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Standard estimation of ARMA models in which the AR and MA roots nearly cancel, so that individual coefficients are only weakly identified, often produces inferential ranges for individual coefficients that give a spurious appearance of accuracy. We remedy this problem with a model that uses a simple mixture prior. The posterior mixing probability is derived using Bayesian methods, but we show that the method works well in both Bayesian and frequentist setups. In particular, we show that our mixture procedure weights standard results heavily when given data from a well-identified ARMA model (which does not exhibit near root cancellation) and weights heavily an uninformative inferential region when given data from a weakly-identified ARMA model (with near root cancellation). When our procedure is applied to a well-identified process the investigator gets the “usual results,” so there is no important statistical cost to using our procedure. On the other hand, when our procedure is applied to a weakly identified process, the investigator learns that the data tell us little about the parameters – and is thus protected against making spurious inferences. We recommend that mixture models be computed routinely when inference about ARMA coefficients is of interest.

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

The firewater deluge system (FDS) can provide water automatically through a deluge valve when a fire breaks out. However, there are many fire hazards caused by the abnormal operating state of the FDS. To monitor and predict the working state of the FDS, this paper aims to propose a firewater deluge monitoring and forecasting system using the Internet of Things (IoT) technology.

The firewater deluge monitoring and forecasting system consists of three layers: the sensing layer, network layer and application layer. The firewater pressure obtained by the monitoring nodes was transmitted to the local gateway and then to the remote monitoring center. In the application layer, an autoregressive moving average (ARMA) model was put forward to forecast the firewater pressure. Furthermore, a genetic algorithm (GA) was proposed to perfect the order determination method of the ARMA model. Finally, a Web application was developed to display the real time and predicted working status of the FDS.

The predicted results show that the ARMA model improved by the GA (GA-ARMA) is significantly better than traditional ARMA models in terms of mean relative error, mean absolute error and mean square error. Moreover, the proposed system is demonstrated to be effective, and an early warning can be alerted to remind users of repairing abnormal FDS equipment ahead of fire dangers.

The proposed system cannot only be applied to the FDS of all buildings to avoid fire hazards by monitoring and predicting the working state of the FDS, but can also be widely used in other fields, such as environmental monitoring, intelligent logistics and intelligent transportation.

This paper focuses on assembly line performance of an automotive body shop that builds body‐in‐white (BIW) assembly utilizing about 700+ process robots. These robots perform various operations such as welding, sealing, part handling, stud welding and inspection. There is no accurate tool available for the plant personnel to predict the future throughput based on plant's data. The purpose of this paper is to provide future throughput performance prediction based on plant data using Box‐Jenkins' ARMA model.

The following data were collected for five major assembly lines. First, the assembly machine‐in‐cycle time: the assembly line machines include robots that perform various functions like load, welding or sealing and unloading parts; the manual operators loading cycle time to the production fixtures. The conveyors act as buffers in between stations, and also feed to the production cells, and carry parts from station to station. The conveyors' downtime and uptime were also part of the machine‐in‐cycle time; second, the number of units produced from the beginning to the end of the assembly line; third, the number of fault occurrences in the assembly line due to various machine breakdowns; fourth, the machine availability percentage – i.e. the machine is readily available to perform its functions (the machine blocked upstream (starving) and blocked down (downstream) state is considered here); fifth, the actual efficiency of the machine measured in percentage based on output percentage; sixth, the expected number of units at designed efficiency.

In summary, this research paper provided a systematic development of a forecast model based on Box‐Jenkin's ARMA methodology to analyze the complex assembly line process performance data. The developed ARMA forecast models proved that the future prediction can be accurately predicted based on the past plant performance data. The developed ARMA forecast models predicted the future throughput performance within 99.52 percent accuracy. The research findings were validated by the actual plant performance data.

In this study, the automotive assembly process machines (robots, conveyors and fixtures) production data were collected, statistically analyzed and verified for viable ARMA model verification. The verified ARMA model has been used to predict the plant future months' throughput with 99.52 percent accuracy, based on the plant production data. This research is unique because of its practical usage to improve production.

The purpose of this paper is to present a novel and simple prediction model of long-term metal oxide semiconductor (MOS) gas sensor baseline, and it brings some new perspectives for sensor drift. MOS gas sensors, which play a very important role in electronic nose (e-nose), constantly change with the fluctuation of environmental temperature and humidity (i.e. drift). Therefore, it is very meaningful to realize the long-term time series estimation of sensor signal for drift compensation.

In the proposed sensor baseline drift prediction model, auto-regressive moving average (ARMA) and Kalman filter models are used. The basic idea is to build the ARMA and Kalman models on the short-term sensor signal collected in a short period (one month) by an e-nose and aim at realizing the long-term time series prediction in a year using the obtained model.

Experimental results demonstrate that the proposed approach based on ARMA and Kalman filter is very effective in time series prediction of sensor baseline signal in e-nose.

Though ARMA and Kalman filter are well-known models in signal processing, this paper, at the first time, brings a new perspective for sensor drift prediction problem based on the two typical models.

I derive the finite-sample bias of the conditional Gaussian maximum likelihood estimator in ARMA models when the error follows some unknown non-normal distribution. The general procedure relies on writing down the score function and its higher order derivative matrices in terms of quadratic forms in the non-normal error vector with the help of matrix calculus. Evaluation of the bias can then be straightforwardly conducted. I give further simplified bias results for some special cases and compare with the existing results in the literature. Simulations are provided to confirm my simplified bias results.

Value at risk (VaR) and expected shortfall (ES) are popular market risk measurements. The former is not coherent but robust, whereas the latter is coherent but less interpretable, only conditionally backtestable and less robust. In this chapter, we compare an innovative artificial neural network (ANN) model with a time series model in the context of forecasting VaR and ES of the univariate time series of four asset classes: US large capitalization equity index, European large cap equity index, US bond index, and US dollar versus euro exchange rate price index for the period of January 4, 1999, to December 31, 2018. In general, the ANN model has more favorable backtesting results as compared to the autoregressive moving average, generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) time series model. In terms of forecasting accuracy, the ANN model has much fewer in-sample and out-of-sample exceptions than those of the ARMA-GARCH model.

Cutting force prediction is pretty important for manufacture management. Thus, the purpose of this paper is to obtain the cutting force of the machining process with high efficiency and low cost. A method based on the improved auto regressive moving average (ARMA) model is proposed for cutting force predictions in milling process.

First, classification and normalization are made for initial cutting force. Second, the cutting force sequences are compressed followed singular and valid value removed. At last, the improved ARMA model is used for cutting force fit and extrapolation considered the time domain characteristics.

A series of cutting force with the spindle speed 595r/min is carried out in the research. It is showed that the mean absolute percentage error value of cutting force extrapolation results which is based on the improved model is smaller. The percentage value is approximately 5.80%. Then the root mean square error test value is only 72.49, which is smaller than that with other traditional method, such as hidden Markov model. The extrapolation results with the proposed model performed good consistency and accuracy in terms of peaks, valleys and volatility compared with the experiment results.

The proposed method that is based on the improved ARMA model can be used for cutting force predictions conveniently. And the predictions can be used for improving the qualities in milling process.

In Islamic finance (IF), the safety-first rule of investing (hifdh al mal) is held to be of utmost importance. In view of the instability in the global financial markets, the IF portfolio manager (mudharib) is committed, according to Sharia, to make use of advanced models and reliable tools. This paper seeks to address these issues.

In this paper, the limitations of the standard models used in the IF industry are reviewed. Then, a framework was set forth for a reliable modeling of the IF markets, especially in extreme events and highly volatile periods. Based on the empirical evidence, the framework offers an improved tool to ameliorate the evaluation of Islamic stock market risk exposure and to reduce the costs of Islamic risk management.

Based on the empirical evidence, the framework offers an improved tool to ameliorate the evaluation of Islamic stock market risk exposure and to reduce the costs of Islamic risk management.

In IF, the portfolio manager – mudharib – according to Sharia, should ensure the adequacy of the mathematical and statistical tools used to model and control portfolio risk. This task became more complicated because of the increase in risk, as measured via market volatility, during the financial crisis that began in the summer of 2007. Sharia condemns the portfolio manager who demonstrates negligence and may hold him accountable for losses for failing to select the proper analytical tools. As Sharia guidelines hold the safety-first principle of investing rule (hifdh al mal) to be of utmost importance, the portfolio manager should avoid speculative investments and strategies that would lead to significant losses during periods of high market volatility.