Weighted Moving Average Forecast Forecast Error (Error)2
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Consider the following gasoline sales time series data. Click on the datafile logo to reference the data.
| Week | Sales (1000s of gallons) |
| 1 | 16 |
| 2 | 20 |
| 3 | 20 |
| 4 | 23 |
| 5 | 18 |
| 6 | 17 |
| 8 | 19 |
| 9 | 23 |
| 10 | 19 |
| 11 | 14 |
| 12 | 21 |
a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers.
Week |
Time-Series Value |
Weighted Moving Average Forecast |
Forecast Error |
(Error)2 |
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| 12 | ||||||
| Total |
b. Compute the MSE for the weighted moving average in part (a).
MSE =
Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 8.90.
Prefer the unweighted moving average here; it has a (greater/smaller) MSE.
c. Suppose you are allowed to choose any weights as long as they sum to 1. Could you always find a set of weights that would make the MSE at least as small for a weighted moving average than for an unweighted moving average? (Yes/ No)
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