Key Formulas Of Chapter 2

1
Key Formulas Of Chapter 2

• Basic Time Series Formula
• Actual values Pattern Error
• The mean
• _ S Xt
• X (2-1)
• n
• The mean is the center of deviations (xt)
• S xt 4 - 3 - 2 5 2 - 5 - 1 0 (2-2)

2

• The Population Standard Deviation
• S(Xt - m) 2
• s (2-3)
• N
• The Sample Standard Deviation as estimation of s
  
• _
• S(Xt - X) 2
• S (2-4)
• n-1

3

• The Normal Distribution
• The m plus and minus 1.96s contains 95 percent
  of the ND.
• Error Statistics _
• S Xt - X
• MAD (2-5)
• n
• MAD .80S or S 1.25 MAD (for ND) (2-6)

4

• Error Statistics
• n ME S et / n 0 /10 0
  (2-7)
• t1
• n MAD S et /n 1960/10
  196 (2-8) t1 n
  SSE S e2t 632,007 (2-9)
  t1

5

• Error Statistics
• n MSE S e2t /n
  63,200.7 (2-10) t1
• RSE S e2t / (n-1)
  632,007/(10-1)
• 7,022.3 265
  (2-11)
• ( Yt - Yt)
• PEt (100) (2-12)
  Yt

6

• Error Statistics
• n MPE S PEt /
  n (2-13) t
  1 n MAPE S PEt /
  n (2-14)
• t 1
• Significance Test For Bias
• _ et t -
  calculated (2-15)
• Se / n

7

• Covariance _ _
• S (Xt - X) (Yt - Y)
  COV(X,Y) (2-16)
  n - 1
• Pearson Correlation Correlation
• COV(X,Y)
• rxY (2-17)
• SxSY

8

• Standard Error Of The Correlation Coefficient
• 1 - r2
• Ser
  n - 2
• Statistical Significance Test Of r
• r - 0
• t r (2-18)
• _1 - r2
• n - 2

9

• Pearson Autocorrelation
• COV(Yt, Yt-k)
• rYt Yt-k (2-19)
  SYt SYt-k
• Autocorrelation Function (ACF)
• n _ _ S
  (Yt - Y) (Yt-k - Y) t
  1k ACF(k) (2-20)
• n _
  S (Yt - Y)2
  t 1

10

• Standard Error of ACF(k)
• 1
• SeACF (2-21)
• (n)
• ACF(k) t-test
• ACF(k)
• t (2-22)
  SeACF

11

• Seasonally Naive Model
• Yt Yt-4 for t 5 to 32 (2-23)
• et Yt - Yt-4 for t 5 to 32 (2-24)