Time Series Based Imputation: A Superior Method for Handling Missing Data

Handling missing data is a critical task in data preprocessing. Various imputation techniques, such as mean, median, and mode imputation, are commonly used. However, these methods often fall short when dealing with time series data. 

In this blog, we will explore a more sophisticated imputation method that leverages the inherent temporal trends in the data. 

We’ll break down a piece of Python code that I wrote which performs time series-based imputation using a sliding window approach which takes into account weighted differences when moving forward or backwards in time and demonstrates why this method is superior to traditional imputation techniques.

The Code

Let’s start by examining the code snippet that performs the time series-based imputation:

def trend_calculate_new(row):

        trend = ['p3', 'p2', 'p1', 'val', 'm1', 'm2', 'm3']

        values = np.array([row[t] for t in trend])

        

        # Filter out NaN values and get their indices

        valid_indices = np.where(~np.isnan(values))[0]

        

        if len(valid_indices) < 2:

            return row

        

        # Calculate differences

        differences = np.diff(values[valid_indices])

        differences = -differences

        

        # Calculate trend_f

        nonzero_denominator_indices = np.where(values[valid_indices[1:]] != 0)[0]

        trend_f = differences[nonzero_denominator_indices] / values[valid_indices[1:]][nonzero_denominator_indices]

        trend_f /= np.diff(valid_indices)[nonzero_denominator_indices]

        

        # Handle ZeroDivisionError

        if len(trend_f) == 0:

            return row

        else:

            row['trend'] = np.mean(trend_f)

        

        return row

 

Understanding the Code

Let’s break down the code step-by-step to understand how it works:

Defining the Trend Window:

trend = ['p3', 'p2', 'p1', 'val', 'm1', 'm2', 'm3']

1. This line defines a list representing the window of data points we consider for calculating the trend. Here, p3, p2, and p1 refer to the values three, two, and one year before the current year (val), respectively. Similarly, m1, m2, and m3 refer to the values one, two, and three years after the current year.

Extracting Values:

values = np.array([row[t] for t in trend])

1. This line creates a NumPy array of values from the input row for the defined trend window. These values are used to calculate the trend.

Filtering Out NaN Values:

valid_indices = np.where(~np.isnan(values))[0]

1. This line filters out any NaN values and retrieves the indices of valid (non-NaN) values. This step ensures that only the available data points are used for calculating the trend.

Checking for Sufficient Data:

if len(valid_indices) < 2:

    return row

1. If there are fewer than two valid data points, the function returns the original row without any imputation. This check ensures that there is enough data to calculate a meaningful trend.

Calculating Differences:

differences = np.diff(values[valid_indices])

differences = -differences

1. This line calculates the differences between consecutive valid data points. The differences are negated to align with the trend direction we are interested in.

Calculating Trend Factors:

nonzero_denominator_indices = np.where(values[valid_indices[1:]] != 0)[0]

trend_f = differences[nonzero_denominator_indices] / values[valid_indices[1:]][nonzero_denominator_indices]

trend_f /= np.diff(valid_indices)[nonzero_denominator_indices]

1. These lines calculate the trend factors (trend_f). The differences are divided by the corresponding values of the valid indices to get the relative changes. The resulting trend factors are then divided by the differences in indices to normalize the changes over the periods.

Handling ZeroDivisionError:

1. If there are no valid trend factors (to avoid division by zero), the function returns the original row. Otherwise, the mean of the trend factors is calculated and assigned to the trend column.

Advantages of Time Series-Based Imputation

1. Captures Temporal Trends:

Unlike mean, median, or mode imputation, which replace missing values with a single central tendency measure, time series-based imputation leverages the temporal order of the data. This method captures the underlying trend, making the imputation more reflective of the actual data patterns.

2. Sliding Window Approach:

The sliding window approach (+3 and -3 years) ensures that the imputation is based on a broader context rather than just a few adjacent points. This approach smooths out short-term fluctuations and captures long-term trends more effectively. The sliding window is dynamic as well, we can change how far in the future or past we want to look depending on the data available to us.

3. Weighted Averages:

Using weighted averages, where recent data points are given more importance, improves the imputation accuracy. The weights can be adjusted to reflect the relevance of different time points, providing a more nuanced imputation.

Comparison with Traditional Imputation Methods

Mean Imputation:

Mean imputation replaces missing values with the average of the available data. While simple, it can distort the data distribution and reduce variability, leading to biased results.

Median Imputation:

Median imputation is more robust to outliers than mean imputation but still fails to capture temporal trends. It replaces missing values with the median of the available data, which might not reflect the actual trend in time series data.

Mode Imputation:

Mode imputation replaces missing values with the most frequent value. This method is useful for categorical data but is inappropriate for continuous time series data, as it does not consider the temporal order.

Conclusion

Time series-based imputation, as demonstrated in the provided code, offers a superior approach for handling missing data in temporal datasets. By leveraging the inherent trends and using a sliding window approach with weighted averages, this method provides more accurate and context-aware imputations. Traditional imputation methods like mean, median, and mode fail to capture the temporal dynamics, leading to less accurate and potentially biased results. Embracing time series-based imputation can significantly enhance the quality of data preprocessing and the reliability of subsequent analyses.

By understanding and implementing advanced imputation techniques like the one presented here, data scientists and analysts can improve their handling of missing data, ultimately leading to better model performance and more insightful results.