Preprocessing Examples¶
This walkthrough covers selected functions from functime.preprocessing. We visualize common time-series preprocessing techniques before and after the time-series transformation. These transformations make the time-series look more "well-behaved", which generally makes the time-series easier to forecast. This chapter https://otexts.com/fpp3/stationarity.html from the Forecasting: Principles and Practice textbook provides an excellent primer on this topic.
import polars as pl
from functime.plotting import plot_forecasts, plot_panel
from functime.preprocessing import (
boxcox,
deseasonalize_fourier,
detrend,
diff,
fractional_diff,
scale,
yeojohnson,
)
Let's first load the commodity prices dataset.
data = pl.read_parquet("../../data/commodities.parquet")
entity_col, time_col, target_col = data.columns
data.head(1)
| commodity_type | time | price |
|---|---|---|
| str | datetime[ns] | f64 |
| "Aluminum" | 1960-01-01 00:00:00 | 511.47 |
There are 71 commodities in total.
data.get_column("commodity_type").n_unique()
71
Let's now visualize the top 4 most volatile time-series by coefficient of variation.
most_volatile_commodities = (
data.group_by(entity_col)
.agg((pl.col(target_col).std() / pl.col(target_col).mean()).alias("cv"))
.top_k(k=4, by="cv")
)
most_volatile_commodities
| commodity_type | cv |
|---|---|
| str | f64 |
| "Natural gas, E… | 1.341444 |
| "Phosphate rock… | 1.104353 |
| "Potassium chlo… | 1.070662 |
| "Crude oil, Dub… | 0.987116 |
selected = most_volatile_commodities.get_column(entity_col)
y = data.filter(pl.col(entity_col).is_in(selected))
figure = plot_panel(y=y, height=800, width=1000)
figure.show(renderer="svg")
These time-series looks quite complex: trending behavior, seasonality effects, changing volatility over time, etc. Let's see if we can preprocess these time-series to make them easier to forecast!
Detrending¶
We can use the plot_forecasts function to compare the time-series before and after the transformation.
transformer = detrend(freq="1mo", method="linear")
y_detrended = y.pipe(transformer).collect()
figure = plot_forecasts(
y_true=y, y_pred=y_detrended.group_by(entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
It's super easy to invert the transformation!
y_original = transformer.invert(y_detrended).group_by(entity_col).tail(64).collect()
subset = ["Natural gas, Europe", "Crude oil, Dubai"]
figure = plot_forecasts(
y_true=y.filter(pl.col(entity_col).is_in(subset)),
y_pred=y_original,
height=400,
width=1000,
)
figure.show(renderer="svg")
Deseasonalize¶
We support deseasonalization via residualized regression on Fourier terms to model seasonality. For this example, let's use the M4 hourly dataset, which has clear seasonal patterns.
m4_data = pl.read_parquet("../../data/m4_1w_train.parquet")
m4_entity_col, m4_time_col, m4_target_col = m4_data.columns
y_m4 = m4_data.filter(pl.col(m4_entity_col).is_in(["W174", "W175", "W176", "W178"]))
figure = plot_panel(y=y_m4, height=800, width=1000)
figure.show(renderer="svg")
Let's plot the seasonal component of the series!
# Fourier Terms
transformer = deseasonalize_fourier(sp=12, K=3)
y_deseasonalized = y_m4.pipe(transformer).collect()
y_seasonal = transformer.state.artifacts["X_seasonal"].collect()
figure = plot_panel(
y=y_seasonal.group_by(m4_entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
y_deseasonalized = y_m4.pipe(transformer).collect()
y_original = transformer.invert(y_deseasonalized).collect()
figure = plot_panel(
y=y_original.group_by(m4_entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
Differencing¶
First differences is a technique used in time-series analysis to transform a non-stationary time-series into a stationary one by taking the difference between consecutive observations. Assumes the time-series is integrated with unit root 1.
transformer = diff(order=1)
y_diff = y.pipe(transformer).collect()
figure = plot_forecasts(
y_true=y, y_pred=y_diff.group_by(entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
Fractional Differencing¶
Sometimes you may want to make a time series stationary without removing all of the memory from a time series. This can especially be useful in specific forecasting tasks where the next value is dependent on a long history of past values (think forecasting the price of a stock). In this case, we can use fractional differencing. Notice the difference between these plots and the previous plots. It is worthwhile to run multiple tests using a scoring function such as the augmented dickey-fuller test to determine the minimum value of d that makes a time series stationary.
transformer = fractional_diff(d=0.3, min_weight=1e-3)
y_diff = y.pipe(transformer).collect()
figure = plot_forecasts(
y_true=y, y_pred=y_diff.group_by(entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
Seasonal Differencing¶
transformer = diff(order=1, sp=12)
y_seas_diff = y.pipe(transformer).collect()
figure = plot_forecasts(
y_true=y, y_pred=y_seas_diff.group_by(entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
Local Scaling¶
Parallelized version of the scaling transformation (less mean, divide standard deviation) across many time-series.
transformer = scale(use_mean=True, use_std=True)
y_scaled = y_m4.pipe(transformer).collect()
figure = plot_panel(y=y_scaled.group_by(m4_entity_col).tail(64), height=800, width=1000)
figure.show(renderer="svg")
Box-Cox¶
This transformation is used to stabilize the variance of the time-series. Requires all values to be positive.
transformer = boxcox(method="mle")
y_boxcox = y.pipe(transformer).collect()
figure = plot_panel(y=y_boxcox.group_by(entity_col).tail(64), height=800, width=1000)
figure.show(renderer="svg")
Yeo-Johnson¶
This transformation is similar to Box-Cox, but without the strictly positive requirement.
transformer = yeojohnson()
y_yeojohnson = y.pipe(transformer).collect()
figure = plot_panel(
y=y_yeojohnson.group_by(entity_col).tail(64), height=800, width=1000
)
figure.show(renderer="svg")
Let's put it all together!¶
- Box-Cox to stabilize the variance
- Deseasonalize to remove seasonality
- First differences to stabilize the mean
The goal is to make the time-series "look" more stationary, which is an important assumption for many time-series forecasting models. Here's an excellent primer on the topic: https://otexts.com/fpp3/stationarity.html
y_new = (
y.pipe(boxcox())
.pipe(deseasonalize_fourier(sp=12, K=3))
.pipe(diff(order=1))
.collect()
)
figure = plot_panel(y=y_new.group_by(entity_col).tail(64), height=800, width=1000)
figure.show(renderer="svg")
