Petrol Prices.

hat does the future hold for us? It would be beneficial to know, so let us begin with gasoline prices. The general view of the data is presented in the figure below.

The series is non-stationary, as confirmed by the analytical Dickey-Fuller test.

Augmented Dickey-Fuller Test

data: Price

Dickey-Fuller = -2.4169, Lag order = 7, p-value = 0.401

alternative hypothesis: stationary

The presence of a "unit root" is evident, as can be clearly seen from the analysis of the first differences in the figure below.

All conclusions are analytically confirmed by the Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests.

Conducting STL decomposition yields the following components of the additive time series decomposition (see the figure),

which allow us to calculate the strength of seasonality and trend:

Trend strength: Ft = 0.9971183

Seasonal strength: Fs = 0.05450987

This ratio is interpreted as follows: the data exhibit a pronounced trend, but seasonal fluctuations are insignificant.

This may be characteristic of time series with a clear long-term trend and minor regular fluctuations.

The forecasted values, obtained using Holt's method, are shown in the figure below.

Unfortunately, prices are projected to rise; the trend is persistent!