Analyzing Federal Reserve Board Interest Rate Yield Curve Data With JMP® Matthew Flynn, PhD, Data Science - Head of Machine Learning

Introduction This presentation walks through retrieving current interest rate data from www.FederalReserve.gov, then explores the dramatic drop in short-term rates after the 2009 recession. We use JMP scripting to automate the process of retrieving publically available data history. Next we explore and transform the data in JMP to generate interactive visualization and analysis reports. Next we identify common factors within the yield curve data via Principal Components to identify parallel shifts, twists and butterfly effects. We then model the yield curve data via the Time Series and Nonlinear platforms to estimate polynomial and Nelson-Siegel-Svensson functions for forecast interest rates. In short, we demonstrate that JMP can be an attractive and powerful analysis platform for yield curve modeling.   We will describe an example JMP JSL application to retrieve interest rate yield curve data from the U.S. Federal Reserve Board web site (www.federalreserve.gov), explore that data via several data visualizations then fit several non-linear models to that historical data.

Outline of task steps Connect to www.federalreserve.gov and download yield data from 2007 forward. Examine missing data patterns and eliminate several rows with missing data (holidays). Define new columns as lags and spread (short term (1 Month) to long term (30 year)). Graph the yield curve over time. Compute Principal Components. Extract the PC loading matrix from the Principal Components report into a new data table. Graph the first three Principal Components vs. term – highlighting three so called factors – “parallel shift”, “twist”, and “butterfly”. Build a scatterplot matrix of Principal Components. Send the data from JMP to R and repeat the three factor plot. Model the yield curve with the JMP nonlinear platform.

The set of scripts are organized and presented in a JMP Journal.

  The first script connects to www.federalreserve.gov and downloads interest rate yield data from 2007 forwards. We also examine missing data patterns and eliminate several rows with missing data (holidays).

After eliminating missing data rows

Define new columns as lags and spread (short term (1 Month) to long term (30 year)).

Graph Builder makes it simple to graph the yield curve over time.

We next compute Principal Components We next compute Principal Components. A large fraction of the total variability can be covered in the first three PCs.

We next extract the PC loading matrix from the Principal Components report into a new data table.

Graph the first three Principal Components vs Graph the first three Principal Components vs. term – highlighting three so called factors – “parallel shift”, “twist”, and “butterfly”.

Build a scatterplot matrix of Principal Components.

Send the data from JMP to R and repeat the three factor plot.

Along the way, we’ll plot the yield curve over time in a 3-D plot.

Another way to see the change in the curve over time is via a yield curve plot matrix.

We are heading to model the yield curve with the JMP nonlinear platform. Here we have added formulas for the several nonlinear models we will fit. .

Model the yield curve with the JMP nonlinear platform Model the yield curve with the JMP nonlinear platform. Here we have optimized one of the yield curve functions

Citations Robert R. Bliss (1997): Testing Term Structure Estimation Methods. Advances in Futures and Options Research, 9 197–232. Bank for International Settlements (2005): Zero-Coupon Yield Curves: Technical Documentation. BIS Papers, No. 25. F.X. Diebold and C. Li (2006): Forecasting the Term Structure of Government Bond Yields. Journal of Econometrics,130:337–364. Robert Ferstl and Josef Hayden (2010): Zero-Coupon Yield Curve Estimation with the Package termstrc, Journal of Statistical Software, 36(1), 1-34. http://www.jstatsoft.org/v36/i01/ J. Huston McCulloch (1971): Measuring the Term Structure of Interest Rates. The Journal of Business, 44 19–31. J. Huston McCulloch (1975): The Tax-Adjusted Yield Curve. The Journal of Finance, 30 811–830. Charles R. Nelson and Andrew F. Siegel (1987): Parsimonious Modeling of Yield Curves. The Journal of Business,60(4):473–489. Michiel De Pooter (2007): Examining the Nelson-Siegel Class of Term Structure Models: In-Sample Fit versus Out-of-Sample Forecasting Performance, Working paper Lars E.O. Svensson (1994): Estimating and Interpreting Forward Interest Rates: Sweden 1992 -1994. Technical Reports 4871, National Bureau of Economic Research.