Year Trend Cycle Seasonal Random Actual
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1 Department Of Economics, University Of Ghana Level 300, Econs 305: Applied Statistics for Economist Lecturer: Dr. D. K. Twerefou Problem Set 3: Time series analysis 1. The table below provides the components of a time series from 1985 to Using the additive model complete the table. Year Trend Cycle Seasonal Random Actual The table below shows some of the values of the components and actual time series from 1996 to Using the multiplicative model complete the table. Years Trend Cycle Seasonal Random Actual Values The table below shows the values of some of the components and actual values of a time series for 1996 to Using the additive model complete the table. Year 1995 Trend Cycle Seasonal Random Actual The table below shows the production of cocoa by a farmer in Ghana from 2000 to a. Fit the trend line using the method of semi-averages. b. Find the equation of the straight line 1
2 Years Tons of Cocoa The table below provides some of the components and actual values of a time series from 1990 to Using the multiplicative model complete the table. Years Trend Cycle Seasonal Random Actual The table below shows the production of rice (in thousands of tons) from 2000 to Find the trend equation using the method of semi-averages. Years Prod. (000 tons) The table below shows the production of timber from 1973 to Find the trend equation using the 3-yearly moving averages. Year Production Year Production The table below shows the nominal GDP of a country from 2000 to Fit the trend equation using 3-yearly moving averages. Year GDP (trillion cedis) The table below shows the number of people who attend morning, afternoon and evening school for a week. Monday Tuesday Wednesday Thursday Friday Morning Afternoon Evening a. Find the trend equation using 3-weekly moving averages b. Draw the trend line. 2
3 10. The data below shows the output of a food processing company. Assume a 4-yearly cycle and find the trend line by the method of moving averages. Using the trend line estimate the output for 1990 Year Output (tons) The table below shows the quarterly sales of a supermarket. Year I II III IV i. Using the method of 4-quaterly moving average find the trend values and the trend equation ii. What will be the sales in the 3 rd quarter of The table below shows the unemployment data of graduates from in a certain country. Year Unemployment i. Determine the least squares trend equation ii. Estimate unemployment for The following data shows the number of road accidents from 1996 to Year No. of accidents i. Obtain the trend equation using the method of least squares ii. Estimate the number of road accidents in The table below shows the production of rice in a country in metric tons. i. Fit the trend line using the method of least squares. ii. Estimate rice production for the year 2020 Year Year The table below shows the number of people who attend morning, afternoon and evening school for a week. Monday Tuesday Wednesday Thursday Friday Morning Afternoon Evening
4 a. Using the method of moving averages and the multiplicative model, Determine the seasonal indices for morning, afternoon and evening b. Deseasonalize the data. 16. The table below shows the actual (Y) and Trend (T) estimate of the production of aluminum ingots in a country. Calculate the cyclical relative and interpret your result Year Y T The table below shows the sales of a supermarket in Ghana in billion cedis. Quarter Year First Second Third Fourth a. Calculate the trend using the method of moving averages b. Calculate the average seasonal Index under the multiplicative model c. Deseasonalize the data. 18. The table below shows the actual (Y), Trend (T) estimate and the cyclical relative (C) of wheat production in a country. Calculate the missing values. Interpret your results for 1998, 1999 and Year Actual Value(Y) Trend value (T) Cyclical relative (%) The data below shows the quarterly sales from a shopping mall from in billion cedis. I II III IV a. Plot the quarterly data for all the years c. Calculate the seasonal indices 4
5 d. Estimate the trend line using the method of least square e. Forecast the sales value for the year 2006 f. Forecast the sales value for the first and fourth quarters of year The data below shows quarterly export of a cash crop from a country from in million metric tons. I II III IV a. Plot the data for all the years c. Calculate the seasonal indices d. Estimate the annual trend line using the method of least square e. Forecast the sales value for the year 2008 f. Forecast the sales value for the first and fourth quarters of year The table below shows the monthly export of cocoa for the first five months of the year in thousand metric tons. January February March April May If the forecast for January is 20,000 metric tons, determine forecasts for February through June using exponential smoothing with a smoothing constant of α= The table below shows the sales of a shopping mall Year I II III IV Total a. Plot the quarterly data for all the years c. Calculate the annual trend equation using the method of semi averages d. Calculate the annual trend equation using the 3 yearly moving averages e. Calculate the annual trend equation using the method of least squares f. Calculate the seasonal index g. Forecast the sales value for the year 2010 h. Forecast the sales value for the first and fourth quarters of year 2010 based on the least square trend equation and the seasonal index. 23. A well known Casino made the following annual sales, in millions of cedis If the forecast for 2004 was 125, forecast the sales for 2009 using the method of exponential smoothing with a smoothing constant of α=0.15 5
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