Motor Vehicle Producer Price Index

A Time Series Investigation

Todd Young

Producer Price Indexes

"A measurement of the average change over time in the selling prices received by domestic producers for their output."

-Bureau of Labor Statistics

The Series

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ACF and PACF of the Series

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Series Decomposition

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A Closer Look at Seasonality

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Holt-Winter's Exponential Smoothing Model

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State Space Model

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Seasonal Arima Model

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Combination Model

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Model Evaluations

Seasonal Arima Model Accuracy Measures
ME RMSE MAE MPE MAPE MASE ACF1 Theil's U R-squared
Training set 0.03 1.41 0.96 0.01 0.70 0.47 -0.01 1.00
Test set 0.12 0.81 0.74 0.08 0.49 0.36 -0.04 0.65 0.88
Combination Model Accuracy Measures
ME RMSE MAE MPE MAPE MASE ACF1 Theil's U R-squared
Training set 0.04 1.24 0.85 0.02 0.61 0.41 0.01 1.00
Test set 1.56 1.76 1.56 1.02 1.02 0.76 -0.04 2.20 0.41
State Space Model Accuracy Measures
ME RMSE MAE MPE MAPE MASE ACF1 Theil's U R-squared
Training set 0.06 1.22 0.87 0.04 0.63 0.42 0.06 0.91
Test set 2.41 2.57 2.41 1.58 1.58 1.17 -0.50 2.20 0.37
Holt-Winter's Model Accuracy Measures
ME RMSE MAE MPE MAPE MASE ACF1 Theil's U R-squared
Training set -0.05 1.23 0.86 -0.05 0.62 0.42 0.05 0.91
Test set 1.88 2.03 1.88 1.24 1.24 0.91 -0.07 2.51 0.22