Notes on the Treasury Yield Curve Forecasts. October Kara Naccarelli
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1 Notes on the Treasury Yield Curve Forecasts October 2017 Kara Naccarelli Moody s Analytics has updated its forecast equations for the Treasury yield curve. The revised equations are the Treasury yields for the one-month, three-month, six-month, one-year, two-year, three-year, five-year, seven-year, 20- year and 30-year tenors (FRTB1MQ.IUSA, FRTB3M.IUSA, FRTB6M.IUSA, FRTB1Y.IUSA, FRTB2Y.IUSA, FRTB3Y.IUSA, FRTB5Y.IUSA, FRTB7Y.IUSA, FRTB20Y.IUSA, FRTB30Y.IUSA). Those yield curve variables are key drivers of other variables in the financial block of Moody s Analytics macro model such as yields on corporate bonds, Libor and swap rates. To model the yield curve, we use two key tenors a short-term rate and a long-term rate to pin down overall shape of the curve, and we express the remaining tenors as a linear combination of adjacent tenors. The large literature on interest rate forecasting has demonstrated that changes in the yields of a short-term and long-term tenor (which combined describe the level and slope of the yield curve) account for the vast majority of the variability in the shape of the yield curve over time. Expressing yields for other tenors as a weighted average of adjacent tenors helps to ensure that the shape of the yield curve is well-behaved. In particular, yields of one tenor should be close to yields of adjacent tenors, and yields should generally increase with tenor when the yield curve overall is upward sloping. The adjacent tenor specification also helps to make the shape of the yield curve stay well-behaved in alternative macro scenarios when intermediate tenors are made exogenous. With the latest revision, the forecast equations have changed in the following key ways. 1. The three-month replaces the one-month as the key short-term tenor. In the new specification, the three-month yield is specified as a linear combination of the federal funds rate and the CBOE Volatility Index for the S&P 500 plus a constant. The one-month yield is specified as a linear function of the three-month yield. One reason that the threemonth bill rate is preferable as the key tenor is that it tends to be more focal in federal policy deliberations than the one-month rate. For example, the macro scenarios specified by the Federal Reserve for stress-testing financial institutions specify exogenous paths for the three-month rate and that is simpler to implement when the three-month is the key tenor. 2. We simplify the equations for the six-month, two-year and 20-year yields by removing lag terms. Those lags can cause implausible forecasts of yields (particularly relative to adjacent tenors) in the Moody s Analytics baseline and alternative scenarios. 3. With the exception of the end points of the curve (the one-month and the 30-year), we impose a restriction that the weights on adjacent tenors sum to one in each equation for the non-key tenors. For example, the yield on the sixmonth bill is expressed as a weighted average of the yield on the three-month tenor with a weight of 68% and the yield on the one-year tenor with a weight of 32% plus a constant 6 basis points. These restrictions help to make the yield curve retain a plausible shape in alternative scenarios. Together, these changes simplify the equations significantly and make them more consistent, which results in better behaved forecasts in the baseline and alternative scenarios at the small price of a modest increase of in-sample and out-of-sample forecast error for some of the short-term tenors. New equation specifications Dependent variable: FRTB1MQ_US Date: 09/28/17 Time: 16:27 Sample (adjusted): 2001Q3 2017Q2 Included observations: 64 after adjustments Variable Coefficient Std. error t-statistic Prob. C FRTB3M_US R-squared Mean dependent var
2 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRTB3M_US Date: 09/28/17 Time: 16:29 Sample (adjusted): 1954Q3 2017Q2 Included observations: 252 after adjustments C FRFED_US FSPVOL_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRTB6M_US-FRTB3M_US Date: 09/28/17 Time: 16:31 Sample (adjusted): 1958Q4 2017Q2 Included observations: 235 after adjustments C FRGT1Y_US-FRTB3M_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT1Y_US-FRTB6M_US Date: 09/28/17 Time: 16:33 Sample (adjusted): 1976Q2 2017Q2 Included observations: 165 after adjustments
3 C FRGT2Y_US-FRTB6M_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT2Y_US-FRGT1Y_US Date: 09/28/17 Time: 16:34 Sample (adjusted): 1976Q2 2017Q2 Included observations: 165 after adjustments C FRGT3Y_US-FRGT1Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT3Y_US-FRGT2Y_US Date: 09/28/17 Time: 16:35 Sample (adjusted): 1976Q2 2017Q2 Included observations: 165 after adjustments C FRGT5Y_US-FRGT2Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT5Y_US-FRGT3Y_US Date: 09/28/17 Time: 16:37 Sample (adjusted): 1969Q3 2017Q2 Included observations: 192 after adjustments
4 C FRGT7Y_US-FRGT3Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT7Y_US-FRGT5Y_US Date: 09/28/17 Time: 16:39 Sample (adjusted): 1969Q3 2017Q2 Included observations: 192 after adjustments C FRGT10Y_US-FRGT5Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT20Y_US-FRGT10Y_US Date: 09/28/17 Time: 16:39 Sample (adjusted): 1993Q4 2017Q2 Included observations: 95 after adjustments C FRGT30Y_US-FRGT10Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT30Y_US Date: 09/28/17 Time: 16:40
5 Sample (adjusted): 1993Q4 2017Q2 Included observations: 95 after adjustments C FRGT20Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Mnemonics referenced in the above equation, for example FET, can be defined using the Mnemonic 411 feature on DataBuffet. Please contact Help@economy.com for assistance.
6 Previous equation specifications Dependent variable: FRTB1MQ_US Date: 09/24/15 Time: 14:23 Sample: 2001Q3 2015Q2 Included observations: 56 FRFED_US FSPVOL_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Dependent variable: FRTB3M_US Date: 09/24/15 Time: 14:21 Sample: 2001Q3 2015Q2 Included observations: 56 C FRTB1MQ_US FRTB6M_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRTB6M_US Date: 09/24/15 Time: 14:22 Sample: 1962Q2 2015Q2 Included observations: 213 C FRTB3M_US FRGT1Y_US(-1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion
7 Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT1Y_US Date: 03/21/16 Time: 12:24 Sample (adjusted): 1976Q2 2015Q4 Included observations: 159 after adjustments FRTB6M_US FRGT2Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Dependent variable: FRGT2Y_US Sample: 1976Q3 2013Q1 Included observations: 147 C FRGT1Y_US FRGT3Y_US(-1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT3Y_US Sample: 1976Q3 2013Q1 Included observations: 147 C FRGT2Y_US FRGT5Y_US
8 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT5Y_US Sample: 1969Q3 2013Q1 Included observations: 175 C FRGT3Y_US FRGT7Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT7Y_US Sample: 1969Q3 2013Q1 Included observations: 175 C FRGT5Y_US FRGT10Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Dependent variable: FRGT20Y_US Method: ARMA conditional least squares (Marquardt - EViews legacy) Sample: 2006Q2 2013Q1 Included observations: 28 Convergence achieved after 7 iterations
9 FRGT10Y_US FRGT30Y_US AR(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Inverted AR Roots.62 Dependent variable: FRGT30Y_US Sample: 1977Q2 2013Q1 Included observations: 144 C FRGT10Y_US R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Mnemonics referenced in the above equation, for example FET, can be defined using the Mnemonic 411 feature on DataBuffet. Please contact Help@economy.com for assistance.
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