Use the Bricks data from aus_production (Australian quarterly clay brick production 1956-2005) for this exercise. (a) Use an STL decomposition to calculate the trend-cycle and seasonal indices. (Experiment with having fixed or changing seasonality.) (b) Use a naive method to produce forecasts of the seasonally adjusted data. (c) Use decomposition_model() to reseasonalise the results, giving forecasts for the original data. (d) Do the residuals look uncorrelated?
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Use the data in BARIUM for this exercise. (i) Estimate the linear trend model chnimp_{t} $=\alpha+\beta t+u_{r}$ using the first 119 observations (this excludes the last 12 months of observations for 1988 ). What is the standard error of the regression? (ii) Now, estimate an $\mathrm{AR}(1)$ model for chnimp, again using all data but the last 12 $\mathrm{months.}$ . Compare the standard error of the regression with that from part (i). Which model provides a better in-sample fit? (iii) Use the models from parts (i) and (ii) to compute the one-step-ahead forecasr for the 12 months in 1988 . You should obtain 12 forecast errors for each method.) Compute and compare the RMSEs and the MAEs for the two methods. Which forecasting method works better out-of-sample for one-step-ahead forecasts? (iv) Add monthly dummy variables to the regression from part (i). Are these jointly significant? (Do not worry about the slight serial correlation in the errors from this regression when doing the joint test.)
Dominador T.
Daily Sales = ̠₀ + ̠₁(Q1(d)) + ̠₂(Q2(d)) + ̠₃(Q4(d)) + ̠₄(t) + ̥ Variable Descriptions: • Daily Sales: The number of units sold in a day. • Q1(d): a dummy variable that equals 1 if the sales came from quarter 1 and 0 if they did not. • Q2(d): a dummy variable that equals 1 if the sales came from quarter 2 and 0 if they did not. • Q4(d): a dummy variable that equals 1 if the sales came from quarter 4 and 0 if they did not. • t: a standard, continuous time series variable that counts by 1 as each day passes. Regression Statistics Multiple R 0.1468 R Square 0.0215 Adjusted R Square 0.0169 Standard Error 71.9733 Observations 842 ANOVA df SS MS F Significance F Regression 4 95432.96158 23858.24039 4.605704365 0.00110533 Residual 837 4335785.719 5180.150202 Total 841 4431218.681 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 75.05 6.84 10.97 0.00 61.62 88.47 Q1(d) -18.40 7.37 -2.50 0.01 -32.86 -3.94 Q2(d) -2.92 7.26 -0.40 0.69 -17.17 11.33 Q4(d) -5.59 6.62 -0.84 0.40 -18.58 7.40 t 0.03 0.01 2.91 0.00 0.01 0.05 Based on the information above, which of the following be the correct prediction of units sold for December 25th, 2019 which is 4 days into the future?
Adi S.
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