Question

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8. Table 3 gives the actual sales, log of sales, and changes in the log of sales of Cisco Systems for the period 10 2001 to 40:2001. Table 3 Date Quarter: Year 10:2001 2Q:2001 3Q:2001 4Q:2001 1Q:2002 2Q:2002 Actual Sales (SMillions) 6,519 6,748 4,728 4,298 Changes in Log of Sales Log of Sales 8.7825 8.8170 8.4613 8.3659 0.1308 0.0345 -0.3557 -0.0954 Forecast the first-and second-quarter sales of Cisco Systems for 2002 using the regression Δ1n (Sales )-00661 + 0469saln (Sales-I)

Answer 1

Hello Sir/ Mam

Q - 8 -

The forecast of sales is $4,391 million for the first quarter of 2002 and $4,738 million for the second quarter of 2002, as the following table shows.

Date	Sales ($ Millions)	Log of Sales	Actual Values of Changes in the Log of Sales Δln (Salest)	Forecast Values of Changes in the Log of Sales Δln (Salest)
1Q:2001	6,519	8.7825	0.1308
2Q:2001	6,748	8.8170	0.0345
3Q:2001	4,728	8.4613	–0.3557
4Q:2001	4,298	8.3659	–0.0954
1Q:2002	4,391	8.3872		0.0213
2Q:2002	4,738	8.4633		0.0761

We find the forecasted change in the log of sales for the first quarter of 2002 by inputting the value for the change in the log of sales from the previous quarter into the equation Δln (Sales_t) = 0.0661 + 0.4698Δln (Sales_t–1). Specifically, Δln (Sales_t) = 0.0661 + 0.4698(–0.0954) = 0.0213, which means that we forecast the log of sales in the first quarter of 2002 to be 8.3659 + 0.0213 = 8.3872.

Next, we forecast the change in the log of sales for the second quarter of 2002 as Δln (Sales_t) = 0.0661 + 0.4698(0.0213) = 0.0761. Note that we have to use our first-quarter 2002 estimated value of the change in the log of sales as our input for Δln (Sales_t–1) because we are forecasting past the period for which we have actual data.

With a forecasted change of 0.0761, we forecast the log of sales in the second quarter of 2002 to be 8.3872 + 0.0761 = 8.4633.

We have forecasted the log of sales in the first and second quarters of 2002 to be 8.3872 and 8.4633, respectively. Finally, we take the antilog of our estimates of the log of sales in the first and second quarters of 2002 to get our estimates of the level of sales: e^8.3872 = 4,391 and e^8.4633 = 4,738, respectively, for sales of $4,391 million and $4,738 million.

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