The weekly demand (in cases) for a particular brand of...

The weekly demand (in cases) for a particular brand of automatic dishwasher detergent for a chain of grocery stores located in Columbus, Ohio, follows. $$\begin{array}{cccc} \text { Week } & \text { Demand } & \text { Week } & \text { Demand } \\ 1 & 22 & 6 & 24 \\ 2 & 18 & 7 & 20 \\ 3 & 23 & 8 & 19 \\ 4 & 21 & 9 & 18 \\ 5 & 17 & 10 & 21\end{array}$$ a. Construct a time series plot. What type of pattern exists in the data? b. Use a three-week moving average to develop a forecast for week 11 c. Use exponential smoothing with a smoothing constant of $\alpha=.2$ to develop a forecast for week 11 d. Which of the two methods do you prefer? Why?

The weekly demand (in cases) for a particular brand of automatic dishwasher detergent for a chain of grocery stores located in Columbus, Ohio, follows.
$$\begin{array}{cccc}
\text { Week } & \text { Demand } & \text { Week } & \text { Demand } \\
1 & 22 & 6 & 24 \\
2 & 18 & 7 & 20 \\
3 & 23 & 8 & 19 \\
4 & 21 & 9 & 18 \\
5 & 17 & 10 & 21\end{array}$$
a. Construct a time series plot. What type of pattern exists in the data?
b. Use a three-week moving average to develop a forecast for week 11
c. Use exponential smoothing with a smoothing constant of $\alpha=.2$ to develop a forecast for week 11
d. Which of the two methods do you prefer? Why?

Key Concepts

Time Series Plot

A time series plot is a graphical representation of data points in the order they were recorded over time. It is used to visualize trends, patterns, and fluctuations, making it easier to identify any underlying structures such as trends, cycles, or randomness in the data.

Pattern Detection

In time series analysis, pattern detection involves identifying regularities such as trends, seasonal variations, cycles, or irregularities within the data. Recognizing these patterns helps in understanding past behavior and guides the selection of appropriate forecasting methods.

Moving Average Forecasting

Moving average forecasting is a technique that smooths out short-term fluctuations by averaging data over a fixed number of periods. Specifically, a three-period moving average calculates the forecast for the next period as the average of the last three observed values, helping to mitigate the influence of random variability.

Exponential Smoothing

Exponential smoothing is a forecasting method that applies weighted averages where recent observations are given more weight than older ones. The smoothing constant (alpha) determines the rate at which the influence of past observations diminishes, providing a flexible method to adjust forecasts in light of new data.

Forecasting Evaluation

Forecasting evaluation involves comparing different forecasting methods to determine which provides a more accurate or suitable prediction based on the data and context. This evaluation often considers factors such as simplicity, responsiveness to changes, and historical forecasting accuracy.

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