Ten weeks of data on the Commodity Futures Index are 7.36, 7.41, 7.56, 7.57, 7.61, 7.53, 7.53, 7.71, 7.63, and 7.56.(a) Construct a time series plot.1234What type of pattern exists in the data?Week5The data appear to follow a horizontal pattern.O The data appear to follow a cyclical pattern.O The data appear to follow a trend pattern.O The data appear to follow a seasonal pattern.68.5-8.38.17.9+77.77.5-87.37.16.96.76.5 +01 23 4567 7 8 9 10 11Week98.5-8.3-108.17.97.7+7.5-7.37.16.96.76.50 1 2Time SeriesValue7.367.417.56(b) Use trial and error to find a value of the exponential smoothing coefficient a that results in a relatively small MSE. (Roundyour answers to two decimal places.)7.577.617.533 47.537.715 67 7 8 9 10 11Week7.637.56a = 0.1Forecastα = 0.3ForecastJCOIndexDICa = 0.8Forecast8.58.3-8.17.97.77.5-7.37.16.96.76.508.5 T8.3-8.17.9-7.7-7.57.37.16.9-6.7-6.512 3 4 5 678Week+0 1 2 3 48 9 10 115 66 7 8Week9 10 11What value of the smoothing constant provides the most accurate forecasts?O Exponential smoothing with a = 0.3 provides more accurate forecasts since its MSE is smaller than the MSE fora=0.1 or 0.8.O Exponential smoothing with a = 0.8 provides more accurate forecasts since its MSE is smaller than the MSE fora=0.1 or 0.3.O Exponential smoothing with a = 0.1 provides more accurate forecasts since its MSE is smaller than the MSE forα = 0.3 or 0.8.All three values of the smoothing constant provide the same MSE, so none provide a more accurate forecast than theothers.

Find the given details below:Find the graph below:Based on the above graph we conclude that the correct graph is the 4th graph and the pattern is the Trend pattern.Trend pattern:A trend pattern is a term in data analysis that refers to a significant shift or development of a certain variable over time. It's a long-term movement in data after other components have been accounted for. It’s often used in time series analysis to identify consistent patterns. For example, an upward trend in stock market performance might suggest a bullish market. Trend patterns can be linear (straight-line increase or decrease), exponential (rapid increase or decrease), or even cyclical (up-and-down fluctuations). Understanding trend patterns can help in forecasting the future behavior of the variable.The data points (index) increase and decrease but exponentially the tren is increased (Green line). So the correct answer is trend projection.Find the Calculations below:Find the Calculations below:Find the Calculations below:Find the explanations below:When comparing the MSE values, we identify that the alpha = 0.8 value (0.009) is less than the other 2 methods. So the correct answer is b) Exponential smoothing with alpha = 0.8 provides more accurate forecasts since its MSE is smaller than the other MSE for alpha 0.1 and alpha 0.3Find the answers below:Q1) Fourth diagramTrend patternQ2) Exponential smoothing with alpha = 0.8 provides more accurate forecasts since its MSE is smaller than the other MSE for alpha 0.1 and alpha 0.3