In data analysis and time series forecasting, it’s often necessary to convert lower-frequency data into higher-frequency data. This process, known as upsampling or disaggregation, involves transforming data from a summarized form (such as quarterly) into a more detailed form (such as monthly).

This article will guide you through the process of upsampling summed quarterly data to monthly data using Python.

What is Upsampling?

Upsampling is the process of increasing the frequency of your time series data. When upsampling, it’s crucial to allocate the quarterly values to the corresponding months accurately. For summed data, this means dividing the quarterly total by the number of months to spread the total evenly across the months.

Why upsample quarterly data to monthly data?

1. Detailed Analysis: Monthly data allows for a more granular analysis of trends and patterns that might be missed in quarterly data.
2. Forecasting: Many forecasting models perform better with higher frequency data.
3. Seasonal Analysis: Monthly data can help in identifying seasonal variations more precisely.
4. Business Decisions: Businesses often make decisions every month, necessitating more frequent data points.

Methods for Upsampling

Upsampling can be performed using several methods, each with its own assumptions and use cases:

1. Forward Fill: This method fills the missing monthly values with the last available quarterly value.
2. Linear Interpolation: This method assumes a linear change between quarterly data points and interpolates the monthly values accordingly.
3. Spline Interpolation: This method uses spline functions to create a smooth curve through the data points, providing a more refined estimate than linear interpolation.
4. Polynomial Interpolation: This method uses polynomial functions for interpolation, which can capture more complex relationships but may introduce overfitting.

Performing Upsampling Methods Using Python

Python, with libraries like Pandas, provides powerful tools to upsample data easily. Here’s a step-by-step guide to upsampling quarterly data to monthly data using different methods.

pip install pandas

Let’s start with some sample quarterly data:

import pandas as pd

# Sample quarterly data
data = {
    'Date': ['2021-03-31', '2021-06-30', '2021-09-30', '2021-12-31'],
    'Value': [10, 20, 30, 40]
}
df = pd.DataFrame(data)
df['Date'] = pd.to_datetime(df['Date'])
df.set_index('Date', inplace=True)

Now, let’s proceed with the implementation of the methods that we have discussed above.

Method 1: Forward Fill Method

At first we will use the forward fill method.

# Upsample to monthly frequency and forward fill
monthly_ffill = df.resample('M').ffill()
print(monthly_ffill)

Output:

            Value
Date             
2021-03-31     10
2021-04-30     10
2021-05-31     10
2021-06-30     20
2021-07-31     20
2021-08-31     20
2021-09-30     30
2021-10-31     30
2021-11-30     30
2021-12-31     40

Method 2: Linear Interpolation

Linear Interpolation involves estimating unknown values that fall within two known values by using a straight line.

# Upsample to monthly frequency and use linear interpolation
monthly_linear = df.resample('M').interpolate(method='linear')
print(monthly_linear)

Output:

                Value
Date                 
2021-03-31  10.000000
2021-04-30  13.333333
2021-05-31  16.666667
2021-06-30  20.000000
2021-07-31  23.333333
2021-08-31  26.666667
2021-09-30  30.000000
2021-10-31  33.333333
2021-11-30  36.666667
2021-12-31  40.000000

Method 3 : Spline Interpolation

Spline Interpolation involves fitting a smooth curve through the data points, typically using piecewise polynomials, to estimate values between known data points.

# Upsample to monthly frequency and use spline interpolation
monthly_spline = df.resample('M').interpolate(method='spline', order=2)
print(monthly_spline)

Output:

                Value
Date                 
2021-03-31  10.000000
2021-04-30  13.300914
2021-05-31  16.699982
2021-06-30  20.000000
2021-07-31  23.370275
2021-08-31  26.750850
2021-09-30  30.000000
2021-10-31  33.384754
2021-11-30  36.638478
2021-12-31  40.000000

Method 4: Polynomial Interpolation

Polynomial Interpolation involves fitting a polynomial of degree nnn through n+1n+1n+1 data points to estimate the values between the known points.

# Upsample to monthly frequency and use polynomial interpolation
monthly_poly = df.resample('M').interpolate(method='polynomial', order=2)
print(monthly_poly)

Output:

                Value
Date                 
2021-03-31  10.000000
2021-04-30  13.310651
2021-05-31  16.717245
2021-06-30  20.000000
2021-07-31  23.377767
2021-08-31  26.743116
2021-09-30  30.000000
2021-10-31  33.367506
2021-11-30  36.628376
2021-12-31  40.000000

Conclusion

Upsampling quarterly data to monthly data is a crucial technique for enhancing the granularity and usefulness of time series data. This process allows analysts and decision-makers to conduct more detailed analyses, improve forecasting accuracy, and uncover finer seasonal patterns that might be overlooked with less frequent data points.

Several methods can be employed to upsample data, each with its advantages and assumptions. Forward fill is simple and quick, while linear, spline, and polynomial interpolations offer more refined estimates by assuming different relationships between data points. Selecting the appropriate method depends on the specific needs of the analysis and the characteristics of the data.