=

S

 

+

1

T

 

 

 

 

 

 

 

 

 

 

t + 1

t

---

t

 

 

 

 

S1S3

S22

 

 

 

 

 α

 

c = exp

 

1

 

 

 

 

 

 

 

 

 

--

-----------------------------------

+ S3

 

-

 

 

 

 

 

 

 

 

 

 

n

S1

2S2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a

= exp

 

(b 1)(S2 S1)

 

-----------------------------------------

2

 

 

 

b(bn 1)

 

 

 

 

Where S1, S2, and S3 are:

n

S1 = Inyi = n lnc +

i = 1

2n

bn 1 b( lna) --------------

b 1

S

 

=

Iny

 

= n lnc + b

n + 1

( lna)

bn

1

2

i

 

--------------

 

 

 

 

 

 

b

1

i = n + 1

a, b and c are determined by solving the three equations above simulta- neously.

Forecasting With Exponential Smoothing

a = smoothing constant (0 < a < 1)

Xt = actual current period usage

156

Page 157
Image 157
HP 12C manual Forecasting With Exponential Smoothing, 156