Question

Consider the following time series data. year value 1 234 2 287 3 255 4 310 5 298 6 250 7 302 8 267 9 225 10 337 use α=0.35 to compute the exponential smoothing values for the time series. compute the forecast for year 11. (use year 1 value for the forecast in year 2. round your answer to the nearest whole number)

Answer 1

To compute the exponential smoothing values for the time series, use the given formula with α=0.35. Calculate the forecasts for each year using the previous forecast and the current value. The forecast for year 11 can be found using the forecast for year 10 and the value of year 11.

Step-by-step explanation:

To compute the exponential smoothing values for the time series, we will use the formula:

Forecast for year t = α * value of year t + (1 - α) * forecast of year (t-1)

Given α = 0.35, we start with the forecast for year 2:

Forecast for year 2 = α * value of year 2 + (1 - α) * value of year 1 = 0.35 * 287 + (1 - 0.35) * 234 = 281.45

Using the same formula, we can calculate the forecasts for the remaining years:

Forecast for year 3 = 0.35 * 255 + (1 - 0.35) * 281.45 = 256.825

Continuing this process, we find:
Forecast for year 4: 297.71375
Forecast for year 5: 296.37234375
Forecast for year 6: 278.7769652344
Forecast for year 7: 289.8450839003
Forecast for year 8: 284.7244499352
Forecast for year 9: 270.3979524503
Forecast for year 10: 280.0982120111

Finally, to find the forecast for year 11, we use the same formula with the forecast for year 10 as the previous forecast:

Forecast for year 11 = 0.35 * value of year 11 + (1 - 0.35) * forecast of year 10