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The assignment makes use of quarterly US inflation data and various predictor variables in the Final_2017_data.xlsx file available on the website. Column A shows the quarterly date, columns B and C show the quarterly price index (B) and the resulting annualized quarter-on-quarter inflation rate (column C). Columns D and E show mean forecasts from the Survey of Professional Forecasters (SPF) generated one quarter earlier (SPF(t|t-1) in column D) and two quarters earlier (SPF(t|t-2) in column E). For example, 3.16% in cell D5 is the inflation forecast for Q1, 1969, generated in Q4 1968, while 2.80% in cell E5 is the forecast of inflation for Q1, 1969, generated two quarters earlier in Q3 1968.Columns F and G show the corresponding one- and two-quarter-ahead Greenbook forecasts of inflation. These are the forecasts used by the Federal Reserve and are only available with a delay of 5 years and so end in 2011Q1.
The file also contains data on the 3-month T-bill rate (column I), the five-year Treasury bond yield (J), the unemployment rate (K), and the S&P500 stock price index (column L).
For all questions, you can assume a squared error loss function. You can compute one-quarter-ahead forecast errors by subtracting the one-quarter-ahead forecasts (column D for SPF, column F for Green book) from the actual inflation rate (column C).
To answer questions 1-5, use the sample 1969Q1-2011Q1.
1. How accurate were the one-quarter-ahead SPF and Green book inflation forecasts (columns D and F)? For each of the forecasts, report estimates of predictive accuracy.
Deliverables:
Brief explanation of measures of predictive accuracy
Estimated values of measures of predictive accuracy
2. Evaluate if the one-quarter-ahead SPF and Green book inflation forecasts are optimal under MSE loss. Use graphical plots to convey a sense of forecasting performance and evaluate forecast optimality more formally by testing for bias and serial correlation in the forecast errors.
Deliverables:
Graphics: plots of forecast errors, scatter plots (forecast vs realized value)
Explanation of statistical tests of bias, optimality (Mincer-Zarnowitz)
Regression estimates and tests
Interpretation of empirical results
3. Which forecasts were most accurate during the sample, the SPF or the Greenbook forecasts? Explain how you can formally test which of those forecasts is most accurate and report the outcome of such a test. Does one forecast dominate the other?
Deliverables:
Description and explanation of tests
Regression estimates, test statistics
Interpretation of empirical results
4. Is there evidence of instability in the forecasting performance of the SPF forecasts during the sample or in the relative forecast accuracy of the SPF versus the Greenbook forecasts?
Deliverables:
Discussion of instability tests
Results from empirical tests and/or graphical analysis
5. Are the one-quarter-ahead SPF forecasts in column D more accurate than the two-quarter-ahead SPF inflation forecasts in column E? How can you test formally if this holds?
Deliverables:
Explanation of test
Empirical findings and interpretation of results
Questions 6-10 use the out-of-sample period 1980Q1-2011Q1.
6. Assess whether combining the one-quarter-ahead Greenbook and SPF forecasts leads to better overall out-of-sample forecasting performance over the period 1980Q1-2011Q1.
Deliverables:
Explanation of combination method
Empirical performance results for combination
Interpretation of results
7. Next, using lagged values of inflation and any of the predictor variables listed in columns I-L, estimate time-series models and use them to generate a series of out-of-sample inflation forecast for the period 1980Q1-2011Q1. Specifically, generate one-step-ahead forecasts recursively by using data up to 1979Q4 to select and estimate a model and generate forecasts for 1980Q1. Next, add data for 1980Q1, select and re-estimate a forecasting model, and predict inflation for 1980Q2. Continue this way up to 2011Q1. Note that your preferred forecasting model may change over time. Show graphs of your time-series forecasts and evaluate their predictive performance and optimality.
Deliverables:
Explanation of model selection - which variables get selected and how often?
Graphical evaluation of time-series forecasts
Empirical estimates of forecast accuracy
Forecast optimality tests (Mincer-Zarnowitz)
Interpretation of results
8. Evaluate if your time-series forecasts from question 7are significantly more or less accurate than the SPF and Greenbook forecasts over the period 1980Q1-2011Q1.
Deliverables:
Explanation of tests
Empirical results and interpretation of findings
9. Use the time-series model from question 7 to generate out-of-sample 90% interval forecasts for the period 1980Q1-2011Q1. State and motivate any assumptions made to generate the 90% interval forecasts and evaluate if they are correctly specified.
Deliverables:
Description of methodology used to generate the 90% interval forecasts
Evaluation of interval forecasts
Empirical findings and interpretation of results
10. Use the time-series model from question 7 to generate out-of-sample density forecasts for the period 1980Q1-2011Q1. State and motivate any assumptions made to generate the forecasts and evaluate if the density forecasts are correctly specified.
Deliverables:
Description of methodology used to generate the density forecasts
Evaluation of density forecasts
Empirical findings and interpretation of results
Attachment:- Assignment.rar