ARMA model

This study aims to develop a stochastic framework of model to forecast future sales for pharmaceutical industry. In this regard, the study focuses on Merck Pharmaceutical monthly sales data. This study examines the Sale forecasting models. The study includes monthly data published in the annual reports of the company from Jan. 2008 to Dec. 2012.The time series diagram shows unequal means over the time period that suggests the data is stationary. Having transformed the data, ARMA (1, 1) model is applied which shows that there will be increase
in sales by $6.784m given that in the last month sales were $1bn. On the contrary, last month’s residual has an
adverse effect on current month sales up to the extent of $432.942m. In this study AR (1) and MA (1) both the processes are significant at 1%.

This article applied GARCH model instead AR or ARMA model to compare with the standard BP and SVM in forecasting of the four international including two Asian stock markets indices.These models were evaluated on five performance metrics or criteria. Our experimental results showed the superiority of SVM and GARCH models, compared to the standard BP in forecasting of the four international stock markets indices.

In this paper, we exactly quantify the bullwhip effect, the variance amplification in replenishment orders, for cases of stochastic demand and stochastic lead time in a simple two-stage supply chain with one supplier and one retailer. In most of the previous research, the impact of order lead time on the bullwhip effect in supply chains with pre-specified demand processes is investigated mostly for cases of deterministic lead time. In this paper, we deal with a first-order autoregressive, AR(1), demand process and investigate the behavior of a measure for the bullwhip effect with respect to autoregressive coefficient and stochastic order lead time. Extension to a mixed first-order autoregressive-moving average, ARMA(1,1), demand process is also considered.

Time series of streamflow plays an important role in planning, design and management of water resources system. In the event of non availability of a long series of historical streamflow record, generation of the data series is of utmost importance. Although a number of models exist, they may not always produce satisfactory result in respect of statistics of the historical data. In such event, artificial neural network (ANN) model can be a potential alternative to the conventional models. Streamflow series, which is a stochastic phenomenon, can be suitably modeled by ANN for its strong capability to perform non-linear mapping. An ANN model developed for generating synthetic streamflow series of the Pagladia River, a major north bank tributary of the river Brahmaputra, is presented in this paper along with its comparison with other existing models. The comparison carried out in respect of five different statistics of the historical data and synthetically generated data has shown that among the different models, viz., autoregressive moving average (ARMA) model, Thomas-Fiering model and ANN model, the ANN based model has performed better in generating synthetic streamflow series for the Pagladia River.

The purpose of this paper is twofold. Firstly, to investigate the merit of estimating probability density functions rather than level or classification estimations on a one- day-ahead forecasting task of the silver time series. This is done by benchmarking the Gaussian mixture neural network model (as a probability distribution predictor) against two other neural network designs representing a level estimator

Accurate prediction of lake-level changes is a very important problem for a wise and sustainable use. In recent years significant lake level fluctuations have occurred and can be related to the climatic change. Such a problem is crucial to the works and decisions related to the water resources and management. This study is aimed to predict future lake levels during hydrometeorological changes and anthropogenic activities taking place in the Lake Eğirdir which is the most important water storage of Lake Region, one of the biggest fresh water lakes of Turkey. For this aim, recurrent neural network (RNN), adaptive network-based fuzzy inference system (ANFIS) as prediction models which have various input structures were constructed and the best fit model was investigated. Also, the classical stochastic models, auto-regressive (AR) and auto-regressive moving average (ARMA) models are generated and compared with RNN and ANFIS models. The performances of the models are examined with the form of numerical and graphical comparisons in addition to some statistic efficiency criteria. The results indicated that the RNN and ANFIS can be applied successfully and provide high accuracy and reliability for lake-level changes than the AR and the ARMA models. Also it was shown that these stochastic models can be used in the lake management policies with the acceptable risk.

This paper considers estimation of the parameters for the fractionally integrated class of processes known as ARFIMA. We consider the small sample properties of a conditional sum-of-squares estimator that is asymptotically equivalent to MLE. This estimator has the advantage of being relatively simple and can estimate all the parameters, including the mean, simultaneously. The simulation evidence we present indicates that estimation of the mean can make a considerable difference to the small sample bias and MSE of the other parameter estimates.