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Time Series Analysis and Forecasting
Presenter: Jian Cao
Time Series Overview and ARIMA Models
The presenter describes the Box-Jenkins Methodology JMP implements for time series analysis and then demonstrates the steps using sample data. He demonstrates how to build ARIMA (AutoRegressive Integrated Moving-Average) models, determine if they are adequate, compare models and modify models. He uses Gross National Product (GNP) quarterly data to show why and how to transform data using differencing, a method built into JMP to compute the differences between consecutive observations, to make the time series stationary so that it can be modeled and used for forecasting. He concludes by saving a table that includes the forecasted data.
The presenter uses monthly airline data to demonstrate how to build Seasonal ARIMA models that handle season components, data that has increasing variability over time or data with a growth pattern that requires data transformation. He explains how JMP calculates these models. He shows how to specify seasonal autoregressive order, seasonal differencing order, seasonal moving average order and the number of periods per season.
Transfer Function and X-11 Decomposition Models
The presenter explains that transfer functions are used when an intervention, such as a policy change or marketing effort, occurs during the time series during which the model will be built. The model will take into account the intervention. These models are often called ARIMA-X and ARIMA with Input Models. He uses data used to model and forecast ozone concentration where the intervention is shown as binary (1 for Yes, 0 for No), shows the Transfer Function options and uses JMP’s Interactive Forecasting to dynamically modify the forecast based on input changes. He demonstrates how to use X-11 Decomposition to remove trend and seasonal effects using the X-11 method developed by the US Bureau of the Census. He mentions the smoothing methods for quick forecasting available in JMP (simple exponential, double exponential, linear exponential, damped-trend linear exponential, seasonal exponential, and Winters method).
Resources related to the information in these videos
- Materials for introducing and applying Time Series concepts. Provided by Professor Bob Stine, Wharton School of Business, University of Pennsylvania.