**Box Jenkins (B-J) Model Definition**

The Box-Jenkins Model is a mathematical model used for forecasting of data following specified time series. This model reflects predictable cycles, trends and patterns of time series data. The Box-Jenkins Model analyses and accurately forecasts diverse time series data for a specified time, usually short-termed.

The outcomes or results of the analysis of the Box-Jenkins model are dependent on the divergences between data points or the time series data. ARIMA (Autoregressive integrated moving average) models are forms of Box-Jenkins model. Both models can be used interchangeably, the Box-Jenkins model uses seasonal differences to pick out trends and predictable patterns in generating forecasts.

**A Little More on What is the Box-Jenkins Model**

The Box-Jenkins Model was first discussed in 1970, in a publication titled; “Time Series Analysis: Forecasting and Control.” It was named after two mathematicians who created this model, they are George Box and Gwilym Jenkins.

This model is used for forecasting of time series data, that is date from specified time. The data forecast can be business data, stock prices and even future security data. It is best used for short-term forecasting of time series data of 18 months and below.

The Box-Jenkins model uses using autoregression model and carries out forecasting using programmed software.

The Box-Jenkins Model is most suitable for data and are stable and less vulnerable. Due to complications in the estimation of the parameters of the Box-Jenkins Model, forecast is done using programmed software. The software is automatic and can be used in the analysis of different types of time series data and presenting their outcomes. Three principles, p, d and q which mean autoregression, differencing and moving average respectively are the principles of forecast that the Box-Jenkins Model uses.

The autoregression (p) principle tests for immobility or stationarity in time series data while the differencing (D) principle tests for the differences between the data. The moving average (q) of the data is also tested before the outcome of the analysis can be determined.

**Forecasting Stock Prices**

Using the R software, the Box-Jenkins model is an effective mathematical model that forecasts stock prices. It can also analyze other business related data and forecast future security prices. The results or outcomes of the analysis conducted with the Box-Jenkins can generate forecasted prices for stocks in future time over a specified period of time.

**References for Box Jenkins Models**

- https://www.investopedia.com/terms/b/box-jenkins-model.asp
- https://en.wikipedia.org/wiki/Box–Jenkins_method
- http://www.businessdictionary.com/definition/Box-Jenkins-B-J-models.html

**Academic Research on Box Jenkins Model **

Refined instrumental variable methods for identification of LPV Box–Jenkins models, Laurain, V., Gilson, M., Tóth, R., & Garnier, H. (2010). *Automatica*, *46*(6), 959-967.

Least squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data, Liu, Y., Wang, D., & Ding, F. (2010). *Digital Signal Processing*, *20*(5), 1458-1467.

Two-stage parameter estimation algorithms for Box–Jenkins systems, Ding, F., & Duan, H. (2013). *IET Signal Processing*, *7*(8), 646-654.

A Comparison of Box—Jenkins and objective methods for determining the order of a non‐seasonal ARMA Model, Beveridge, S., & Oickle, C. (1994). *Journal of Forecasting*, *13*(5), 419-434.

The superiority of analyst forecasts as measures of expectations: Evidence from earnings, Brown, L. D., & Rozeff, M. S. (1978). *The Journal of Finance*, *33*(1), 1-16.

The Box–Jenkins analysis and neural networks: prediction and time series modelling, BuHamra, S., Smaoui, N., & Gabr, M. (2003). *Applied Mathematical Modelling*, *27*(10), 805-815.

Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model, Young, P. C. (2015). *Automatica*, *52*, 35-46.

The time-series properties of annual earnings, Albrecht, W. S., Lookabill, L. L., & McKeown, J. C. (1977). *Journal of Accounting Research*, 226-244.

Box–Jenkins identification revisited—Part I: theory, Pintelon, R., & Schoukens, J. (2006). *Automatica*, *42*(1), 63-75.

Refined instrumental variable identification of continuous-time hybrid Box-Jenkins models, Young, P. C., Garnier, H., & Gilson, M. (2008). In *Identification of continuous-time models from sampled data* (pp. 91-131). Springer, London.