Spectral Analysis & Filtering

Code

Data

Spectral Analysis of US Gas Prices

I used the R function mvspec() to create a smoothed Periodogram of US gas prices. I did this on differenced data because of a clear trend in prices over time.

The maximum value occurs around value .083, which corresponds to a period of 12 months (the data is recorded monthly). An annual pattern could make sense for gas prices, perhaps related to patterns of travel. There are also important frequencies at .19 and .27, which correspond to cycles of around 5 months and 3.7 months, respectively. I am not sure what might drive this sort of pattern.

Spectral Analysis of Google Trends Search for 'Cheap Gas'

I used the R function mvspec() to create a smoothed Periodogram of Google Trends data.

When I difference the data, I get the following figure, which contains a peak at .25, or around 4 months. There are also peaks at .09, .16, and .39, corresponding to periods of around 11 months, 6 months, and 2.5 months.

For both gas prices and google trends on gas prices, I would need more knowlege of the gas market in the United States, and perhaps what factors drive people to search for 'cheap gas' in the US. It is not immediately clear what would be driving the periodicities that I observe with this spectral analysis.