Box jenkins method of forecasting, stationary non stationary data sets

1. OPERATIONS MANAGEMENT
By-:
Er. Vaibhav Agarwal
Asst. Prof.
SOM, BBDU
Lucknow
BOX-JENKINS METHOD OF
FORECASTING

2. BOX-JENKINS METHOD OF FORECASTING
• In time series analysis, the Box–Jenkins method, named after the statisticians George Box and Gwilym
Jenkins.
• Box-Jenkins Model is a mathematical model designed to forecast data within a time series.
• Time-Series is of two types:
TIME-
SERIES
STATIONARY
SEASONAL
NON-
SEASONAL
NON-
STATIONARY
SEASONAL
NON-
SEASONAL

3. If the ACF(autocorrelation factor) of the time series values either cuts off or dies down
fairly quickly, then the time series values should be considered STATIONARY.

4. If the ACF (auto correlation factor) of the time series values either cuts off or dies down
extremely slowly, then it should be considered NON-STATIONARY.

6. • A stationary process is one whose statistical properties do not change over time.
• A non-stationary process/time-series have properties which change over time.
• The Box-Jenkins model alters the non-stationary time series to make it stationary by using the
differences between data points.
• All stationary time series can be modeled as Auto Regressive(AR) or Moving Average(MA) or
ARMA models.
• The BOX-JENKINS method applies Autoregressive Moving Average ARMA or ARIMA models
to find the best fit of a time-series model to past values of a time series.
• This allows the model to pick out trends, typically using autoregresssion, moving averages and
seasonal differencing in the calculations.

7. DEFINITION of 'Autoregressive Integrated Moving Average - ARIMA.
• A statistical analysis model that uses time series data to predict future trends.
• Box-Jenkins (ARIMA) is an important forecasting method that can yield highly accurate
forecasts for certain types of data.
• It is a form of regression analysis that seeks to predict future movements.
• It considers the random variations.
• It examining the differences between values in the series instead of using the actual data
values.
• Lags of the differenced series are referred to as “autoregressive" and lags within forecasted
data are referred to as “moving average”.

8. • This model type is generally referred to as ARIMA(p, d, q), model.
• p represents autoregressive,
• d represents integrated, and
• q represents the moving average parts of the data set.
• ARIMA modeling can take into account trends, seasonality, cycles, errors and non-
stationary aspects of a data set when making forecasts.
• A seasonal Box-Jenkins model is symbolized as ARIMA(p,d,q)*(P,D,Q), where the p,d,q
indicates the model orders for the short-term components of the model and P,D,Q
indicate the model orders for the seasonal components of the model.

9. • Box-Jenkins is an important forecasting method that can generate more accurate forecasts than
other time series methods for certain types of data.
• As originally formulated, model identification relied upon a difficult, time consuming and highly
subjective procedure.
• Today, software packages such as Forecast Pro use automatic algorithms to both decide when to use
Box-Jenkins models and to automatically identify the proper form of the model.
• Box-Jenkins models are similar to exponential smoothing models.
• Box-Jenkins models are adaptive, can model trends and seasonal patterns, and can be automated.
• Box-Jenkins models are based on autocorrelations (patterns in time) rather than a structural view of
level, trend and seasonality.
• Box-Jenkins tends to succeed better than exponential smoothing for longer, more stable data sets
and not as well for noisier, more volatile data.

10. The Box-Jenkins methodology
has four steps:
• Model Identification,
• Estimation,
• Diagnostics checking,
• Forecasting.

11. THANK YOU
REFERENCES:
1. ‘The Box-Jenkins Methodology for Time Series Models’, Theresa Hoang Diem Ngo,
Warner Bros. Entertainment Group, Burbank, CA, SAS Global Forum 2013, Paper 454-
2013.
2. https://en.wikipedia.org/wiki/Box%E2%80%93Jenkins
3. http://www.forecastpro.com/Trends/forecasting101June2012.html
4. ‘Stationary and non-stationary time series’, G. P. Nason, Chapter 11.
5. A Study of Sales Data using Box-Jenkins ARIMA Techniques, Michaelmas Term, Sample
Report, 2011.