Simple Statistical Features

• Minimum, first quantile, median, third quantile, maximum, mean of the time series

ACF (Auto Correlation Function) Features

• First autocorrelation coefficient from the original data
• Sum of square of the first ten autocorrelation coefficients from the original data
• First autocorrelation coefficient from the differenced data
• Sum of square of the first ten autocorrelation coefficients from the differenced data
• First autocorrelation coefficient from the twice differenced data
• Sum of square of the first ten autocorrelation coefficients from the twice differenced data
• Seasonal data, the autocorrelation coefficient at the first seasonal lag is also returned

STL Features

• Time Series decomposition can be used to measure the strength of trend and seasonality. In case, there are large collection of time series, we may have to identify the series with the most trend and seasonality.
• For strongly trended data, seasonally adjusted data should have much more variation that the reminder component
• For strongly seasonal data, detrended data should have much more variation that the reminder component
• For additive decomposition, y(t) = T(t) + S(t) + R(t)
• Strength of the trend is measured by, F(Trend) = max(0, 1 - Var(R)/Var(T+R)).
  • For strongly trended data, seasonally adjusted data should have much more variation that the reminder component. Thus Var(R)/Var(T+R) should be small.
  • For data with little or no trend, two variance should be approximately small.
  • Measure of strength varies between 0 & 1.
  • Variance of the reminder may occasionally be even larger than the variance of the seasonally adjusted data. In that case, Var(R)/Var(R+T) would be > 1, resulting in negative F. To avoid that, minimum possible value of F has been set to 0.
• Strength of the seasonality is measured by, F(Seasonal) = max(0, 1 - Var(R)/Var(S+R)).
  • Here variance of reminder is compared with the variance of the detrended data
  • For almost no seasonality, Var(R) will be almost equal to Var(S+R). Thus, F(Seasonal) will tend to zero.
  • For strong seasonality, Var(R) << Var(S+R). Hence F(Seasonal) will tend to 1.
• Strength of Trend vs Seasonality can be plotted based for different time periods (Scatter plot)

Other Useful Features from decomposition

• Timing of peaks and troughs
  • Which period (month, quarter) contains largest seasonal component and which period contains smallest seasonal component