# Time Series Classification Synthetic vs Real Financial Time Series – Part V

See Part IPart II , Part III and Part IV in this article for instructions from Matthew Smith on which R packages and data sets you need.

An important note in the code here is that I randomly sample by group, that is, I do not take a random sample from all observations across all groups. Instead I `group_by` each time series (each of the 6,000 observations after I filtered by the `class == 0`, likewise when I filter by the `class == 1`), I then `nest()` the data to collapse the daily time series for each asset into a `list`. From here I will have 6,000 observations, each of which has their time series nested inside a list. Thus, I can sample 1 of the 6,000 observations and then `unnest()` and obtain a full time series set of one of the random assets selected, – instead of sampling randomly over all assets time series data (which would be completely wrong).

For example the following commented out code `group_by()` the ID variable and `nest()` the data, takes a random `sample_n()` of the grouped data and then `unnest()` the data to its original form, this time with a random sample of the IDs.

# group_by(row_id) %>%
# nest() %>%
# ungroup() %>%
# sample_n(1) %>%
# unnest() %>%

Next I compute the Dickey Fuller test on both series for a single random observation, hence the `sample_n(1)` argument (it’s too computationally expensive to compute it on all 12,000 observations).

For the synthetically created series.

# Dickey Fuller test on the 0 class
# I only randomly sample 1 of the assets for the 0 class to save on output space

df %>%
filter(class == 0) %>%
group_by(row_id) %>%
nest() %>%
ungroup() %>%
sample_n(1) %>%
unnest() %>%
nest(-row_id) %>%

## Augmented Dickey-Fuller Test
## alternative: stationary
## ## Type 1: no drift no trend
## [1,] 0 -17.94 0.01
## [2,] 1 -11.75 0.01
## [3,] 2 -8.66 0.01
## [4,] 3 -7.62 0.01
## [5,] 4 -7.13 0.01
## Type 2: with drift no trend
## [1,] 0 -17.94 0.01
## [2,] 1 -11.76 0.01
## [3,] 2 -8.67 0.01
## [4,] 3 -7.64 0.01
## [5,] 4 -7.15 0.01
## Type 3: with drift and trend
## [1,] 0 -18.00 0.01
## [2,] 1 -11.83 0.01
## [3,] 2 -8.77 0.01
## [4,] 3 -7.74 0.01
## [5,] 4 -7.26 0.01
## —-
## Note: in fact, p.value = 0.01 means p.value <= 0.01

## # A tibble: 3 x 3
## >
## 1 7807 [260 x 4]
## 2 7807 [260 x 4]
## 3 7807 [260 x 4]

The same but on the real financial series.

# Dickey Fuller test on the 1 class
# I only randomly sample 1 of the assets for the 1 class to save on output space

df %>%
filter(class == 1) %>%
group_by(row_id) %>%
nest() %>%
ungroup() %>%
sample_n(1) %>%
unnest() %>%
nest(-row_id) %>%

## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## [1,] 0 -15.99 0.01
## [2,] 1 -10.71 0.01
## [3,] 2 -9.12 0.01
## [4,] 3 -8.74 0.01
## [5,] 4 -7.58 0.01
## Type 2: with drift no trend
## [1,] 0 -16.10 0.01
## [2,] 1 -10.84 0.01
## [3,] 2 -9.27 0.01
## [4,] 3 -8.93 0.01
## [5,] 4 -7.81 0.01
## Type 3: with drift and trend
## [1,] 0 -16.27 0.01
## [2,] 1 -10.99 0.01
## [3,] 2 -9.46 0.01
## [4,] 3 -9.18 0.01
## [5,] 4 -8.06 0.01
## —-
## Note: in fact, p.value = 0.01 means p.value <= 0.01

## # A tibble: 3 x 3
## >
## 1 10833 [260 x 4]
## 2 10833 [260 x 4]
## 3 10833 [260 x 4]

Stay tuned for the next installment, in which Matthew will review he Jarque-Bera tests for normality.

Visit Matthew Smith – R Blog to see the next step in his analysis.

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