Applied business forecasting

ARIZONA STATE UNIVERSITY Carey School of Business ECN 410 Applied Business Forecasting Practice Final Duration: 75 minutes

Name: ASU#:

Question #1……………………………………………….

Question #2……………………………………………….

Question #3……………………………………………….

Question #4……………………………………………….

Total………………………………………………………

Question #1 Consider the following data series of monthly sales Month January 2005 FebruaryMarch April May June July August September October November December January 2006 February March April May June July August September October November December t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sales 430 420 436 452 477 420 398 501 514 532 512 410 442 449 458 472 463 431 400 487 503 503 548 432

a. Plot the time series in an adequate graph and identify anypatterns you can observe. b. Decompose the time series into its different components. Justify your decision of using either an additive or multiplicative model. Use the following values if needed. Mean Sales = 462.083

Mean t = 12.5 Variance of Sales = 1,739.66 Variance of t = 209.635 Covariance between Sales and t = 99.2934 c. Forecast the values of sales for the first 6 months of 2007.

Question#2 a. Identify the different forms non-stationary can be observed in a time series and what actions would you employ to eliminate it from the time series. b. What is an autoregressive model?

Question #3 Consider the following regression output for Electric Usage data (Q1 1980 to Q2 1996)

Predictor Constant Time 2nd Quarter 3rd Quarter 4th Quarter ` S = 52.2488 Source Regression ResidualError Total

Coefficient 968.39 0.9383 -341.94 -471.60 -230.23

SE Coefficient 16.88 0.3377 17.92 18.20 18.20

T 57.38 2.78 -19.08 -25.91 -12.65

P-value 0.0000 0.0007 0.0000 0.0000 0.0000

R-squared = 92.4% DF 4 61 65 SS 2,012,975 166,526 2,179,502

Adj. R-squared = 91.9% MS 503,244 2,730 F 184.34 P-value 0.0000

Durbin-Watson statistic = 1.48 a. From the regression output, can youdescribe the overall behavior of the data? b. Interpret the coefficient of Time from the linear regression. c. Interpret the coefficient of 3rd Quarter from the linear regression. d. Forecast the Electric Usage for the next two quarter of 1996. e. Explain why a coefficient for the 1st Quarter of the year was not included in the regression.

Question #4 Consider the plot and correlogram for thedata series for the weekly stock price of IBM, from January 6 and December 29th.

IBM
310 300 290 280 270 260 250 240 230 5 10 15 20 25 30 35 40 45 50

Date: 12/05/11 Time: 13:12 Sample: 1 52 Included observations: 52 Autocorrelation . |******| . |***** | . |***** | . |**** | . |*** | . |** | . |** | . |** | . |*. | . |*. | . |*. | . |*. | .|. | .|. | .|. | .|. | .|. | .|. | .*| . | **| . | **|. | ***| . | ***| . | ***| . | Partial Correlation . |******| .|. | .|. | .*| . | .|. | .|. | . |*. | .|. | .*| . | . |*. | . |*. | .*| . | . |*. | .|. | .|. | .*| . | .*| . | .*| . | .*| . | .|. | .*| . | .|. | .|. | . |*. | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 AC 0.874 0.759 0.659 0.543 0.440 0.344 0.284 0.224 0.158 0.127 0.119 0.078 0.066 0.069 0.074 0.052 -0.002-0.055 -0.145 -0.231 -0.308 -0.372 -0.408 -0.412 PAC 0.874 -0.021 0.000 -0.120 -0.026 -0.042 0.092 -0.043 -0.067 0.077 0.074 -0.141 0.087 0.032 0.027 -0.113 -0.155 -0.093 -0.182 -0.034 -0.094 -0.044 0.045 0.082 Q-Stat 42.050 74.375 99.233 116.50 128.06 135.27 140.30 143.50 145.12 146.21 147.18 147.60 147.91 148.26 148.68 148.89 148.89 149.14 150.92 155.62 164.23 177.19 193.31 210.34 Prob 0.000 0.0000.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

a. Is the IBM series stationary? What correction would you recommend if the series is non-stationary? b. Your research assistant tried to fit an autoregressive model to the original data series. Looking at the regression output, residual correlogram and residual...