Assignment Excel

Chapter_3_Notes(1).doc

Chapter 3 Notes

“Elisha replied, “Hear the word of the LORD. This is what the LORD says : About this time tomorrow , a seah of the finest flour will sell for a shekel[ b ] and two seahs[ c ] of barley for a shekel at the gate of Samaria.” (2 Kings 7:1 NIV)

“Then the people went out and plundered the camp of the Arameans. So a seah of the finest flour sold for a shekel, and two seahs of barley sold for a shekel, as the LORD had said .” (2 Kings 7:16 NIV)

1. Basic assumption: the fluctuations in the past values represent a random departures from some smooth curve ( the task is to find the smooth curve.

2. Moving averages:

a. For stationary time-series data (Table 2.1)

b. MAt (n) = (Xt + Xt-1+…+Xt-n+1) / n; X=actual value, n=the moving average order.

c. Equal weight ( 1/n ) for every observation.

d. Three-quarter moving average: MAt = (Xt + Xt-1+Xt-2) / 3

t	X (actual value)	MAt(3)	Ft
1	10	--	--
2	6	--	--
3	12	28/3=9.3	--
4	4	22/3=7.3	9.3
5	10	?	7.3

· MA3 = (X3+ X2+X1) / 3

· Five-quarter moving average: _________________________

e. The forecast value Ft+1 = MAt

f. The naïve model is a one - period moving average

· MAt = Xt / 1 = Xt ( Ft+1 = Xt

g. Exchange rate between U.S. dollar and Japanese Yen (Wilson and Keating, Table 3.1)

h. 4-quarter and 12-month moving average can be used to average out the seasonal effect ( no seasonality in the annual data.

i. Initial claims for unemployment insurance ( 4-week moving average.

T	X	MA(4)
1Q	10	--
2	6	--
3	12	--
4	4	--
1Q	10	8
2	6	8
3	12	8
4	4	8

3. Simple exponential ( one parameter α ) smoothing:

a. For stationary time-series data (Table 2.1)

b. The smoothed value Ft+1 = α Xt + (1- α) Ft ; α: the smoothing constant

( Ft+1 is also the forecast value

c. Ft+1= α Xt + (1- α) Ft ( Ft+1 = Ft + α (Xt - Ft), learn from the past error (Xt - Ft)

d. Ft+1= α Xt + (1- α) Ft ( Ft+1 = α Xt + (1- α) α Xt-1 +

· smooth past values in a decreasing ( exponential ) manner

· contain more information than moving average

e. The initial value F1 can be set to be X1 or other value, such as the mean of the data (footnote 3)

f. The smoothing constant α is between 0 and 1 , choose the one which minimizes RMSE.

g. Compare the weights with α= 0.1 and α=0.9 (pp. 108–109)

h. ForecastX ( simple exponential smoothing ) will choose α automatically

· Index of consumer sentiment (Table 3.2)—only forecast one period ahead.

4. Holt’s two -parameter (α and γ) exponential smoothing:

a. For linear trend time-series data (Table 2.1)

b. The smoothed value or the level estimate

· Ft+1 = α Xt+ (1- α) (Ft + Tt), T is the trend estimate.

· α : smoothing constant for the level . If there is no trend in the data, there is no need for Tt. (4.b. is the same as 3.b.)

c. The trend estimate, Tt+1 = γ (Ft+1 - Ft) + (1- γ) Tt, γ: the smoothing constant for the trend estimate;

d. The forecast value: H t+m= Ft+1+ mTt+1 , m=1,2,3,… ( a straight line.

· m=1, H t+1= Ft+1+ 1*Tt+1

· m=2, H t+2= Ft+1+ 2*Tt+1

· m=3, H t+3= Ft+1+ 3*Tt+1

e. ForecastX ( Double Holt ) will choose α and γ automatically.

f. Personal consumption expenditures (Figure 3.5)

5. Winter’s three -parameter (α, β, and γ) exponential smoothing:

a. For linear trend and seasonal time-series data (Table 2.1)

b. The smooth value or the level estimate (deseasonalized):

· multiplicative seasonality Ft = α Xt/S t-p+ (1- α) (Ft-1 + Tt-1)

· additive seasonality Ft = α(Xt - S t-p )+ (1- α) (Ft-1 + Tt-1)

c. The trend estimate, Tt = γ (Ft - Ft-1) + (1- γ) Tt-1

d. The seasonality estimate, St=β Xt/Ft + (1-β) St-p

· β=smoothing constant for seasonality; p=number of periods in the seasonal cycle.

e. The forecast value (reseasonalized): Wt+m = (Ft+ mTt) S t+m-p m=1,2,3,

f. ForecastX ( Holt Winters ) will choose α, β, and γ automatically.

g. Light truck production (Table 3.4)

· seasonal indices

6. Adaptive-response-rate single exponential smoothing:

a. For stationary time-series data (Table 2.1)

b. Ft+1= αt Xt + (1- αt) Ft; the term α adapts to the mean change.

c. Compare with simple exponential smoothing (Table 3.5)

7. Forecasting seasonal data without using Winter’s exponential smoothing:

a. Obtain the seasonal index from Winter’s exponential smoothing or decomposition method (p. 147)

b. Deseasonalize the data ( seasonally adjusted ): SA=X/SI, SI: seasonal index

c. Specify a forecasting model for SA data and perform the forecast, SAF

d. Reseasonalize the series: F = SAF*SI

e. Light truck production (Table 3.6).

8. New-product forecasting (growth curve, S-shape):

a. Gompertz curve: (Table 3.7 & Figure 3.10)

b. Logistics curve: symmetric about its inflection point (Table 3.9 & Figure 3.13)

c. ForecastX ( Gompertz Curve and Logistic Curve )

d. Bass model (pp. 25–26):

· St = pm + (q-p) Yt – (q/m) Yt 2

· choose the innovation rate (p) and the imitation rate (q or r) (Table 3.10 & Figure 3.16)

9. Event modeling:

a. The event index, similar to the seasonal index

b. Mustard consumption (Figure 3.17 & Table 3.13)

c. ForecastX ( Event Model )

d. Forecast Pro webinar http://www.forecastpro.com/resources/webinar/index.htm

10. Cases:

a. Jewelry sales (Figure 3.18)

b. Houses sold (Figures 3.19) – an inconsistent trend.

11. From the Wilson and Keating text, complete questions 6, 11, 13 from the Exercises section at the end of chapter 3 and duplicate Figure 3.13. Discuss these questions in your assigned Group Discussion Board for credit before submitting your answers in Excel via the Weekly Exercise 3 assignment link.