Scenario: You will be using your statistical expertise to forecast future time-s

Question

Scenario: You will be using your statistical expertise to forecast future time-series values.   A time series model is a forecasting technique that attempts to predict the future values of a variable by using only historical data on that one variable. Here are some examples of variables you can use to forecast. You may use a different source other than the ones listed (be sure to reference the website). There are many other variables you can use, as long as you have values that are recorded at successive intervals of time.

Variable Opening Prices:

1. Compare the MAD (mean absolute deviation) scores of all three forecasts (moving average, weighted moving average and exponential smoothing) and state which forecasting method gives the most accurate forecast.

2. Based on your forecasts, do you think any of them are a good model for this variable? Why or why not? Explain.

3. After you have contemplated the questions above, draft your reflective essay. Every piece of writing should have an introduction, body, and conclusion. A good way to plan this reflective essay is to write an introduction to the essay. Next, write at least three body paragraphs and address each of the points listed above. End your essay with a conclusion paragraph tying all your ideas together. The essay should be at least 5 paragraphs in length and include a title page and reference page. The essay should be double spaced and in 12-point Times New Roman font.

please Answer the following ASAP by looking at the excel sheets given above.

Thanks

Forecasting Moving averages - 5 period moving average Errors as a function of n Forecasts and Error Analysis Date OpenForecast Error Ab 3/1/201178.54 2/2018172. 3/5/201175.21 3/62018 177.91 3/7/2018 174.94 3/8/2018 175.48 39/201 177.96 3/12/2018 180.29 3/13/2018 182.59 3/14/2018180.32 175.88 175.268 2.692 0.4 0.4000058 0.16000464 00.239 177.316 5.274 5.2739956 27.81502959 252 2.0682.0680082 4.276657915 2018178.5 3/16/2018 178.65 3/192018177.32 3/202018 175.24 212018 175.04 179.3281-0828| 0.82799981 0.6855836691 00.46% 2.749991 7.5624505 3/22/2018 3/23/2018168.39 3/26/2018 168.07 3/27/2018 173.68 175.251-686| 6.86000081 47.05961098| 04.07% 173.198 -5.128 5.127993| 26.29632041 03 171.3482.332 2.3319922 5.433187621 Average|-1.0746| 3.411142386|15.65340459| 01.96% BiasMAD MAPE 4.273441862

Explanation / Answer

1) The mean absolute deviation (MAD) for each of the forecasting techniques are shown below:

The mean absolute deviation is a measurement of forecasting error and a lower value represents a greater forecasting accuracy. Keeping this in view we can say that:

MAD (weighted 5 period moving average) > MAD (5 period moving average)>MAD (exponential smoothing)

So clearly the forecasting accuracy of the exponential smoothing is the best.

2) To understand if the model is a good forecast model, we should understand that percentage forecasting error should be tolerable and within acceptable tolerances.

If we see the stated models, we see that highest(maximum) percentage absolute deviation for the models are as below:

Since the maximum deviation of a forecasted data point from the actual value is less than 5%, we can say that the forecasted values are within tolerances and the models are a fairly good representation of the data.

3) Reflective Essay:

Introduction:

The forecasting of time series data involves prediction of data points in the future. There are several alternatives for forecasting which can be used for such forecasting and which includes: Moving Average (Simple), Moving Average (Weighted) and Exponential Smoothing. These forecasting techniques are then evaluated using various metrics such as MAD (Mean Absolute Deviation), MSE (Mean Squared Error) & MAPE (Mean Absolute Percentage Error).

The forecasting technique which is chosen has got the lowest value of the above mentioned error metrics.

Description:

The evaluation of the forecasting techniques is done through few metrics such as:

MAD = Sum (Absolute Error)/Number of data points

MSE = Sum ((Forecasted value – Actual Value)^2)/Number of data points

Percentage Error = ((Forecasted value – Actual Value)/Actual Value)*100

MAPE = Sum (Percentage Error)/Number of data points

Now the forecasting technique which is considered to be the most superior will have the lowest value of MAD, MSE & MAPE. In this case the values of the MAD, MSE & MAPE are following:

                                    MAD                            MSE                                         MAPE

5 yr MA                       3.411                           15.653                                     01.96%

5 yr Wt MA                 3.159                           13.249                                     01.81%

Exp Smooth                 2.701                           10.848                                     01.55%

Clearly we can see that the method of Exponential smoothing is best for forecasting given that it’s forecasting metrics are superior.

References

1. Bowerman, B. L., & O'Connell, R. T. (1979). Time series and forecasting. North Scituate, MA: Duxbury Press.

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