Time Series Filtering App

• Demonstrates the use of a band pass filter on time series data
• Visualizes the impact of bound changes on the trend and cycle components
• Multiple dataset with different properties are available in app

Filter Basics

• Many filters have been developed to decompose trend and cyclical movements from time series data
• The Hodrick-Prescott filter has been used extensively in economics. Altternatives include Christiano-Fitzgerald and Baxter-King
• The Christiano-Fitzgerald filter uses a band pass that filters cycles that occur in a specific range of frequencies
• The Christiano-Fitzgerald produces and additive decomposition: \[ y_{t} =g_t + c_t \]

Trend Component

Cycle Component

The cycle component for the "AirPassengers" dataset can be extracted with the following code:

cfModel <- cffilter(AirPassengers, pl=3, pu=24)

plot(as.zoo(cfModel$cycle), main="", ylab="", xlab="")
grid()

Limitations

• The tool uses stock datasets. Adding the ability to upload would allow the tool to be used for actual analysis not just a pedantic tool.
• The lower end of the band pass cannot exceed the upper bound. This tool sets a maximum of 12 on the lower bound and a minimum of 13 on the upper bound to enforce this. A more flexible tool would allow a greater range of inputs on each.