Question

1. Using the index (with 2007) of new housing starts in a large metropolitan area in the table below. Use the following index data to develop three-period and five- period moving average forecasts and single exponentials smoothing forecast with 0.3 and a 0.5 respectively 132 137 2011 175 012 187 5 194 7 240 a) Plot the index data and briefly explain the pattern. b) Forecast the next period for each method. c) Which method (i.e. МАЗ, M1A5, ES03 and ES04) provides the better forecast? Briefly explain why? (Use only RMSE technique) Having calculated MA3, MA5, ES03 with 0.3 and ES05 with 0.5, draw their patterns on the same diagram. Briefly explain. Use trend linear model to forecast next 5 years. Also check the estimated figures whether they are consistent with the actual data or not. Calculate standard deviation, correlation coefficient and coefficient of determination Also verify your answer estimated in section e. Briefly explain. d) e) f)

Answer 1

a) Please find the plot below. The plot shows that the trend for the index is upwards with every passing year.

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b) Please find the table below. It shows the forecasts for the next period using the different methods.

Movng average is caluclated by adding the X number of months for the forecast of X+1 number of month.

Exponential smoothing is calculated by F_t+1 = aA_t + (1-a)F_t   where A_t is the actual value for perirod t and F_t is the forecast value for period t

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c) The best method is exponential smoothing with a = 0.5, It has the lowest mean square of error. It is shown on the table below. MSE is the mean of square of error. The error is obtained by subtracting forecasted value from actual value (index)

d) The plotting is shown below. All the methods show similar trend (upward). However their degree of trend varies.

투! Add Chart Quick Change Element Layout Colors Switch Rowi SelectChange Column Data Chart Move Type Chart Type Location Chart Layouts Chart Styles Data Chart 2 ▼ | F G Chart Title 3 300 6 250 9 20D 12 150 15 100 16 17 18 50 21 0 2010 2011 2013 2014 2015 2017 24 MSheet47 Sheet48 Sheet49 Sensitivity Report1 Sheet50 Sheet51G AVERAGE: 528.63064 16 COUNT: 58 SUM: 2748879336 ! EI + 100% -