Answer to Question #197228 in Statistics and Probability for Saira

Question

The given table shows the rainfall of Gujarat Region. Forecast the rainfall using

Exponential Smoothing. Use Alpha =0.2, 0.5 and 0.8. Data is available from 1997 to

2016, use this series for the calculation and forecast rainfall for the year 2017. To

know, what extent the prediction is correct, actual rainfall for 2017 (1024.4millimeters) is provided. Based on MSE and MAD, find out which alpha values

among the three suggestions are relatively near to actual value?

SUBDIVISION YEAR ANNUAL (in MM)

Gujarat Region 1997 1068.9

Gujarat Region 1998 1070

Gujarat Region 1999 568.4

Gujarat Region 2000 550.6

Gujarat Region 2001 849

Gujarat Region 2002 637.2

Gujarat Region 2003 1160.3

Gujarat Region 2004 1005.8

Gujarat Region 2005 1316.4

Gujarat Region 2006 1478

Gujarat Region 2007 1178.9

Gujarat Region 2008 911.1

Gujarat Region 2009 641.6

Gujarat Region 2010 1088.7

Gujarat Region 2011 890.5

Gujarat Region 2012 714

Gujarat Region 2013 1118.6

Gujarat Region 2014 705.7

Gujarat Region 2015 622.9

Gujarat Region 2016 764.9

Answer 1

Exponential smoothing:

$s_0=x_0$

$s_t=\alpha x_{t}+(1-\alpha)s_{t-1}$

where $x_t$ is the initial time series,

$s_t$ is smoothing time series.

Mean squared error:

$MSE=\frac{1}{n}\sum (x_i-\hat x_i)^2$

$\hat x_i$ is predicted value.

Median absolute deviation:

$MAD=median(|x_i-\tilde{x}|)$

$\tilde{x}=median(X)$

Using online calculator https://mathcracker.com/:

for $\alpha=0.2$ :

$MSE=76053.66$

$MAD=227.6$

for $\alpha=0.5$ :

$MSE=72354.26$

$MAD=226.16$

for $\alpha=0.8$ :

$MSE=75516.54$

$MAD=234.91$

$\alpha=0.5$ suggestion is relatively near to actual value, because it has minimal values of MSE and MAD, that is, values of MSE and MAD for $\alpha=0.5$ are less than values of MSE and MAD for $\alpha=0.2$ or $\alpha=0.8$