Introduction

The data for the case study focuses on major natural gas prices. The data comes from the U.S energy information Administration EIA Data. The dataset contains monthly prices of natural gas starting from January 1997 to August 2020.

Data Description

The data set focuses on the monthly gas prices from January 1997 - August 2020.

Month: Month of each year average gas price

Price: Price of gas each month

Research Question

The research question is, given the monthly gas prices from January 1997 - August 2020, can predict the monthly gas prices.

We are also going to be looking to see what patterns repeat for fixed periods, underlying trends of the metrics, and if there are residuals.

Define time series object

A time series is a data set that tracks a sample over time. Using time series allows us to see what factors influence certain variables from period to period.

The Time series analysis we will be using is looking at the monthly prices of gas. Since the data is monthly we will have a data frequency = 12 to define the series object.

Simple exponential smoothing

Simple exponential smoothing is used a lot when looking at time series. The main goal is to smooth out the random fluctuations to see a trend and cycle.

When using exponential smoothing we know that more recent data will affect the forest trend more than older data points. We can accomplish the unequal weighing of variables by using a damped trend model.

Dampened trend models introdue a damping parameter to the trend componenents of the forecasting model. The parameter controls the rate the trend will diminish over time. We will use the additive and multiplicative seasonal components for our data analysis.

When the damping parameter, phi, is equal to 1 we will have no trend reduction. As phi begins to decrease the damping affect will increase.

Our study will be looking at the damping trend of price of gas per month. We will begin by finding the train and test data. We will make sure all of the numbers being used are numeric.

We will fit exponential smoothing method for fits 1-8. We will have two optimal fits, one exponential, two additive, and two multiplicative fit tests. We will then find the accuracy of the fits.

Accuracy measures

The accuracy measures of various exponential smoothing models
ME RMSE MAE MPE MAPE MASE ACF1
SES 0.0031 0.9150 0.5902 -1.0067 11.00 0.9993 -0.0008
Holt Linear 0.0068 0.9176 0.5932 -0.8674 11.10 1.0044 -0.0278
Holt Add. Damped 0.0131 0.9164 0.5960 -0.6430 11.14 1.0092 -0.0006
Holt Exp. Damped 0.0297 0.9142 0.5930 -0.0871 11.10 1.0040 -0.0017
HW Add. 0.0259 0.8796 0.5991 -0.2296 12.30 0.3109 0.0331
HW Exp. -0.0586 0.8412 0.5688 -2.4312 11.38 0.2951 0.0506
HW Add. Damp 0.0400 0.8848 0.5925 0.5912 11.88 0.3074 0.0537
HW Exp. Damp 0.0375 0.8390 0.5904 0.5737 11.90 0.3064 0.0591

From the accuracy table we see HW’s linear trend for the Exp seasonal model is the best smoothing model out of all eight models. The same result is shown in the original series plot which further confirms the use of the HW Exp model.

Using the model for training and finding the best model using both the training and test data we identified the best model. We find that both models have given the same result.

We now must refit our model using the entire data to change the smoothing parameters for the final model. We will use the final model to see the real-forecast.

We will refit the model by using the multiplying the test data by 100 and subtracting the mean and then dividing by the mean. The new calculations will result in an accuracy metric.

We will ensure that the lengths for test.p and fit1$mean are the same. we will them find the accuracy measures of the exponential smoothing models using the testing data.

The accuracy measures of various exponential smoothing models based on the testing data
MSE MAPE
SES 0.1454 8.380
Holt.Add 0.1449 8.350
Holt.Add.Damp 0.1440 8.331
Holt.Exp 0.1484 8.493
HW.Add 0.3712 10.556
HW.Exp 0.3244 9.496
HW.Add.Damp 0.2124 8.613
HW.Exp.Damp 0.2440 11.311

From the table we see that Holt.Add.Damp is our best model. This is not consistent with the patterns seen in the original plot. This brings up many questions about why the models are not the same.

Conclusion

The case study looked at the Holt-winterd trend and seasonal smoothing models. The study focused on the price of gas per month based on year.

We find conflicting responses with our study as the accuracy of the models based on training and the model based on testing data are not the same. We find that there should be further investigation into the models to see if there are any problems. We also would like to take a smaller sample size to see if that will make the most accurate model for both training and testing data.

References

Datopian. (n.d.). Natural gas prices. DataHub. https://datahub.io/core/natural-gas#data-cli