Albert Lee CHUNDepartment of Finance
Copenhagen Business School
Forecasting Interest Rates and Inflation: Blue Chip Clairvoyants or
Econometrics?
Albert Lee CHUN Forecasting Interest Rates and Interest Rates 2009 ESSM
Forecasting Interest Rates and Interest Rates 2009 ESSM
• Accurate forecasts of bond yields and inflation are of interest to traders, investors, portfolio managers and monetary policy makers (central banks).
• There are many ways of obtaining forecasts:
- Econometric methods
- Financial Market Based forecasts
- Surveys! Blue Chip Financial Forecasts
Which forecasting model(s) generate(s) the best forecasts of interest rates and inflation?
Motivation
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
How do the surveys (Blue Chip Financial Forecasts) compare with standard econometric forecasting models?
Many studies look at the mean or consensus survey forecast. Is individual-level data important?
If so, then does there exist an individual forecaster that consistently makes the best forecasts?
Moreover, can we improve econometric forecasting by shrinking the parameters? (Qrinkage)
Are the characteristics of interest rate forecasts different from inflation forecasts?
Which Forecasting Model is the Best?
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
1. Evaluation of forecasting performance of a new data set of individual survey forecasters.
2. Application of shrinkage to econometric forecasting models, including the Diebold and Li class of models.
Main Innovations
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Summary of Findings
•Futures contracts are the best for very short horizon forecasts of the federal funds rate.
•Individual survey forecasters do well at short horizon forecasts of short-medium maturity yields.
•Qrinkage version of Diebold-Li with VAR(3) dynamics does the best at long horizon forecasts of short-medium maturity yields.
•Surveys not great at forecasting long yields as the Qrinkage class of AR(2) models dominate.
•Individuals forecasters do the best at forecasting inflation.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Outline for Today
• Introducing the Blue Chip Financial Forecasts
• Econometric benchmarks and Qrinkage
• Empirical Results
• Conclusion and Future Research
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
•Monthly survey of professional analysts (many are PhD economists) at investment banks, financial firms, consulting groups, etc.
•Variables forecast: Fed Funds Rate, entire set of CMT Treasuries (bond yields), CPI inflation, GDP deflator inflation and GDP growth.
Blue Chip Financial Forecasts
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Blue Chip Financial Forecasts
•BCFF are gathered around the 25th of the month, published on the 1st of the following month.
•Forecast horizons range from the current quarter to 5 quarters ahead.
•Forecasts are for the AVERAGE over a calendar quarter - i.e., 1st , 2nd , 3rd or 4th calendar quarter of the year. The monthly frequency of the data induces a time varying forecast horizon.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Blue C
hip Financial F
orecasts
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
• I obtained the data from the publisher and extracted the time series of individual-level forecasts for each participant from 1993-2006.
•Approximately 40-50 forecasters take part each month.
• Over 100 different forecasters participated over the period 1993-2006.
•However, only 13 + 8 = 21 individual forecasters participated consistently over this period.
•Very unique data! This is first and only study to use individual-level data from the BCFF over the period 1993-2006.
Individual Time Series Data
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
13 company-specific models
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
plus 8 individual models
for a total of 21 Blue Chip forecasting models
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Why Study BCFF Survey Forecasts?
The BCFF are the only known survey data set with forecasts of the complete term structure of interest rates, including the funds rate and the macroeconomic variables that influence them.
Several recent academic papers use the BCFF data set:
Chun (2005), Kim and Orphanidies (2005)
Chernov and Mueller (2007), Piazessi and Schneider (2008) , Orphanidies and Wei (2008), Ichiue and Yuyama (2007), Grishchenko and Huang (2008)
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Competing Clairvoyants• Autoregressive models with rolling and recursive
estimation windows, using 1, 2 and 3 lags.• Vector Autoregressive models with rolling and
recursive estimation windows, using 1, 2 and 3 lags.
• Dynamic Nelson and Siegel model of Diebold and Li extended to all the above dynamics for the factors.
• Qrinkage versions of all the above models including the DL models, where we shrink the parameters either toward the random walk forecastor the long run mean.
Competing Econometricians
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Shrinking Univariate Forecasting Models
AR(p)
Shrink estimated coefficients toward 0 using Qrinkage.
1 0 0 0
^ ^ ^ ^
By shrinking β1 towards 1 and the other β’s toward 0, we are shrinking toward to the long run mean.
0 0 0 0
^ ^ ^ ^
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Shrinking Univariate Forecasting Models
AR(p)
Shrink estimated coefficients toward 0 using Qrinkage.
0 1 0 0
^ ^ ^ ^
By shrinking βo towards 1 and the other β’s toward 0, we are shrinking toward to the random walk forecast.
0 0 0 0
^ ^ ^ ^
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
More generally...
AR(p)
α 1 - α 0 0
^ ^ ^ ^
By shrinking βo towards α, β1 toward1- α, and the other β’s toward 0,
we are shrinking toward α LRM + (1- α) RW.
.
0 0 0 0
^ ^ ^ ^
Shrink to α LRM + (1- α) RW
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
• Criteria-based Shrinkage or Qrinkage forecasts were developed by Peter Reinhard Hansen.
• In-sample models will tend to over-fit the data, leading to out-of-sample under-fit.
• Peter’s Working paper: “In-Sample and Out-of-Sample Fit: Their Joint Distribution and its Implications for Model Selection”
• Qrinkage adjusts for the in-sample over-fit in an optimal way, Hansen (2008).
• Quick intuition: Shrink estimated parameters toward 0.
Criteria-based Shrinkage (Qrinkage)
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
• Peter Reinhard Hansen (2006)
Criteria-based Shrinkage (Qrinkage)
Shrink toward 0. Larger the t (more data, greater regressor variance, less noise), the less shrinkage.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Dynamic Nelson Siegel Models
• Dielbold and Li (2005) generalize the Nelson and Siegel framework and allow for dynamic factors.
• 3 factors can capture dynamic movements in bond yields
•We extend the dynamics of the factors B1, B2 and B3, by allowing for additional lags.
• My theoretical and methodological contribution is to shrink the parameters using Qrinkage!
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Forecasting Interest Rates and Interest Rates 2009 ESSM
• Following Hansen, Lund and Nason (2003, 2005) we use MCS p-values as a criteria for judging model performance.
• Iterative procedure removes worst performing model from the set until the test accepts the null of equal predictive ability.
• Poor information content of the data leads to large MCS.
• Generates MCS p-values for each forecasting model – the largest level of the test such that the null of equal predictive ability is not rejected.
Model Confidence Set P-values
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Summary of Forecasting Performance
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Fed Funds Rate
1) Fed Funds Futures forecast (at 1 and 2 months ahead),
2) In general, for short horizon forecasts, the surveys do well.
3) For long horizon forecasts, the best model is the Qrinkage version of the Diebold-Li model with VAR(3) dynamics and a 5 year rolling window, that shrinks toward the long run mean.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSMAlbert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Fed Funds Rate
RMSFE MCS p-values
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
MCS p-values: Fed Funds Rate
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
MCS p-values: Fed Funds Rate
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Short-Medium Yields
For short horizon forecasts, individual survey participants are the best.
For long horizon forecasts, the Qrinkage version of the Diebold-Li model with VAR(3) dynamics and a 5 year rolling window, that shrinks toward the long run mean, is the best performer.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSMAlbert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSMAlbert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Long Maturity Yields
Dominated by Qrinkage AR(2) models with a 5-year rolling window.
Shrinking towards the long run mean seems to be most useful for longer horizon forecasts.
Shrinking toward the random walk forecast only useful for very short horizons.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSMAlbert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Inflation
• Surveys including the mean forecaster do well at forecasting inflation.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
MCS-pvals: CPI Inflation
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Impact of Transient Forecasters
RMSFE M21 – RMSFE MHL
Albert Lee CHUN
Transient forecasters help at forecasting inflation, but add noise to interest rate forecasts.
Forecasting Interest Rates and Interest Rates 2009 ESSM
Summary
•Futures contracts are the best for very short horizon forecasts of the federal funds rate.•Individual survey forecasters do well at short horizon forecasts of short-medium maturity yields.•Qrinkage version of Diebold-Li with VAR(3) dynamics does the best at long horizon forecasts of short-medium maturity yields.•Surveys not great at forecasting long yields as Qrinkage AR2 models dominate.•Individuals forecasters do the best at forecasting inflation.
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
• What about no-arbitrage forecasts? In my view, this is only a second order effect. Can one shrink the parameters for forecasting?
• Explore forecast combinations using Qrinkage.• Can we find an economically motivated loss
function, by construction a bond portfolio as in work in progress by Carriero and Giacomini, or find some trading based criteria?
• Why? Why do surveys do well in certain cases?
In Progress
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Jeff Thredgold
James W. Coons
Irwin L. Kellner
A Few of Our Distinguished Forecasters
Joel Naroff
Albert Lee CHUN
Forecasting Interest Rates and Interest Rates 2009 ESSM
Thank you☺☺☺☺
Albert Lee CHUN
