Introduction


For this weeks discussion, I have decided to analyze the time-series dataset of the Henry Hub Natural Gas Spot Price. I will use the Holt’s method, Holt’s damped method, and the Holt-Winter’s Damped Method in my analysis, hoping to generate some predictive power using these models.

Graphs


For convenience reasons, I limit the dataset to only include observations between 2010 and 2020, however with monthly observations the 120 observations are sufficient to run our time series modelss. 

## # A tibble: 6 × 2
##   Date          SpotPrice         
##   <chr>         <chr>             
## 1 January 1997  3.4500000000000002
## 2 February 1997 2.1499999999999999
## 3 March 1997    1.8899999999999999
## 4 April 1997    2.0299999999999998
## 5 May 1997      2.25              
## 6 June 1997     2.2000000000000002


From the autoplot, we quickly see that there is not much seasonality or cyclicality. Potentially, an argument could be made that the dataset has a downwards sloping trend, however even that is not very clear.


The difference we see between Dampened Holt’s Method and regular Holt’s Method is what one would expect. Holt’s method tends to over-exaggerate trends in the data, and since we can see a slight downtick at the very end of the time series, it is no surprise. that Holt’s method is downward sloping, while Holt’s dampened method more closely resembles a naive forecast. I also included Holt-Winters Damped Method, which preforms exceptionally well with forecasting heavily seasonal data, and for that reason is often used in consulting and other real world applications. An issue with this dataset iss that it is practically devoid of seasonality, and so HWDM is just Damped Holt’s Method with a slight seasonal component.

## Series: SpotPrice 
## Model: ETS(A,A,N) 
##   Smoothing parameters:
##     alpha = 0.9998999 
##     beta  = 0.000711601 
## 
##   Initial states:
##      l[0]        b[0]
##  5.823133 -0.01717167
## 
##   sigma^2:  0.1453
## 
##      AIC     AICc      BIC 
## 395.8235 396.2997 410.2375
## Warning: Removed 1 row containing missing values (`geom_line()`).

## Series: SpotPrice 
## Model: ETS(A,Ad,N) 
##   Smoothing parameters:
##     alpha = 0.9599693 
##     beta  = 0.0001000224 
##     phi   = 0.8000004 
## 
##   Initial states:
##      l[0]       b[0]
##  6.591787 -0.7612754
## 
##   sigma^2:  0.1412
## 
##      AIC     AICc      BIC 
## 393.0564 393.7284 410.3532
## Warning: Removed 1 row containing missing values (`geom_line()`).

## Series: SpotPrice 
## Model: ETS(M,Ad,M) 
##   Smoothing parameters:
##     alpha = 0.9029679 
##     beta  = 0.03919132 
##     gamma = 0.00010078 
##     phi   = 0.9159422 
## 
##   Initial states:
##      l[0]       b[0]     s[0]   s[-1]     s[-2]     s[-3]    s[-4]    s[-5]
##  4.973299 -0.2422467 1.046178 1.02006 0.9852566 0.9911476 0.996506 1.003273
##     s[-6]    s[-7]   s[-8]     s[-9]   s[-10]   s[-11]
##  1.000072 0.977173 0.95303 0.9564785 0.999357 1.071469
## 
##   sigma^2:  0.0154
## 
##      AIC     AICc      BIC 
## 407.4597 413.5127 459.3501
## Warning: Removed 12 rows containing missing values (`geom_line()`).

Conclusion


I will admit, these results are not very convincing. If I was to attempt to predict Natural Gas Prices in the future, I would gather data on an array of other variables, including weather, trade routes and others, and use regression analysis to generate more reliable results. However, as that is outside of the scope for this assignment, I will simply rely on the AIC and BIC values to choose the most superior model. By applying this deciding factor, it turns out the best preforming model seems to be the Damped Holt’s Method model, with the lowest AIC, and a BIC practically equal to that of the regular Holt’s Method.