Alphonse contributes $345 per year at the end of each year to his pension plan. Assuming he can earn 8.46 per year from his plan, what is the total value of his account at the end of 7 years? Submit your answer in dollars and round to two decimal places (Ex. $0.00).

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Q1. You have corrected historical quarterly data on U.S. one-year Treasury bond interest rate from 1957 and 2005, including total 193 observations, with the aim to analyze the U.S. Bond, and to forecast the demand for the U.S. one-year Treasury bond. One-Year Treasury Bond Interest Rate, 1957-2005 wathy Generat 19571 19011 199301 20051 As a part of preliminary diagnostics for the time series data, you first inspect (eye-balling) the plots above for the U.S. one-year Treasury bond interest rates. (a) Inspecting the U.S. one-year Treasury bond interest rate plot and having calculated the first autocorrelation to be 0.93 for the sample period, do you suspect that U.S. one-year Treasury bond interest rate has a stochastic trend? [Note: Discuss: (1) autocorrelation; (2) the stationarity of the data; and (3) the presence of: (i) trends; and (ii) stochastic trends and a unit root that contribute to trends found in (i)] (3) In order to confirm the result shown in (a), you consider formal methods and calculate the following autocorrelation function (ACF) and the partial autocorrelation function (PACF) to test stationarity. -1 0 1 LAG AC FAC (Autocorrelation] ¡Partial Autocer) 3 4 $ Q Prob- 0.9307 0.9349 169.8 0.0000 0.0016 0.1319 322.96 0.0000 0.8513 0:1564 466.5 0.0000 0.7959 -0.1555 592.65 0.0000 0.7363 -0.0678 701.18 0.0000 796.29 0.0000 877.04 0.0000 948.09 0.0000 1013.5 0.0000 1070 0.0000 6 9 . 0.6874 0.0046 0.6317 -0.0653 0.3943 0.1336 0.5620 9 10 0.0343 -0.0063 (b) Based on the ACF and the PACF, is the data stationary? (1) Explain why? (1) [Note: Perform an appropriate hypothesis test: (i) set up the hypothesis (0.5); (ii) calculate the test statistics (0.5); and (iii) define the decision rule, rejection region, decision, and conclusion (1) to support your answer] (2) (c) If you wish to confirm the result shown in (a), what additional formal methods do you have available to test for a unit root? (2) (d) What methods do you use when you select an appropriate model for estimating time series variable such as U.S. one-year Treasury bond interest rate? (2) 1 2 Q1. You have corrected historical quarterly data on U.S. one-year Treasury bond interest rate from 1957 and 2005, including total 193 observations, with the aim to analyze the U.S. Bond, and to forecast the demand for the U.S. one-year Treasury bond. One-Year Treasury Bond Interest Rate, 1957-2005 wathy Generat 19571 19011 199301 20051 As a part of preliminary diagnostics for the time series data, you first inspect (eye-balling) the plots above for the U.S. one-year Treasury bond interest rates. (a) Inspecting the U.S. one-year Treasury bond interest rate plot and having calculated the first autocorrelation to be 0.93 for the sample period, do you suspect that U.S. one-year Treasury bond interest rate has a stochastic trend? [Note: Discuss: (1) autocorrelation; (2) the stationarity of the data; and (3) the presence of: (i) trends; and (ii) stochastic trends and a unit root that contribute to trends found in (i)] (3) In order to confirm the result shown in (a), you consider formal methods and calculate the following autocorrelation function (ACF) and the partial autocorrelation function (PACF) to test stationarity. -1 0 1 LAG AC FAC (Autocorrelation] ¡Partial Autocer) 3 4 $ Q Prob- 0.9307 0.9349 169.8 0.0000 0.0016 0.1319 322.96 0.0000 0.8513 0:1564 466.5 0.0000 0.7959 -0.1555 592.65 0.0000 0.7363 -0.0678 701.18 0.0000 796.29 0.0000 877.04 0.0000 948.09 0.0000 1013.5 0.0000 1070 0.0000 6 9 . 0.6874 0.0046 0.6317 -0.0653 0.3943 0.1336 0.5620 9 10 0.0343 -0.0063 (b) Based on the ACF and the PACF, is the data stationary? (1) Explain why? (1) [Note: Perform an appropriate hypothesis test: (i) set up the hypothesis (0.5); (ii) calculate the test statistics (0.5); and (iii) define the decision rule, rejection region, decision, and conclusion (1) to support your answer] (2) (c) If you wish to confirm the result shown in (a), what additional formal methods do you have available to test for a unit root? (2) (d) What methods do you use when you select an appropriate model for estimating time series variable such as U.S. one-year Treasury bond interest rate? (2) 1 2

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