(a) Generate a tsibble named recent using aus_production containing the quarterly commodities production in Australia from 1992. (b) Compute seasonal naive forecasts for quarterly Australian beer production of the next two years. Visualize the forecasts along with the historical data. (c) Plot histogram of residuals. Explain your finding. (d) Plot ACF of residuals. Explain your finding. (e) Test if the residuals are white noise. What do you conclude?
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If you do not have the packages installed, install them first (fpp3 contains the required packages: tsibble, tsibbledata, fable, feasts, fabletools, ggplot2). Then load the packages and the aus_production data. R code: install.packages("fpp3") # run only if not Show more…
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10.39. U.S. beer production. The accompanying table shows U.S. beer production for the years 1980–2007. Suppose you are interested in forecasting U.S. beer production in 2010. (a) Construct a time series plot for the data. Do you detect a long-term trend? (b) Hypothesize a model for yt that incorporates the trend. (c) Fit the model to the data using the method of least squares. (d) Plot the least squares model from part a and extend the curve to forecast y31, the U.S. beer production (in millions of barrels) in 2010. How reliable do you think this forecast is? (e) Calculate and plot the residuals for the model obtained in part a. Is there visual evidence of residual autocorrelation? 1980 188 1981 194 1982 194 1983 195 1984 193 1985 193 1986 195 1987 195 1988 198 1989 200 1990 204 1991 203 1992 202 1993 203 1994 202 1995 199 1996 201 1997 199 1998 198 1999 198 2000 199 2001 199 2002 200 2003 195 2004 198 2005 197 2006 198 2007 199 (f) How could you test to determine whether residual autocorrelation exists? If you have access to a computer package, carry out the test. Use α = .05. (g) Hypothesize a time series model that will account for the residual autocorrelation. Fit the model to the data and interpret the results. (h) Compute a 95% prediction interval for y31, the U.S. beer production in 2010. Why is this forecast preferred to that in part b?
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