4.2 ACF features
We can also summarise the autocorrelations to produce new features; for example, the sum of the first ten squared autocorrelation coefficients is a useful summary of how much autocorrelation there is in a series, regardless of lag.
The
feat_acf()function computes a selection of the autocorrelations discussed here. It will return six or seven features:the first autocorrelation coefficient from the original data;
the sum of squares of the first ten autocorrelation coefficients from the original data;
the first autocorrelation coefficient from the differenced data;
the sum of squares of the first ten autocorrelation coefficients from the differenced data;
the first autocorrelation coefficient from the twice differenced data;
the sum of squares of the first ten autocorrelation coefficients from the twice differenced data;
For seasonal data, the autocorrelation coefficient at the first seasonal lag is also returned.
When applied to the Australian tourism data, we get the following output.
## # A tibble: 304 × 10
## Region State Purpose acf1 acf10 diff1_acf1 diff1_acf10 diff2_acf1
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Adelaide Sout… Busine… 0.0333 0.131 -0.520 0.463 -0.676
## 2 Adelaide Sout… Holiday 0.0456 0.372 -0.343 0.614 -0.487
## 3 Adelaide Sout… Other 0.517 1.15 -0.409 0.383 -0.675
## 4 Adelaide Sout… Visiti… 0.0684 0.294 -0.394 0.452 -0.518
## 5 Adelaide Hills Sout… Busine… 0.0709 0.134 -0.580 0.415 -0.750
## 6 Adelaide Hills Sout… Holiday 0.131 0.313 -0.536 0.500 -0.716
## 7 Adelaide Hills Sout… Other 0.261 0.330 -0.253 0.317 -0.457
## 8 Adelaide Hills Sout… Visiti… 0.139 0.117 -0.472 0.239 -0.626
## 9 Alice Springs Nort… Busine… 0.217 0.367 -0.500 0.381 -0.658
## 10 Alice Springs Nort… Holiday -0.00660 2.11 -0.153 2.11 -0.274
## # ℹ 294 more rows
## # ℹ 2 more variables: diff2_acf10 <dbl>, season_acf1 <dbl>