Statistical computation of maximum likelihood estimates using R Math Problem

Statistical computation of maximum likelihood estimates using R - Math Problem ExampleSMA do not account for seasonal modifications. The duration of the moving second-rate can best be resolved according to the type of application information to forecast. Long clipping periods gives smoother response by removing random variations but react slower to changes in the data as it lags the trend. Short magazine periods engender more oscillation but closely embody the trend. SMA is calculated by averaging the most recent number of actual values. SMA is calculated by using the following(a) equation (Chase & Jacobs 2006) Where Ft Forecast for coming periodAt-1Actual value in the prehistoricAt-2, At-3,Actual values two, three, periods ago.NNumber of periods to be averagedIn the attached excel document, SMA is calculated for three periods three, four, and five. Different n time periods will produce different results of data values. The values of MAD corresponding to each period ar sho wn in the following tableTable 1 MAD values for different periods of SMATime achievement (n)MAD 34.3643.1053.95Table one demonstrates that the sm bothest value of MAD exists for the period of n=4. This indicates that the type of data being analyse is best estimated using a period of four. Figure 1 SMA for periods of 3,4, and 5. Figure one confirms the results of MAD analysis from table one. The best fit trend decipher is the SMA for n=4. This line follows the actual data curve specially on the 15th, 22, and 25 where major change occurred in wind speed. The period that best fits the actual data is dependent on the type of data analyzed which is the wind speed. Weighted Simple Moving Average (WSMA)A weighted moving average puts different weights to each element, providing that the sum of all weights equals 1. Weights are...Short time periods produce more oscillation but closely follow the trend.In the attached excel document, SMA is calculated for three periods three, four, and fiv e. Different n time periods will produce different results of data values. The values of MAD corresponding to each period are shown in the following tableFigure one confirms the results of MAD analysis from table one. The best fit trend line is the SMA for n=4. This line follows the actual data curve specially on the 15th, 22, and 25 where major change occurred in wind speed. The period that best fits the actual data is dependent on the type of data analyzed which is the wind speed.A weighted moving average puts different weights to each element, providing that the sum of all weights equals 1. Weights are chosen by experience and trial and error. A general rule applies that recent past is more indicative of the future and should get higher weighting. However, if the data are seasonal weights should be effected accordingly. The weighted moving average advantage over the simple moving average is the ability to pull up stakes the effects of past data.In the excel document, in the Wei ghted SMA sheet, the weights of the moving average are determined by trial and error to produce the least value of MAD since there is no smart opinion as to guide the setup of