SYS670_FINALEXAM_ROHIT_S_CWID_10466264
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EM670
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Industrial Engineering
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Dec 6, 2023
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SYS 670 - Final Exam
Fall 2021
Name: Rohit Shegokar CWID - 10466264
Problem 1:
1950
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2002
2005
2008
2011
2014
2017
2020
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
Ice Cream, 1000 gal
Frozen Yogurt, 1000 gal
The above plotted graph helps in understanding the sales of the given products from the year 1950 – 2020 and thus helps in determining the trend. The sales of ice cream keep on increasing but drops at certain point and the same trend still keeps on.
Ice cream, 1000gal model:
These are model comparison done for this problem. From these models, I’m considering top 2 for the
further analysis.
Comparison of top 2 models:
Model 1: Linear (holt) Exponential smoothing
This model is considered as the preferred model because it has a good Rsquare value of 0.945. The Residual graph shows good fit because the values aren't spread out across a large area and the lag value isn't above the blue line. This shows that the curve is well-fitting.
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Model 2: ARIMA (1,1,1)
This model has a good R-square value, but it cannot be used for further analysis because of
the high probability value.
Conclusion:
After comparing and analyzing the above models, Linear (Holt) Exponential Smoothing is the best model for the above problem.
From the above model comparison, these are the observations made:
Rsquare is low because of the unavailability of full data.
Since the dataset is incomplete, seasonal ARIMA can’t be performed.
The probability and residuals are not good in any cases.
Conclusion:
Therefore, none of the models fit for the frozen yogurt. Problem 2:
Simple exponential smoothing (zero to one) must be used as it has less error i.e 5.837 and Rsquare is 0.279.
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Problem 3:
The graph shows the monthly average retail price of residential electricity in Arizona from Jan 1990 till Sep 2021.
The trend of the graph seems to be varying constantly with same pattern. The retail prices are more or less in the same range for the given years.
These are the model comparison I did for this problemThe best model for this problem is Seasonal Exponential Smoothing (12, zero to one).
Model Seasonal Exponential Smoothing (12, zero to one) (preferred model):
(a)
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This model is considered as the best model for this problem because of the following reasons:
It has good Rsquare value of 0.939.
It also has very good residuals and they are not scattered, they are compressed which is a good fit.
The residual graph lag is also good.
(b) Calculate the forecast errors and discuss the reasonableness of the forecasts.
The forecasted values are very less reasonable and can be used but not accurate for calculating the data. As can be seen from the errors, they have a wide variation from the true reading.
(c) Would it more reasonable to begin the series data at another point in time (later than 1990)? If yes, which year would you recommend starting the time series and why?
Yes, 2000. Because at the end of year 1999, the forecast error reaches its second maximum value.
From the year 2000, time series would be constant with minimum errors.
Problem 4:
The graph shows the monthly computer and electronics manufacturing shipments (in millions of dollars) from Jan 1992 till 2021.
The graph's trend appears to be highly complicated, with monthly drops and rises. This isn't a
graph with a consistent trend.
(a)
ARIMA model using the data from 1992 to June 2021
These are the model comparison I did for this above problem. The Rsquraes values are almost similar.
Based on the ranking, Seasonal ARIMA(0,0,0)(1,2,1)12 would be a suitable fit for this problem.
Seasonal ARIMA(0,0,0)(1,2,1)12 (preferred model):
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From the detailed analysis of the model Seasonal ARIMA(0,0,0)(1,1,1)12, it has the most suitable Rsquare value and also has a lesser probability with good values of residual curves. There, this is the preferred model.
Discuss the presence (or lack) of seasonality in the data
.
The seasonality occurs because of very close readings occurring in a certain period of time intervals.