Assignment - Air Rpm, Rail Pm

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Plot for the Cubic Trend with the summary statistics is as follows: -

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Plot for the Linear Trend with the summary statistics is as follows: -

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In order to evaluate the best model out of the above two, we will be looking at all the parameters present in the summary statistics of both the Trend Models. From the above summary statistics, we can conclude that the Cubic Trend Model is the best.

Trend Models for Rail PM: -

I have evaluated two trend models for Rail PM time series i.e. Cubic Trend and Quadratic Trend.

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Plot for the Cubic Trend with the summary statistics is as follows: -

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Plot for the Quadratic Trend with the summary statistics is as follows: -

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In order to evaluate the best model out of the above two, we will be looking at all the parameters present in the summary statistics of both the Trend Models. From the above summary statistics, we can conclude that the Cubic Trend Model performs slightly better than the Quadratic Trend Model.

Trend Models for VMT: -

I have evaluated two trend models for VMT time series i.e. Cubic Trend and Quadratic Trend.

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Plot for the Cubic Trend with the summary statistics is as follows: -

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Plot for the Quadratic Trend with the summary statistics is as follows: -

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In order to evaluate the best model out of the above two, we will be looking at all the parameters present in the summary statistics of both the Trend Models. From the above summary statistics, we can conclude that the Cubic Trend Model performs slightly better than the Quadratic Trend Model.

- Is there a need for modeling seasonality in theses time series? If so redo 2) and present the best model that includes trend and seasonality.

Seasonality is present only in Air RPM time series and thus creating a model for Air RPM that includes both trend and seasonality. As we introduce seasonality into the model the Mean Absolute Error decreases when compared to only the models with trend component and hence the overall accuracy of the model increases.

Since cubic trend model was the best so introducing seasonal dummies in the model gives the best model.

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Cubic Trend with Seasonal Dummies plot is as follows: -

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Summary Statistics of the model (with Cubic Trend and Seasonal Dummies)are as follows: -

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- Did 9/11/2001 affect Air RPM, Rail PM, and VMT? If so fix the time series by modeling 9/11 as an event for each series

9/11/2001 affect Air RPM as the plot dropped by a large number. To model the 9/11/2001 event we have added the intervention to the model. Since Cubic Trend with Seasonal Dummies gives the best model for Trend and Seasonality, I have introduced the factor of intervention in this model.

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Plot for the model is as follows: -

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Summary Statistics are as follows: -

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