Traditional ARMA Model Research Articles

Research on Temperature Prediction based on BP Neural Network Approach

Weather changes have an important impact on human production and life as well as socio-economic activities. In recent years, people have also gradually paid attention to the study of weather, especially the study of temperature, and it is of great practical significance to find an accurate temperature prediction model. At the same time, the use of machine learning methods to construct a temperature model can predict temperature changes more accurately and quickly, and provide a more reliable basis for weather forecasting. Therefore, in response to the unsatisfactory accuracy of temperature prediction by traditional prediction models, this paper uses the time series of daily average temperature of Hangzhou City, China, from 2013 to 2022 as the sample data, and combines the traditional ARMA model with the BP neural network model, which enables the BP neural network model to better fit and predict the temperature changes. The study shows that the prediction accuracy of the BP neural network model is significantly improved compared with the ARMA model.

Transformed‐Linear Models for Time Series Extremes

To capture the dependence in the upper tail of a time series, we develop non‐negative regularly varying time series models that are constructed similarly to classical non‐extreme ARMA models. Rather than fully characterizing tail dependence of the time series, we define the concept of weak tail stationarity which allows us to describe a regularly varying time series via a measure of pairwise extremal dependencies, the tail pairwise dependence function (TPDF). We state consistency requirements among the finite‐dimensional collections of the elements of a regularly varying time series and show that the TPDF's value does not depend on the dimension of the random vector being considered. So that our models take non‐negative values, we use transformed‐linear operations. We show existence and stationarity of these models, and develop their properties such as the model TPDFs. We fit models to hourly windspeed and daily fire weather index data, and we find that the fitted transformed‐linear models produce better estimates of upper tail quantities than a traditional ARMA model, classical linear regularly varying models, a max‐ARMA model, and a Markov model.

Attribution of Seasonal Wildfire Risk to Changes in Climate: A Statistical Extremes Approach

Abstract Wildfire risk is greatest during high winds after sustained periods of dry and hot conditions. This paper is a statistical extreme-event risk attribution study that aims to answer whether extreme wildfire seasons are more likely now than under past climate. This requires modeling temporal dependence at extreme levels. We propose the use of transformed-linear time series models, which are constructed similarly to traditional autoregressive–moving-average (ARMA) models while having a dependence structure that is tied to a widely used framework for extremes (regular variation). We fit the models to the extreme values of the seasonally adjusted fire weather index (FWI) time series to capture the dependence in the upper tail for past and present climate. We simulate 10 000 fire seasons from each fitted model and compare the proportion of simulated high-risk fire seasons to quantify the increase in risk. Our method suggests that the risk of experiencing an extreme wildfire season in Grand Lake, Colorado, under current climate has increased dramatically relative to the risk under the climate of the mid-twentieth century. Our method also finds some evidence of increased risk of extreme wildfire seasons in Quincy, California, but large uncertainties do not allow us to reject a null hypothesis of no change.

Generalized discrete autoregressive moving‐average models

AbstractThis article proposes the generalized discrete autoregressive moving‐average (GDARMA) model as a parsimonious and universally applicable approach for stationary univariate or multivariate time series. The GDARMA model can be applied to any type of quantitative time series. It allows to compute moment properties in a unique way, and it exhibits the autocorrelation structure of the traditional ARMA model. This great flexibility is obtained by using data‐specific variation operators, which is illustrated for the most common types of time series data, such as counts, integers, reals, and compositional data. The practical potential of the GDARMA approach is demonstrated by considering a time series of integers regarding votes for a change of the interest rate, and a time series of compositional data regarding television market shares.

Quantifying uncertainty in short-term traffic prediction and its application to optimal staffing plan development

In this paper, we aim to quantify uncertainty in short-term traffic volume prediction by enhancing a hybrid machine learning model based on Particle Swarm Optimization (PSO) and Extreme Learning Machine (ELM) neural network. Different from the previous studies, the PSO-ELM models require no statistical inference nor distribution assumption of the model parameters, but rather focus on generating the prediction intervals (PIs) that can minimize a multi-objective function which considers two criteria, reliability and interval sharpness. The improved PSO-ELM models are developed for an hourly border crossing traffic dataset and compared to: (1) the original PSO-ELMs; (2) two state of the art models proposed by Zhang et al. (2014) and Guo et al. (2014) separately; and (3) the traditional ARMA and Kalman filter models. The results show that the improved PSO-ELM can always keep the mean PI length the lowest, and guarantee that the PI coverage probability is higher than the corresponding PI nominal confidence, regardless of the confidence level assumed. The study also probes the reasons that led to a few points being not covered by the PIs of PSO-ELMs. Finally, the study proposes a comprehensive optimization framework to make staffing plans for border crossing authority based on bounds of PIs and point predictions. The results show that for holidays, the staffing plans based on PI upper bounds generated much lower total system costs, and that those plans derived from PI upper bounds of the improved PSO-ELM models, are capable of producing the lowest average waiting times at the border. For a weekday or a typical Monday, the workforce plans based on point predictions from Zhang et al. (2014) and Guo et al. (2014) models generated the smallest system costs with low border crossing delays. Moreover, for both holiday and normal Monday scenarios, if the border crossing authority lacked the required staff to implement the plans based on PI upper bounds or point predictions, the staffing plans based on PI lower bounds from the improved PSO-ELMs performed the best, with an acceptable level of service and total system costs close to the point prediction plans.

Combined deterministic – stochastic forecasting of monthly river flows for water management

Monthly discharges can be modelled and predicted by the decomposition of the runoff process model into two components – deterministic and stochastic. For such approach the term hybrid was often adopted. In this study a hybrid (deterministic-stochastic) modelling approach for one step ahead forecasting of mean monthly discharges at the gauging stations Banská Bystrica and Brehy on the Hron River in Slovakia was developed. The aim was to join the conceptual monthly rainfall runoff model KVHK and several time series models of the forecasting error time series of the conceptual model into a hybrid framework. Since these rainfall-runoff model error series may exhibit nonstationarity and heteroscedasticity, beside traditional ARMA models, GARCH type nonlinear time series models were also considered.

Modelling and trading the English stock market with novelty optimization techniques

The scope for this paper is to introduce short term adaptive models to trade the FTSE100 index. There are five major innovations on this paper which include the introduction of an input selection criteria when utilising an expansive universe of inputs, adaptive sliding window modelling, a hybrid combination of PSO and RBF algorithms, the application of a PSO algorithm to a traditional ARMA model, and finally the introduction of a multi-objective algorithm to optimise statistical and trading performance when trading an equity index.

Short-term wind power forecasting using hybrid method based on\xa0enhanced boosting algorithm

Day-ahead wind power forecasting plays an essential role in the safe and economic use of wind energy, the comprehending- intrinsic complexity of the behavior of wind is considered as the main challenge faced in improving forecasting accuracy. To improve forecasting accuracy, this paper focuses on two aspects: ①proposing a novel hybrid method using Boosting algorithm and a multi-step forecast approach to improve the forecasting capacity of traditional ARMA model; ②calculating the existing error bounds of the proposed method. To validate the effectiveness of the novel hybrid method, one-year period of real data are used for test, which were collected from three operating wind farms in the east coast of Jiangsu Province, China. Meanwhile conventional ARMA model and persistence model are both used as benchmarks with which the proposed method is compared. Test results show that the proposed method achieves a more accurate forecast.

A New Method for Modal Parameter Identification Based on Natural Excitation Technique and ARMA Model in Ambient Excitation

Due to the interference of strong vibration signal, a big error exists in modal parameter identification based on traditional ARMA model. In order to solve this problem, a new method for modal parameter identification based on natural excitation technique (NExT) and ARMA model is presented. Firstly, NExT is used to obtain cross-correlation function of different response sequences. Then, ARMA model of cross-correlation function is established, and the parameters of ARMA model are estimated by least squares method. Finally, the modal parameter identification is achieved using the relationship between the ARMA parameters and structural modal parameters. Experiment shows that the identification results of our method are more accurate than the traditional ARMA model.

On autoregressive moving-average models as a tool of virtual stock-exchange: experimental investigation

The objective of this work is to investigate experimentally the well-known autoregressive models as simplest algorithms simulating prediction processes of the stockholders using the historical stock rates only. The “virtual” stock exchange which applies these algorithms can help in testing various assumptions of investor behavior. To represent users that prefer linear utility functions, the autoregressive moving-average model (ARMA-ABS(p, q)), minimizing the absolute values of prediction errors is regarded, in addition to the traditional ARMA(p, q) model which minimize the least square errors. The results of two hundred actual financial time series and a hundred of virtual ones are discussed in short.

Uncertainty analysis of hydrological processes based on ARMA-GARCH model

Uncertainty analysis and risk analysis are two important areas of modern water resource management, in which accurate variance estimation is required. The traditional runoff model is established under the assumption that the variance is a constant or it changes with the seasons. However, hydrological processes in the real world are often heteroscedastic, which can be tested by McLeod-Li test and Engle Lagrange multiplier test. In such cases, the GARCH model of hydrological processes is established in this article. First, the seasonal factors in the sequence are removed. Second, the traditional ARMA model is established. Then, the GARCH model is used to correct the residual. At last, the daily runoff data in 1949–2001 of Yichang Hydrological Station is taken to be an example. The result shows that compared to the traditional ARMA model, the GARCH model has the ability to predict more accurate confidence intervals under the same confidence level.

Currency trading in volatile markets: Did neural networks outperform for the EUR/USD during the financial crisis 2007–2009?

The motivation for this article is to check whether neural network models have remained a superior method for forecasting the EUR/USD exchange rate during the financial crisis of 2007–2009. Alternative neural network architectures (Multi-Layer Perceptron (MLP), Recurrent Neural Network and Higher Order Neural Network (HONN)) are benchmarked against a random walk and a traditional ARMA model, and evaluated in terms of statistical accuracy and through a trading simulation on daily data over the period from January 2000 to February 2009, the period from August 2007 to February 2009, providing the out-of-sample testing period. Transaction costs and a confirmation filter devised to reduce false signals and thus also reduce losses and transaction costs were also taken into consideration. It is shown that the HONN structure gives the overall best results on a simple trading simulation; however, for an advanced trading simulation with a confirmation filter, the MLP outperforms all other models on most performance measures. On the whole, the results show that neural networks are still able to produce forecasts that yield a positive return and are superior to those of linear and more traditional models, with respect to both trading performance and statistical accuracy, even under very volatile market conditions.

Communication traffic forecasting model based on multiple SVM regression functions

According to the characteristics of communication traffic,a traffic forecasting model based on multiple Support Vector Machines(SVM) regression functions was proposed.In this model,the traffic data will be divided into two groups by the date,which are the working-day traffic data and the weekend traffic data.Then two different SVM models are trained using those data.The experimental results show that this model is very effective.Moreover,the performance of this model outperforms that of traditional ARMA model.

Modelling dynamic portfolio risk using risk drivers of elliptical processes

The situation of a limited availability of historical data is frequently encountered in portfolio risk estimation, especially in credit risk estimation. This makes it difficult, for example, to find statistically significant temporal structures in the data on the single asset level. By contrast, there is often a broader availability of cross-sectional data, i.e. a large number of assets in the portfolio. This paper proposes a stochastic dynamic model which takes this situation into account. The modelling framework is based on multivariate elliptical processes which model portfolio risk via sub-portfolio specific volatility indices called portfolio risk drivers. The dynamics of the risk drivers are modelled by multiplicative error models (MEMs)–as introduced by Engle [Engle, R.F., 2002. New frontiers for ARCH models. J. Appl. Econom. 17, 425–446]–or by traditional ARMA models. The model is calibrated to Moody’s KMV Credit Monitor asset returns (also known as firm-value returns) given on a monthly basis for 756 listed European companies at 115 time points from 1996 to 2005. This database is used by financial institutions to assess the credit quality of firms. The proposed risk drivers capture the volatility structure of asset returns in different industry sectors. A characteristic cyclical as well as a seasonal temporal structure of the risk drivers is found across all industry sectors. In addition, each risk driver exhibits idiosyncratic developments. We also identify correlations between the risk drivers and selected macroeconomic variables. These findings may improve the estimation of risk measures such as the (portfolio) Value at Risk. The proposed methods are general and can be applied to any series of multivariate asset or equity returns in finance and insurance.

Modelling Dynamic Portfolio Risk Using Risk Drivers of Elliptical Processes

The situation of a limited availability of historical data is frequently encountered in portfolio risk estimation, especially in credit risk estimation. This makes it, for example, difficult to find temporal structures with statistical significance in the data on the single asset level. By contrast, there is often a broader availability of cross-sectional data, i.e., a large number of assets in the portfolio. This paper proposes a stochastic dynamic model which takes this situation into account. The modelling framework is based on multivariate elliptical processes which model portfolio risk via sub-portfolio specific volatility indices called portfolio risk drivers. The dynamics of the risk drivers are modelled by multiplicative error models (MEM) - as introduced by Engle (2002) - or by traditional ARMA models. The model is calibrated to Moody's KMV Credit Monitor asset returns (also known as firm-value returns) given on a monthly basis for 756 listed European companies at 115 time points from 1996 to 2005. This database is used by financial institutions to assess the credit quality of firms. The proposed risk drivers capture the volatility structure of asset returns in different industry sectors. A characteristic temporal structure of the risk drivers, cyclical as well as a seasonal, is found across all industry sectors. In addition, each risk driver exhibits idiosyncratic developments. We also identify correlations between the risk drivers and selected macroeconomic variables. These findings may improve the estimation of risk measures such as the (portfolio) Value at Risk. The proposed methods are general and can be applied to any series of multivariate asset or equity returns in finance and insurance.

Intelligent short-term load forecasting in Turkey

A method is proposed to forecast Turkey’s total electric load one day in advance by neural networks. A hybrid learning scheme that combines off-line learning with real-time forecasting is developed to use the available data for adapting the weights and to further adjust these connections according to changing conditions. Data are clustered due to the differences in their characteristics. Special days are extracted from the normal training sets and handled separately. In this way, a solution is provided for all load types, including working days, weekends and special holidays. A traditional ARMA model is constructed for the same data as a benchmark. Proposed method gives lower percent errors all the time, especially for holidays. The average error for year 2002 is obtained as 1.60%.

Volatility of changes in G‐5 exchange rates and its market transmission mechanism

AbstractThis paper studies the transmission mechanism of G‐5 exchange rate changes within each market and across the three major markets: London, New York and Tokyo. It is found that the volatility in both the London and New York markets leads that of Tokyo. In addition, the New York market slightly leads the London market in its volatility. After the Euro monetary system crisis, the frequencies of both the volatility spillover effect from London to New York and mutual feedback phenomena have increased. Furthermore, the volatility spillover effects from both London and New York to Tokyo have been on the rise after the Asian financial debacle. Within the framework of the causality model, we find better forecasting performance in predicting G‐5 exchange rates across the three markets. It outperforms the traditional ARMA model in terms of both in‐ and out‐sample forecasting. Copyright © 2002 John Wiley & Sons, Ltd.

Canonical correlation analysis, approximate covariance extension, and identification of stationary time series

In this paper we analyze a class of state space identification algorithms for time-series, based on canonical correlation analysis, in the light of recent results on stochastic systems theory. In principle, these so called “subspace methods” can be described as covariance estimation followed by stochastic realization. The methods offer the major advantage of converting the nonlinear parameter estimation phase in traditional ARMA models identification into the solution of a Riccati equation but introduce at the same time some nontrivial mathematical problems related to positivity. The reason for this is that an essential part of the problem is equivalent to the well-known rational covariance extension problem. Therefore, the usual deterministic arguments based on factorization of a Hankel matrix are not valid for generic data, something that is habitually overlooked in the literature. We demonstrate that there is no guarantee that several popular identification procedures based on the same principle will not fail to produce a positive extension, unless some rather stringent assumptions are made which, in general, are not explicitly reported. In this paper the statistical problem of stochastic modeling from estimated covariances is phrased in the geometric language of stochastic realization theory. We review the basic ideas of stochastic realization theory in the context of identification, discuss the concept of stochastic balancing and of stochastic model reduction by principal subsystem truncation. The model reduction method of Desai and Pal (1982) [A realization approach to stochastic model reduction. Proc. 1 st Decision and Control Conf., pp. 1105–1112.], based on truncated balanced stochastic realizations, is partially justified, showing that the reduced system structure has a positive covariance sequence but is in general not balanced. As a byproduct of this analysis we obtain a theorem prescribing conditions under which the ‘subspace identification’ methods produce bona fide stochastic systems.