link prediction method for heterogeneous networks based on bp neural network
Physica A
Performance enhancement of the branch length similarity entropy descriptor for shape recognition by introducing critical points
J. Korean Phys. Soc.
Time-localized wavelet multiple regression and correlation
Physica A
Quantifying cross-correlations using local and global detrending approaches
Eur. Phys. J. B
1/f behavior in cross-correlations between absolute returns in a us market
Physica A
Statistical tests for power-law cross-correlated processes
Phys. Rev. E
Detrended partial cross-correlation analysis of two time series influenced by common external forces
Phys. Rev. E
Detrended cross-correlation analysis for non-stationary time series with periodic trends
Europhys. Lett.
Orbital entanglement and violation of bell inequalities in mesoscopic conductors
Phys. Rev. Lett.
Positive cross-correlations in a three-terminal quantum dot with ferromagnetic contacts
Phys. Rev. Lett.
And phase recovery via cross-correlation measurements of electrons
Phys. Rev. Lett.
Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series
Phys. Rev. Lett.
Phys. Rev. E
Physica A
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