First run a moving average model using the revenue data.

a. State the moving average period you picked and briefly discuss whether you think the model can do a good job forecasting and why.

Simple exponential smoothing

a. State the reason for your choice of the smoothing model and run the model. Make sure to store the residuals.

d. Show the resulting graph from the smoothing method. State the model you picked and the parameter values such as , , , if any.

c. Examine the residuals using time series plot and ACF graph. Do you observe any significant autocorrelation?

d. Briefly discuss whether you think the model can do a good job forecasting and why.

*Date / Revenue Chart*

1990-03-30 3019.0

1990-06-29 3076.0

1990-09-28 3099.0

1990-12-31 3105.0

1991-03-29 2996.0

1991-06-28 3081.0

1991-09-30 3104.0

1991-12-31 3099.0

1992-03-31 3019.0

1992-06-30 3149.0

1992-09-30 3167.0

1992-12-31 3254.0

1993-03-31 3163.0

1993-06-30 3220.0

1993-09-30 3290.0

1993-12-31 3317.0

1994-03-31 3373.0

1994-06-30 3394.0

1994-09-30 3415.0

1994-12-30 3609.0

1995-03-31 3450.0

1995-06-30 3564.0

1995-09-29 3261.0

1995-12-29 3265.0

1996-03-31 3208.0

1996-06-30 3224.0

1996-09-30 7377.0

1996-12-31 7405.0

1997-03-31 7416.0

1997-06-30 7708.0

1997-09-30 7374.0

1997-12-31 7696.0

1998-03-31 7651.0

1998-06-30 7928.0

1998-09-30 7910.0

1998-12-31 8077.0

1999-03-31 7967.0

1999-06-30 14510.0

1999-09-30 14660.0

1999-12-31 15260.0

2000-03-31 14530.0

2000-06-30 16770.0

2000-09-30 16530.0

2000-12-31 16870.0

2001-03-31 16270.0

2001-06-30 16910.0

2001-09-30 17000.0

2001-12-31 17010.0

2002-03-31 16430.0

2002-06-30 16750.0

2002-09-30 17110.0

2002-12-31 16910.0

2003-03-31 16490.0

2003-06-30 16830.0

2003-09-30 17060.0

2003-12-31 17200.0

2004-03-31 17060.0

2004-06-30 17760.0

2004-09-30 18210.0

2004-12-31 12730.0

2005-03-31 18180.0

2005-06-30 18050.0

2005-09-30 18490.0

2005-12-31 15300.0

2006-03-31 21230.0

2006-06-30 21890.0

2006-09-30 22460.0

2006-12-31 22610.0

2007-03-31 22580.0

2007-06-30 23270.0

2007-09-30 23770.0

2007-12-31 23840.0

2008-03-31 23830.0

2008-06-30 24120.0

2008-09-30 24750.0

2008-12-31 24640.0

2009-03-31 26590.0

2009-06-30 26860.0

2009-09-30 27260.0

2009-12-31 27090.0

2010-03-31 26910.0

2010-06-30 26770.0

2010-09-30 26480.0

2010-12-31 26400.0

2011-03-31 26990.0

2011-06-30 27540.0

2011-09-30 27910.0

2011-12-31 28440.0

2012-03-31 28240.0

2012-06-30 28550.0

2012-09-30 29010.0

2012-12-31 30040.0

2013-03-31 29420.0

2013-06-30 29790.0

2013-09-30 30280.0

2013-12-31 31060.0

2014-03-31 30820.0

2014-06-30 31480.0

2014-09-30 31590.0

2014-12-31 33190.0

2015-03-31 31980.0

2015-06-30 32220.0

2015-09-30 33160.0

2015-12-31 34250.0

2016-03-31 32170.0

2016-06-30 30530.0

2016-09-30 30940.0

2016-12-31 32340.0

2017-03-31 29810.0

2017-06-30 30550.0

2017-09-30 31720.0

Moving Average Plot for Revenue 35000 Variable Actual Fits 30000 -- Forecasts - 95.0% PI 25000 Moving Average Length 4 20000 Revenue Accuracy Measures MAPE G MAD 955 15000 MSD 2360987 10000 5000 0 1 11 22 33 44 55 66 77 88 99 110 Index Smoothing Plot for Revenue Single Exponential Method 35000 Variable Actual Fits 30000 Smoothing Constant 0.738697 a 25000 Accuracy Measures MAPE 4 20000 Revenue 701 MAD MSD 1749221 15000 10000 5000 0 1 11 22 33 44 55 66 77 88 99 110 Index Autocorrelation Function for Revenue (with 5% significance limits for the autocorrelations) 1.0 0.8 0.6 0.4 0.2 Autocorrelation 0.0 -0.2 -0.4- -0.6 -0.8 -1.0 2 4 6 09 8 10 12 14 16 18 20 22 24 26 28 Lag Time Series Plot of Revenue 35000 30000 osobe 25000 20000 Revenue 15000 10000 5000 0 1990-03-30 1995-06-30 1992-09-30 1998-03-31 2000-12-31 2003-09-30 2006-06-30 2009-03-31 2011-12-31 2014-09-30 2017-06-30 Date Moving Average Plot for Revenue 35000 Variable Actual Fits 30000 -- Forecasts - 95.0% PI 25000 Moving Average Length 4 20000 Revenue Accuracy Measures MAPE G MAD 955 15000 MSD 2360987 10000 5000 0 1 11 22 33 44 55 66 77 88 99 110 Index Smoothing Plot for Revenue Single Exponential Method 35000 Variable Actual Fits 30000 Smoothing Constant 0.738697 a 25000 Accuracy Measures MAPE 4 20000 Revenue 701 MAD MSD 1749221 15000 10000 5000 0 1 11 22 33 44 55 66 77 88 99 110 Index Autocorrelation Function for Revenue (with 5% significance limits for the autocorrelations) 1.0 0.8 0.6 0.4 0.2 Autocorrelation 0.0 -0.2 -0.4- -0.6 -0.8 -1.0 2 4 6 09 8 10 12 14 16 18 20 22 24 26 28 Lag Time Series Plot of Revenue 35000 30000 osobe 25000 20000 Revenue 15000 10000 5000 0 1990-03-30 1995-06-30 1992-09-30 1998-03-31 2000-12-31 2003-09-30 2006-06-30 2009-03-31 2011-12-31 2014-09-30 2017-06-30 Date