Business Statistics

636 Business Statistics

Double exponential smoothing method

Forecast for the next period (F

t+1

) = E

t

+ T

t

where

1 1

(1 )( )

t t t t

E X E T

− −

= ⋅ + − + 

and

1 1

( ) (1 ) .

t t t t

T E E T

− −

= − + − 

Forecast for the k periods in future = E

t

+ kT

t

Deseasonalized data =

i i i i

i i i

i

T S C R

T C R

S

× × ×

= × ×

A pth order autoregression model

0 1 1 2 2

ˆ

− − −

= + + + +

i i i p i p

y b b y b y b y

where y

i

is the observed value of the time series at time i, y

i – 1

the observed value of the time series at time i – 1, y

i – 2

the observed value of

the time series at time i – 2, y

i – p

the observed value of the time series at time i – p, b

o

the fixed parameter ...