Optimal Strategies for Time Series Decomposition Analysis
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Introduction to Time Series Decomposition
Abraham Maslow famously stated, "If the only tool you have is a hammer, you tend to treat everything like a nail." This analogy resonates with many budding data scientists when they engage with time series data. They often resort to the seasonal_decompose function from Python's Statsmodels library, using it as a one-size-fits-all solution. However, while this function serves its purpose, there are far more effective techniques available. In this article, we aim to:
- Highlight the significance of time series decomposition
- Discuss the limitations of the seasonal_decompose function
- Present alternative methods for time series decomposition
Why Decompose Time Series Data?
Time series decomposition involves breaking down time series data into four core components:
- Trend [T]
- Cycle [C]
- Seasonality [S]
- Remainder [R]
1) Trend
The trend indicates the overall movement of the time series. It can exhibit a positive or negative trajectory, or at times, remain relatively stable. For instance, the GDP growth rate in the United States has shown stability, indicating no significant trend due to various economic factors.
2) Cycle
This component reflects fluctuations in the data that occur at irregular intervals. It's often associated with business cycles found in economic datasets.
3) Seasonal
Unlike cycles, the seasonal component signifies predictable variations occurring at regular intervals. A prime example is the tourism sector, which experiences peaks during summer months and declines during winter.
4) Remainder
The remainder is the portion of the time series that remains after accounting for the trend, cycle, and seasonal components. It represents random variations that cannot be attributed to the other three components.
By utilizing a 'seasonally-adjusted' time series (one from which the seasonal component has been removed), forecasters can focus on predicting the overarching trend more effectively. Additionally, decomposing time series data can help identify intriguing behaviors within the seasonal component, prompting further investigation into the underlying causes.
The Pitfalls of Conventional Time Series Decomposition
Interestingly, Statsmodels acknowledges that there are superior methods for decomposing time series data compared to the basic seasonal_decompose function. They caution that:
"This [seasonal_decompose] is a naive decomposition. More sophisticated methods should be preferred." - Statsmodels Documentation
The seasonal_decompose function relies on classical decomposition methods, which fall into two categories: additive and multiplicative.
Additive Decomposition
This model asserts that time series data is represented as a sum of its components:
[ Y = T + S + R ]
Multiplicative Decomposition
In contrast, the multiplicative model views time series data as the product of its components:
[ Y = T times S times R ]
Identifying whether a time series is additive or multiplicative can often depend on the variation of the seasonal component over time. If the magnitude of the seasonal component changes, it suggests a multiplicative relationship; otherwise, it indicates an additive one.
The classical approach to decomposition, however, presents several challenges:
- It employs two-sided moving averages for estimating trends, resulting in the exclusion of early and late observations.
- It assumes a constant seasonal component throughout the series, which can be misleading over extended timeframes.
- The trend line often smooths out fluctuations, leading to a significant remainder component.
Fortunately, there are advanced techniques that address these issues.
Alternative Approaches to Time Series Decomposition
X11 Decomposition
X11 Decomposition generates a trend-cycle for all observations and allows gradual changes in the seasonal component. While no direct Python implementation exists, it can be achieved using the seas function in R's seasonal package. For a comparative analysis, we can visualize the differences between X11 and classical decompositions.
This video explains time series decomposition, highlighting the roles of trend, seasonality, and noise.
STL Decomposition
Developed in 1990, the STL (Seasonal-Trend Decomposition based on Loess) method offers several advantages over X11:
- It accommodates various seasonal patterns.
- Users can modify the rate of change in the seasonal component.
- It is resilient to outliers.
In Python, the STL can be implemented using the following code:
from statsmodels.tsa.seasonal import STL
import matplotlib.pyplot as plt
import pandas as pd
df = df[:len(df) - 1] # Removes the last row in the data set
columns = ['Month', 'Passengers']
df.columns = columns
df.head()
df = df.set_index('Month') # Set the index to datetime object.
df = df.asfreq('MS') # Set frequency
# Set robust to True to handle outliers
res = STL(df, robust=True).fit()
res.plot()
plt.show()
The resulting seasonal component from STL is likely to be more accurate due to its robust handling of outliers, allowing for better identification of meaningful patterns in the data.
Conclusion
Understanding these alternative decomposition methods equips data scientists with enhanced tools for analyzing time series data. By moving beyond the basic seasonal_decompose function, you can achieve more precise forecasts and uncover interesting patterns in your datasets.
Bibliography
[1] Hyndman, R.J., & Athanasopoulos, G. (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. OTexts.com/fpp2.
[3] Sutcliffe, Andrew. (1993) "X11 Time Series Decomposition and Sampling Errors", Australian Bureau of Statistics: Melbourne, Australia.
[4] Cleveland, R.B., Cleveland W.S., McRae J.E., & Terpenning, I. (1990) "STL: Seasonal-Trend Decomposition Procedure Based on Loess", Journal of Official Statistics.
[5] Gardner, Dillon R. (2017) "STL Algorithm Explained: STL Part II".