## 4.4 Other features

Many more features are possible, and the `feasts`

package computes only a few dozen features that have proven useful in time series analysis. It is also easy to add your own features by writing an R function which takes a univariate time series input and returns a numerical vector containing the feature values.

The remaining features in the `feasts`

package, not previously discussed, are listed here for reference. The details of some of them are discussed later in the book.

`coef_hurst`

will calculate the Hurst coefficient of a time series which is a measure of “long memory”. A series with long memory will have significant autocorrelations for many lags.`spectral_entropy`

will compute the (Shannon) spectral entropy of a time series, which is a measure of how easy the series is to forecast. A series which has strong trend and seasonality (and so is easy to forecast) will have entropy close to 0. A series that is very noisy (and so is difficult to forecast) will have entropy close to 1.`bp_stat`

gives the Box-Pierce statistic for testing if a time series is white noise, while`bp_pvalue`

gives the p-value from that test. This test is discussed in Section 5.4.`lb_stat`

gives the Ljung-Box statistic for testing if a time series is white noise, while`lb_pvalue`

gives the p-value from that test. This test is discussed in Section 5.4.- The \(k\)th partial autocorrelations measure the relationship between observations \(k\) periods apart after removing the effects of observations between them. So the first partial autocorrelation (\(k=1\)) is identical to the first autocorrelation, because there is nothing between them to remove. Partial autocorrelations are discussed in Section 9.5. The
`pacf5`

feature contains the sum of squares of the first five partial autocorrelations. `diff1_pacf5`

contains the sum of squares of the first five partial autocorrelations from the differenced data.`diff2_pacf5`

contains the sum of squares of the first five partial autocorrelations from the differenced data.`season_pacf`

contains the partial autocorrelation at the first seasonal lag.`kpss_stat`

gives the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) statistic for testing if a series is stationary, while`kpss_pvalue`

gives the p-value from that test. This test is discussed in Section 9.1.`pp_stat`

gives the Phillips-Perron statistic for testing if a series is non-stationary, while`pp_pvalue`

gives the p-value from that test.`ndiffs`

gives the number of differences required to lead to a stationary series based on the KPSS test. This is discussed in Section 9.1`nsdiffs`

gives the number of seasonal differences required to make a series stationary. This is discussed in Section 9.1.`var_tiled_mean`

gives the variances of the “tiled means” (i.e., the means of consecutive non-overlapping blocks of observations). The default tile length is either 10 (for non-seasonal data) or the length of the seasonal period. This is sometimes called the “stability” feature.`var_tiled_var`

gives the variances of the “tiled variances” (i.e., the variances of consecutive non-overlapping blocks of observations). This is sometimes called the “lumpiness” feature.`shift_level_max`

finds the largest mean shift between two consecutive sliding windows of the time series. This is useful for finding sudden jumps or drops in a time series.`shift_level_index`

gives the index at which the largest mean shift occurs.`shift_var_max`

finds the largest variance shift between two consecutive sliding windows of the time series. This is useful for finding sudden changes in the volatility of a time series.`shift_var_index`

gives the index at which the largest mean shift occurs`shift_kl_max`

finds the largest distributional shift (based on the Kulback-Leibler divergence) between two consecutive sliding windows of the time series. This is useful for finding sudden changes in the distribution of a time series.`shift_kl_index`

gives the index at which the largest KL shift occurs.`n_crossing_points`

computes the number of times a time series crosses the median.`n_flat_spots`

computes the number of sections of the data where the series is relatively unchanging.`stat_arch_lm`

returns the statistic based on the Lagrange Multiplier (LM) test of Engle (1982) for autoregressive conditional heteroscedasticity (ARCH).