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Forecast uncertainty and forecast intervals . Mean Squared Forecast Error. Three ways to estimate the RMSFE . Pseudo out-of-sample forecasting. Constructing forecast intervals . Example #1: the Bank of England “ Fan Chart ” , 11/05 . - PowerPoint PPT Presentation
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Forecast uncertainty and forecast intervals
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Mean Squared Forecast Error
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Three ways to estimate the RMSFE
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Pseudo out-of-sample forecasting
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Constructing forecast intervals
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Example #1: the Bank of England “Fan Chart”, 11/05
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Example #2: Monthly Bulletin of the European Central Bank, Dec. 2005, Staff macroeconomic projections
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Example #3: Fed, Semiannual Report to Congress, 7/04
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Lag Length Selection Using Information Criteria
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Bayes Information Criterion (BIC)
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Akaike Information Criterion (AIC)
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Example: AR model of inflation
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Generalization of BIC to multivariate (ADL) models
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Nonstationarity from Trends
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1. What is a trend?
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Deterministic and stochastic trends
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Deterministic and stochastic trends
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Deterministic and stochastic trends
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Deterministic and stochastic trends
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Stochastic trends and unit roots
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Unit roots in an AR(2)
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Unit roots in an AR(2), ctd.
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Unit roots in the AR(p) model
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Unit roots in the AR(p) model, ctd.
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2. What problems are caused by trends?
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Log Japan gdp (smooth line) and US inflation (both rescaled), 1965-1981
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Log Japan gdp (smooth line) and US inflation (both rescaled), 1982-1999
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3. How do you detect trends?
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DF test in AR(1), ctd.
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Table of DF critical values
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The Dickey-Fuller test in an AR(p)
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When should you include a time trend in the DF test?
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Example: Does U.S. inflation have a unit root?
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Example: Does U.S. inflation have a unit root?
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DF t-statstic = –2.69 (intercept-only):
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4. How to address and mitigate problems raised by trends
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Summary: detecting and addressing stochastic trends
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Nonstationarity from breaks (changes) in regression coefficients
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Case II: The break date is unknown
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The Quandt Likelihod Ratio (QLR) Statistic (also called the “sup-Wald” statistic)
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The QLR test, ctd.
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Has the postwar U.S. Phillips Curve been stable?
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QLR tests of the stability of the U.S. Phillips curve.
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Assessing Model Stability using Pseudo Out-of-Sample Forecasts
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Application: U.S. Phillips Curve
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POOS forecasts of Inf using ADL(4,4) model with Unemp
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POOS forecasts of Inf using ADL(4,4) model with Unemp
