### What is the Box-Jenkins Model?

The Box-Jenkins Model is a mathematical model designed to forecast data ranges based on inputs from a specified time series. The Box-Jenkins Model can analyze many different types of time series data for forecasting.

Its methodology uses differences between data points to determine outcomes. The methodology allows the model to identify trends using autoregresssion, moving averages and seasonal differencing to generate forecasts. Autoregressive integrated moving average (ARIMA) models are a form of Box-Jenkins model. The terms ARIMA and Box-Jenkins Model can be used interchangeably.

### Key Takeaways

- The Box-Jenkins Model is a forecasting methodology using regression studies.
- The methodology is best used as a computer-calculated forecast based on a regression of time-series data.
- It is best suited for forecasting within time frames of 18 months or less.
- Modernly ARIMA calculations are done with sophisticated tools such as programmable statistical software in R programming language.

### Understanding the Box-Jenkins Model

Box-Jenkins Models are used for forecasting a variety of anticipated data points or data ranges including business data and future security prices.

The Box-Jenkins Model was created by two mathematicians George Box and Gwilym Jenkins. The two mathematicians discussed the concepts that comprise this model in a 1970 publication "Time Series Analysis: Forecasting and Control."

Estimations of the parameters of the Box-Jenkins Model can be very complicated. Therefore, similar to other time-series regression models, the best results will typically be achieved through the use of programmable software. The Box-Jenkins Model is also generally best suited for short-term forecasting of 18 months or less.

### Box-Jenkins Methodology

The Box-Jenkins Model is one of several time series analysis models a forecaster will encounter when using programmed forecasting software. In many cases the software will be programmed to automatically use the best fitting forecasting methodology based on the time series data to be forecasted. Box-Jenkins is reported to be a top choice for data sets that are mostly stable with low volatility.

The Box-Jenkins Model forecasts data using three principles, autoregression, differencing and moving average. These three principles are known as p, d and q respectively. Each principle is used in the Box-Jenkins analysis and together they are collectively shown as ARIMA (p, d, q).

The autoregression (p) process tests the data for its level of stationarity. If the data being used is stationary it can simplify the forecasting process. If the data being used is non-stationary it will need to be differenced (d). The data is also tested for its moving average fit which is done in part q of the analysis process. Overall, initial analysis of the data prepares it for forecasting by determining the parameters (p, d and q) which are applied to develop a forecast.

### Forecasting Stock Prices

One use for Box-Jenkins Model analysis is to forecast stock prices. This analysis is typically built out and coded through R software. The analysis results in a logarithmic outcome which can be applied to the data set to generate the forecasted prices for a specified period of time in the future.