1. A Trace Plot:
Oil price can be affected by different kinds of factors. The key factors are demand, supply, US dollar, and geopolitics. For example, weak US dollar will make the price of oil comparatively cheaper in imported countries, causing an increase in demand of WTI crude oil. Thus, it bids up the oil prices. It is definitely the case when the U.S. Federal Reserve committed loose monetary policy. An other example for geopolitics, when there were wars / conflicts (e.g. Gulf War in 1990 - 1991, and Libyan Revolution in 2011), these will make the supplies of oil become unstable, raising the oil prices. Those are reasons why the WTI spot prices exhibited some sudden jumps during the period.
From the above trace plot, the daily returns have a constant mean of about zero. However, the daily returns exhibit volatility clustering, which means a high volatility seems to be followed by a high volatility. In the sense of time series analysis, the return series is stationary in mean but non-stationary in variance.
2. Descriptive Statistics and Distribution Plots:
At the next step, I will give out some graphs and descriptive statistics for analyzing the distributions of the two series.
First, we would plot the histograms, normal QQ-plots and boxplots for the two series. From the diagram below, the price series is not Gaussian-like and positively skewed. There are many outliars from the right side (larger side). For the return series, it is more Gaussian-like (much more like a bell-shape distribution) but with a fatter tail. We can see there are many outliars from both the right and left side.
From the descriptive statistics, for the price series, the mean is 38, however, the price in this few years never met this value, meaning that the series exhibit non-stationarity in mean or an trend. There is also positive skewness and a slight excess kurtosis.
For the return series, I would say it is much more like a Gaussian white noise (the return series seem to cross over the mean (0.0002) more frequently). But it is slightly negatively skewed with a very fat tail (excess kurtosis is a bit large).
Descriptive Statistics:
Price Return
Observations 6812 6811
Minimum 10.2500 -0.4064
Quartile 1 18.8175 -0.0121
Median 24.1500 0.0007
Arithmetic Mean 38.7353 0.0002
Geometric Mean 31.0842 -0.0001
Quartile 3 58.2725 0.0133
Maximum 145.3100 0.1915
SE Mean 0.3447 0.0003
LCL Mean (0.95) 38.0596 -0.0004
UCL Mean (0.95) 39.4110 0.0008
Variance 809.4131 0.0007
Stdev 28.4502 0.0257
Skewness 1.2610 -0.7566
Kurtosis 0.4732 14.5647
3. Autocorrelation Plots:
At the third step, I want to investigate the serial dependence of the two series. For the price series, the sample autocorrelation coefficients are significantly large. It showed that the price series exhibit serial dependence and it is distributed as a Gaussian white noise. For the return series, the autocorrelation coefficients are quite small. I would conclude that the series should be independent with one another. The series is distributed like a Gaussian white noise but essentially it is not due to fatter tail. A t-distribution may be more appropriate.
4. Autocorrelation Plots concerning the Volatility:
As we can see the return series probably exhibits volatility clustering, I want to use acf plot to see whether it is the case. I used absolute values of the returns and squared returns to construct the acf plots. The plots showed that autocorrelation coefficients are significant, meaning that a big move is usually followed by a big move, and vice versa. Therefore, there is volatility clustering in the return series. There is a need to model the volatility.
(Data source: U.S. Energy Information Administration)
***In the coming future, I will use statistical tools to model / forecast / explain the WTI oil spot prices.
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