TS module 12 method of moments practice problem

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NEAS	NEAS posted 14 Years Ago #10161 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	TS module 12 method of moments practice problem Estimates of ì, ã₀, and ñ do not depend on the ARIMA process. A. Estimate ì from the mean of the observations. B. Estimate ã₀ from the variance of the observations. C. Estimate ñ from the sample autocorrelations. Exercise 12.1: The first five values of a stationary time series are 6, 5, 4, 6, and 4. A. What is the estimate of ì? B. What is the estimate of ã₀? C. What is the estimate of ñ₁? Part A: An unbiased estimator of ì is ∑ Y_t / N = (6 + 5 + 4 + 6 + 4) / 5 = 25/5 = 5. Part B: An unbiased estimator of ã₀ is the variance of the observed values = (1² + 0² + (–1)² + 1² + (–1)² ) / 4 = 1. Part C: The numerator of the sample autocorrelation is (1 × 0 + 0 × -1 + -1 × 1 + 1 × -1) = –2. The denominator is ã₀ = 4 (see Part B), so ñ₁ = –2/4 = –½. Jacob: Why doesn’t this exercise ask for ó²_ε? Rachel: The estimate of ó²_ε depends on the type of model, such as AR(1), MA(1), or ARMA(1,1). Jacob: Can’t we select the best model? Rachel: With only five observed values, the standard error of the observed sample autocorrelations is high: 1/√5 = 0.44721. The width of the 95% confidence interval is 2 × 1.96 × 0.44721 = 1.75308. The data are too sp** to select the best model. Attachments** TS module 12 method of moments practice problem.pdf (1.7K views, 57.00 KB) 0
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GeoxploreMI	G GeoxploreMI posted 7 Years Ago #15717 #
G Forum Newbie Group: Forum Members Posts: 1, Visits: 12	Part B says that gamma_0=1. Yet Part C references Part B and states that gamma_0=4. Am I not understanding this or is this a typo? 0
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NEAS	NEAS posted 7 Years Ago #15718 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	+x NEAS - 11/8/2010 1:25:35 PM TS module 12 method of moments practice problem Estimates of ì, ã₀, and ñ do not depend on the ARIMA process. A. Estimate ì from the mean of the observations. B. Estimate ã₀ from the variance of the observations. C. Estimate ñ from the sample autocorrelations. Exercise 12.1: The first five values of a stationary time series are 6, 5, 4, 6, and 4. A. What is the estimate of ì? B. What is the estimate of ã₀? C. What is the estimate of ñ₁? Part A: An unbiased estimator of ì is ∑ Y_t / N = (6 + 5 + 4 + 6 + 4) / 5 = 25/5 = 5. Part B: An unbiased estimator of ã₀ is the variance of the observed values = (1² + 0² + (–1)² + 1² + (–1)² ) / 4 = 1. Part C: The numerator of the sample autocorrelation is (1 × 0 + 0 × -1 + -1 × 1 + 1 × -1) = –2. The denominator is ã₀ = 4 (see Part B), so ñ₁ = –2/4 = –½. Jacob: Why doesn’t this exercise ask for ó²_ε? Rachel: The estimate of ó²_ε depends on the type of model, such as AR(1), MA(1), or ARMA(1,1). Jacob: Can’t we select the best model? Rachel: With only five observed values, the standard error of the observed sample autocorrelations is high: 1/√5 = 0.44721. The width of the 95% confidence interval is 2 × 1.96 × 0.44721 = 1.75308. The data are too sp**** to select the best model. [NEAS: Yes, a typo] 0
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