Standard Scientific Research and Essays Vol 2(12): 636-648, December 2014 (ISSN: 2310-7502) http://www.standresjournals.org/journals/SSRE Research Article Forecasting ARIMA model for foreign trade statistics Habib Ahmed Elsayir Department of Mathematics, Umm AlQura University, Saudi Arabia Author E-mail:Habibsayiroi@yahoo.com Accepted 16 December 2014 --------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Time series models are applied with time series data of variables measured over time. The study focuses on examining the forecasting performance of the autoregressive Moving Average (ARMA). The study investigates the statistical properties of the series, the residuals of the ARIMA model. The model attempts to identify the trend and statistical properties. The question studied was whether information from the proposed model gave a better trade forecast. The "forecasting" situation examined really involved added useful information. The analysis of the data demonstrates that the model applied here may be useful to understand the properties of the time series model of Saudi-US foreign trade statistics. Keywords: ARIMA Models, Autocorrelation, Box-Jenkins Models, Correlograms, Identification. introduction Time series analysis accounts for the fact that data points taken over time may have an internal structure (such as autocorrelation, trend or seasonal variation) that should be account for. Time series models are used to obtain an understanding of the underlying forces and structure that produced the observed data as well as fitting a model and proceed to forecast. The purpose of this article is to provide an analysis of time series model for foreign trade statistics. In the following sections, the techniques those are useful for analyzing and identifying patterns in time series data will be introduced. As in most other analysis, in time series analysis it is assumed that the data consist of a certain pattern (usually a set of identifiable components and random noise (error), which makes the pattern difficult to identify. Some recommendations based on the results obtainable from foreign trade data are to be introduced. Early detailed discussion of the methods described in this topic can be found in Box and Jenkins (1976), Box et al.(1970), Brockwell and Davis(1996). Other related issues on time series models ,such as multivariate and univariate time series analysis ,pooling and residual analysis were found in Journal of Time Series Analysis (see Ginger et al. (2007), Jean-Marc et al. (2007), Massimiliano (2007), Elena (2007). Recently Robert et al. (2011) has covered time series analysis and its applications presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. In addition to coverage of classical methods of time series regression, ARIMA (autoregressive integrated moving averages) models, spectral analysis and state-space models. In his page, Robert (2014) has presented linear regression and time series forecasting models with focus on ARIMA models. Testing for trends in ARIMA models was also found in Rob (2014). The Model The original Box-Jenkins modeling procedure involved an iterative process of model selection, parameter estimation and model checking. According to Rob J (2001), recent explanations of the process (e.g., Makridakis et al., 1998) often add a preliminary stage of data preparation and a final stage of model application or forecasting. Consider the simple time series model, then each observation would be consisting of a constant (b) and an error component (epsilon), that is: